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DD Joseph - Publications

All the information here on Prof. Daniel D Joseph's Publications page are for Published or Accepted (some Submitted) articles in professional journals. They are arranged in chronological order. Unpublished articles, Proposals, Memos, Presentations (from 1995 on) are in the Archive page. Soon to be added are books published, at least the table of contents.

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Irrotational and rotational effects of viscosity on Kelvin-Hemholtz instability for two fluids with small density ratio. Submitted to Phys. Rev. E.

abst: The effects of viscosity on the Kelvin Helmholtz (KH) instability of uniform flow on an unbounded domain are analyzed using two irrotational theories (VPF), an exact rotational theory (ES) and a hybrid rotational/irrotational theory (HS). One of the irrotational theories arises from evaluation of the viscous normal stress on potential flow (VPF1).The second irrotational theory is the dissipation method here derived specially for the KH problem(VPF2). The two irrotational theories give rise to different results. The rotational theory can give rise to KH instability if and only if the gas is inviscid and irrotational (IPF) but the analysis can be extended to account viscous effects by replacing (IPF) with viscous potential flow. To our knowledge quantitave results for KH instability of an unbounded domain are unavailable.

Viscous irrotational analysis of the deformation and break-up time of a bubble or drop in uniaxial straining flow. Submitted to J. Fluid Mech.

abst: The non-linear deformation and break-up of a bubble or drop immersed in a uniaxial extensional flow of an incompressible viscous fluid is analyzed by means of viscous potential flow. In this approximation, the flow field is irrotational and viscosity enters through the balance of normal stresses at the interface. The governing equations are solved numerically to track the motion of the interface by coupling a boundary-element method with a time-integration routine. When break-up occurs, the break-up time computed here is compared with results obtained elsewhere from numerical simulations of the Navier-Stokes equations, which thus keeps vorticity in the analysis, for several combinations of the relevant dimensionless parameters of the problem [Revuelta et al. (2006), J. Fluid Mech., 551, 175]. For the bubble, for Weber numbers 3 ≤ We ≤ 6, predictions from viscous potential flow shows good agreement with the results from the Navier-Stokes equations for the bubble break-up time, whereas for larger We, the former under-predicts the results given by the latter. When viscosity is included, larger break-up times are predicted with respect to the inviscid case for the same We. For the drop and considering moderate Reynolds numbers, Re, increasing the viscous effects of the irrotational motion produces large, elongated drops that take longer to break up in comparison with results for inviscid fluids. For larger Re, it comes as a surprise that break-up times smaller than the inviscid limit are obtained. Unfortunately, results from numerical analyses of the incompressible, unsteady Navier-Stokes equations for the case of a drop have not been presented in the literature, to the best of our knowledge; hence comparison with the viscous irrotational analysis is not possible.

abst: When small particles, e.g., flour, pollen, etc., come in contact with a liquid surface they immediately disperse. The dispersion can be explosive, especially for small particles on the surface of mobile liquids like water. This is due to the fact that the capillary force pulls particles into the interface causing them to accelerate to a relatively large velocity. The maximum velocity increases with decreasing particle size; for nanometer sized particles, e.g., viruses and proteins, the velocity on an air-water interface can be as large as ~47 m/s. We also show that particles oscillate at a relatively high frequency about their floating equilibrium before coming to stop under viscous drag. The observed dispersion is a result of strong repulsive hydrodynamic forces that arise because these oscillations.

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Colloidal coal in water suspensions. Submitted to Energy and Environmental Science.

abst: In this paper we discuss the possible clean coal applications of colloidal dispersions of coal in water (CCW) that we manufacture with a proprietary wet-comminution device. These dispersions are a new material because the coal particles do not settle but are held in suspension by Brownian motions. The closest coal water slurries used previously are dispersions of micronized coal with mean particle sizes greater than fifteen microns; these dispersions are not colloidal because the particles settle rapidly under gravity leaving clear water behind. A new material like CCW has a possibly vast but unknown field of applications in improvements and strategies for new clean coal technologies.

Viscous potential flow analysis of radial fingering in a Hele-Shaw cell. Physics of Fluids, 21, 074106.

abst: The problem of radial fingering in two phase gas/liquid flow in a Hele-Shaw cell under injection of gas is studied here. The fingers arise as an instability of a time-dependent flow. The instability is analyzed as a viscous potential flow, in which potential flow analysis of Paterson [L. Paterson, J. Fluid Mech. 113, 513 (1981)] and others is augmented to account for the effects of viscosity on the normal stress at the gas/liquid interface. The addition of these new effects brings our theory into a much better agreement with experiments of Maxworthy [T. Maxworthy, Phys. Rev. A 39, 5863 (1989)] than other theories.

Particle-wall collision in a viscoelastic fluid. J. Fluid Mech., 633, 475-483.

abst: In this study, we present experimental results on particle-wall collision in viscoelastic fluids. A sphere is released in a tank filled with poly(ethylene-oxide) (PEO) mixed with water with varying concentrations up to 1.5%. The effect of Stokes and Deborah numbers on the rebound velocity of a spherical particle colliding onto a wall is considered. It has been observed that the slope at which the coefficient of restitution increases with Stokes number is smaller for higher Deborah numbers. Higher rebound occurs for higher PEO concentration at the same stokes number. However, the results for the coefficient of restitution in polymeric liquids can be collapsed together with the Newtonian fluid behaviour if one defines the Stokes number based on the local strain rate.

Two-dimensional and axisymmetric viscous flow in apertures. J. Fluid Mech., 605, 1-18.

abst: The flow in a plane liquid jet from an aperture is obtained by direct simulation of the Navier–Stokes equations. The gas–liquid interface is tracked using the level set method. Flows are calculated for different Reynolds and Weber numbers. When We = ∞, the maximum value of the discharge coefficient appears around Re = O(100). The regions that are vulnerable to cavitation owing to the total stress are identified from calculations based on Navier–Stokes equations and viscous potential flow; the two calculations yield similar results for high Reynolds numbers. We prove that the classical potential flow solution does not give rise to a normal component of the rate of strain at the free streamline. Therefore, the normal component of the irrotational viscous stresses also vanishes and cannot change the shape of the free surface. The results of calculations of flows governed by the Navier–Stokes equations are close to those for viscous potential flow outside the vorticity layers at solid boundaries. The Navier–Stokes solutions for the axisymmetric aperture are also given for two values of Reynolds numbers. The results for axisymmetric and planar apertures are qualitatively similar, but the axisymmetric apertures have a lower discharge coefficient and less contraction.

B. H. Yang , D.D. Joseph. 2009. Virtual Nikuradse. Journal of Turbulence, 10(11), 1-28.

abst:

In this paper we derive an accurate composite friction factor versus Reynolds number correlation formula for laminar, transition and turbulent flow in smooth and rough pipes. The correlation is given as a rational fraction of rational fractions of power laws which is systematically generated by smoothly connecting linear splines in log-log coordinates with a logistic dose function algorithm. We convert Nikuradse's (1933) (J. Nikuradse, 1933 Stromungsgesetz in rauhren rohren, vDI Forschungshefte 361. (English translation: Laws of flow in rough pipes). Technical report, NACA Technical Memorandum 1292. National Advisory Commission for Aeronautics (1950), Washington, DC.) data for six values of roughness into a single correlation formula relating the friction factor to the Reynolds number for all values of roughness. Correlation formulas differ from curve fitting in that they predict as well as describe. Our correlation formula describes the experimental data of Nikuradse's (1932, 1933) (J. Nikuradse, Laws of turbulent flow in smooth pipes (English translation), NASA (1932) TT F-10: 359 (1966).) and McKeon et al. (2004) (B.J. McKeon, C.J. Swanson, M.V. Zaragola, R.J. Donnelly, and J.A. Smits, Friction factors for smooth pipe flow, J. Fluid Mech. 511 (2004), 41-44.) but it also predicts the values of friction factor versus Reynolds number for the continuum of sand-grain roughness between and beyond those given in experiments. Of particular interest is the connection of Nikuradse's (1933) data for flow in artificial rough pipes to the data for flow in smooth pipes presented by Nikuradse (1932) and McKeon et al. (2004) and for flow in effectively smooth pipes. This kind of correlation seeks the most accurate representation of the data independent of any input from theories arising from the researchers ideas about the underlying fluid mechanics. As such, these correlations provide an objective metric against which observations and other theoretical correlations may be applied. Our main hypothesis is that the data for flow in rough pipes terminates on the data for smooth and effectively smooth pipes at a definite Reynolds number Rσ(σ); if λ = f(Re, σ) is the friction factor in a pipe of roughness parameter σ then λ = f(Rσ(σ), σ) is the friction factor at the connection point. An analytic formula giving Rσ(σ) is obtained here for the first time.

Friction factor correlations for laminar, transition and turbulent flow in smooth pipes. Physica D , accepted.

abst: In this paper we derive an accurate composite friction factor vs. Reynolds number correlation formula for laminar, transition and turbulent flow in smooth pipes. The correlation is given as a rational fraction of rational fractions of power laws which is systematically generated by smoothly connecting linear splines in log-log coordinates with a logistic dose function algorithm. This kind of correlation seeks the most accurate representation of the data independent of any input from theories arising from the researchers ideas about the underlying fluid mechanics. As such, these correlations provide an objective metric against which observations and other theoretical correlations may be applied. Our correlation is as accurate, or more accurate, than other correlations in the range of Reynolds numbers in which the correlations overlap. However, our formula is not restricted to certain ranges of Reynolds number but instead applies uniformly to all smooth pipe flow data for which data is available. The properties of the classical logistic dose response curve are reviewed and extended to problems described by multiple branches of power laws. This extended method of fitting which leads to rational fractions of power laws is applied to data of Marusic and Perry (1995) for the velocity profile in a boundary layer on a flat plate with an adverse pressure gradient, to data of Nikuradse (1932) and McKeon et al (2004) on friction factors for flow in smooth pipes and to the data of Nikuradse (1933) for effectively smooth pipes.

The role of Potential flow in the theory of the Navier-Stokes equations in Advances in Mathematical Fluid Mechanics, Eds. R. Rannacher and A. Sequeira, Springer Verlag, Berlin.

Viscous Irrotational Theories and the Force on an Expanding Bubble: A Cell-Model Analysis. Ind. & Eng. Chem. Res., 48(1), 110-127

abst: The dynamics of a bounded viscous incompressible fluid surrounding a spherical bubble in rectilinear motion simultaneously experiencing volume changes is examined by means of two viscous irrotational theories, namely, viscous potential flow and the dissipation method. The forces that the liquid produces on the bubble and on the outer spherical boundary of the liquid are determined from these two approaches at the instant when the bubble is concentric with the outer surface. Viscous potential flow involves surface integration of the irrotational normal stress; the dissipation method stems from the mechanical energy balance, including the dissipation integral, evaluated in potential flow. In the inner boundary, zero tangential stress is enforced. Two choices for the tangential stress condition on the outer boundary are considered: zero tangential stress or irrotational tangential stress. In a sense, this is an extension to include viscous effects of the inviscid analysis by Sherwood [Int. J. Multiphase Flow, 1999, 25, 705]. The potential flow that follows from Sherwood's work is used in the derived formulas to compute the drag. To the added-mass forces associated with the bubble acceleration and rate of change of the bubble radius determined by Sherwood, a viscous contribution is added here that is dependent on the instantaneous bubble velocity and the inner and outer instantaneous radii of the bubble-liquid cell. When the outer radius is taken to infinity, the expressions for the drag yield results given in the literature. If the inner and outer radii are held fixed, results from the cell model may be used to approximate the drag on a bubble moving in a bubbly suspension with the same volume fraction as the cell. The analysis yields two results for the viscous drag on the bubble, contingent on the boundary condition applied on the outer sphere. These formulas have been presented in the literature, although regarded as contradictories. By emphasizing the role of the tangential stress on the outer boundary, it is shown that both results are valid, because they are dependent on the choice of the outer dynamic boundary condition. These results agree to first order in the volume fraction. The terminal rise velocity of a bubble swarm is derived using the drag from the viscous irrotational theories. Results for the drag coefficient and bubble rise velocity are compared with other theoretical results, as well as data from numerical simulations and experiments, with emphasis in the regime of high Reynolds and low Weber numbers.

Two spheres in a free stream of a second-order fluid. Phys. Fluids., 20, 063101.

abst: The forces acting on two fixed spheres in a second-order uniform flow are investigated. When α1+α2=0, where α1 and α2 are fluid parameters related to the first and second normal stress coefficients, the velocity field for a second-order fluid is the same as the one predicted by the Stokes equations while the pressure is modified. The Stokes solutions given by Stimson and Jeffery [Proc. R. Soc. London, Ser. A 111, 110 (1926)] for the case when the flow direction is along the line of centers and Goldman et al. [Chem. Eng. Sci. 21, 1151 (1966)] for the case when the flow direction is perpendicular to the line of centers are utilized and the stresses and the forces acting on the particles in a second-order fluid are calculated. For flow along the line of centers or perpendicular to it, the net force is in the direction that tends to decrease the particle separation distance. For the case of flow at arbitrary angle, unequal forces are applied to the spheres perpendicularly to the line of centers. These forces result in a change of orientation of the sedimenting spheres until the line of centers aligns with the flow direction. In addition, the potential flow of a second-order fluid past two fixed spheres in a uniform flow is investigated. The normal stress at the surface of each sphere is calculated and the viscoelastic effects on the normal stress for different separation distances are analyzed. The contribution of the potential flow of a second-order fluid to the force applied to the particles is an attractive force. Our explanations of the aggregation of particles in viscoelastic fluids rest on three pillars; the first is a viscoelastic ``pressure'' generated by normal stresses due to shear. Second, the total time derivative of the pressure is an important factor in the forces applied to moving particles. The third is associated with a change in the normal stress at points of stagnation which is a purely extensional effect unrelated to shearing.

Potential Flows of Viscous and Viscoelastic Fluids. (Book) Cambridge University Press.

abst: We carry out the linear viscous-irrotational analysis of capillary instability with heat transfer and phase change. We consider the cylindrical interface shared by two viscous incompressible fluids enclosed by two concentric cylinders. In viscous potential flow, viscosity enters the model through the balance of normal stresses at the interface. We write the dispersion relation from the stability analysis for axisymmetric disturbances in terms of a set of dimensionless numbers that arise in this phase change problem. For the film boiling condition, plots depicting the effect of some of these parameters on the maximum growth rate for unstable perturbations and critical wavenumber for marginal stability are presented and interpreted. Viscous effects of a purely irrotational motion in the presence of heat and mass transfer can stabilize an otherwise unstable gas-liquid interface.

Motion of a sphere normal to a wall in a second-order fluid. J. Fluid Mech., 587, 163-172.

abst: The motion of a sphere normal to a wall is investigated. The normal stress at the surface of the sphere is calculated and the viscoelastic effects on the normal stress for different separation distances are analysed. For small separation distances, when the particle is moving away from the wall, a tensile normal stress exists at the trailing edge if the fluid is Newtonian, while for a second-order fluid a larger tensile stress is observed. When the particle is moving towards the wall, the stress is compressive at the leading edge for a Newtonian fluid whereas a large tensile stress is observed for a second-orderfluid. The contribution of the second-order fluid to the overall force applied to the particle is towards the wall in both situations. Results are obtained using Stokes equationswhen α1+α2=0. In addition, a perturbation method has been utilized for a sphere very close to a wall and the effect of non-zero α1+α2 is discussed. Finally, viscoelastic potential flow is used and the results are compared with the other methods.

abst: The purpose of this study is to identify the potential locations for cavitation induced by total stress on the flow of a liquid through an orifice of an atomizer. A numerical simulation of two-phase incompressible flow is conducted in an axisymmetric geometry of the orifice for Reynolds numbers between 100 and 2000. The orifice has a rounded upstream corner and a sharp downstream corner with length-to-diameter ratio between 0.1 and 5. The total stress including viscous stress and pressure has been calculated in the flow field and, from there, the maximum principal stress is found. The total-stress criterion for cavitation is applied to find the regions where cavitation is likely to occur and compared with those of the traditional pressure criterion. Results show that the viscous stress has significant effects on cavitation. The effect of geometry and occurrence of hydraulic flip in the orifice on the total stress are studied. The Navier-Stokes equations are solved numerically using a finite-volume method and a boundary-fitted orthogonal grid that comes from the streamlines and potential lines of an axisymmetric equipotential flow in the same geometry. A level-set formulation is used to track the interface and model the surface tension.

Correction of Lamb's dissipation calculation for the effects of viscosity on capillary-gravity waves. Physics of Fluids, 19(8), 082105.

abst: Purely irrotational theories of the flow of a viscous liquid are applied to model the effect of viscosity on the decay and oscillation of capillary-gravity waves. In particular, the dissipation approximation used in this analysis gives rise to a viscous correction of the frequency of the oscillations which was not obtained by Lamb's [H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, UK, 1932) (reprinted in 1993)] dissipation calculation. Moreover, our dissipation method goes beyond Lamb's in the sense that it yields an eigenvalue relation valid for the entire continuous spectrum of wave numbers. Comparisons are presented between the purely irrotational theories and Lamb's exact solution, showing good to reasonable agreement for long, progressive waves and for short, standing waves, even for very viscous liquids. The performance of the irrotational approximations deteriorates within an interval of wave numbers containing the cutoff where traveling waves become standing ones.

Laminar and turbulent comparisons for channel flow and flow control, J. Fluid Mech., 570, 467-477.

abst: A formula is derived that shows exactly how much the discrepancy between the volume flux in laminar and in turbulent flow at the same pressure gradient increases as the pressure gradient is increased. We compare laminar and turbulent flows in channels with and without flow control. For the related problem of a fixed bulk-Reynolds-number flow, we seek the theoretical lowest bound for skin-friction drag for control schemes that use surface blowing and suction with zero-net volume-flux addition. For one such case, using a crossflow approach, we show that sustained drag below that of the laminar -Poiseuille-flowcase is not possible. For more general control strategies we derive a criterion for achieving sublaminar drag and use this to consider the implications for control strategy design and the limitations at high Reynolds numbers.

Purely irrotational theories for the viscous effects on the oscillations of drops and bubbles. Int. J. Multiphase Flow., 34(1), 61-75.

abst: In this paper, we apply two purely irrotational theories of the motion of a viscous fluid, namely, viscous potential flow (VPF) and the dissipation method to the problem of the decay of waves on the surface of a sphere. We treat the problem of the decay of small disturbances on a viscous drop surrounded by gas of negligible density and viscosity and a bubble immersed in a viscous liquid. The instantaneous velocity field in the viscous liquid is assumed to be irrotational. In VPF, viscosity enters the problem through the viscous normal stress at the free surface. In the dissipation method, viscosity appears in the dissipation integral included in the mechanical energy equation. Comparisons of the eigenvalues from VPF and the dissipation approximation with those from the exact solution of the linearized governing equations are presented. The results show that the viscous irrotational theories exhibit most of the features of the wave dynamics described by the exact solution. In particular, VPF and DM give rise to a viscous correction for the frequency that determines the crossover from progressive to standing waves. Good to reasonable quantitative agreement with the exact solution is also shown for certain ranges of modes and dimensionless viscosity: For large viscosity and short waves, VPF is a very good approximation to the exact solution. For small viscosity and long waves, the dissipation method furnishes the best approximation.

Symmetric model of capillary collapse and rupture. FEDSM2007-37262, 5th joint ASME/JSME Fluids Engineering Conf. July 30-Aug.2, 2007. San Diego, CA.

Friction factor improved correlations for laminar and turbulent gas-liquid flow in horizontal pipelines, Int. J. Multiphase Flow, 33(12), 1320-1336.

abst: We develop improved correlations for two-phase flow friction factor that consider the effect of the relative velocity of the phases, based on a database that includes 2560 gas–liquid flow experiments in horizontal pipes. The database includes a wide range of operational conditions and fluid properties for two-phase friction factor correlations. We classify the experiments by liquid holdup ranges to obtain composite analytical expressions for two-phase friction factor vs. the Reynolds number by fitting logistic dose curves to the experimental data with. We compute the liquid holdup values used to classify the experimental data using correlations proposed previously. The Reynolds number is based on the mixture velocity and the liquid kinematic viscosity. The Fanning friction factor for gas–liquid is defined in term of the mixture velocity and density. Additionally, we sort the experimental data by flow regime and obtain the two-phase friction factor improved correlations for dispersed bubble, slug, stratified and annular flow for different holdup ranges. We report error estimates for the predicted vs. measured friction factor together with standard deviation for each correlation. The accuracy of the correlations developed in this study is compared with that of other 21 correlations and models widely available in the specialized literature. Since different authors use different definitions for friction factors and Reynolds numbers, we present comparisons of the predicted pressure drop for each and every data point in the database. In most cases our correlations predict the pressure drop with much greater accuracy than those presented by previous authors.

Helmholtz decomposition coupling rotational to irrotational flow of a viscous fluid. PNAS, 103, 14272-14277.

abst: In this work, I present the form of the Navier–Stokes equations implied by the Helmholtz decomposition in which the relation of the irrotational and rotational velocity fields is made explicit. The idea of self-equilibration of irrotational viscous stresses is introduced. The decomposition is constructed by first selecting the irrotational flow compatible with the flow boundaries and other prescribed conditions. The rotational component of velocity is then the difference between the solution of the Navier–Stokes equations and the selected irrotational flow. To satisfy the boundary conditions, the irrotational field is required, and it depends on the viscosity. Five unknown fields are determined by the decomposed form of the Navier–Stokes equations for an incompressible fluid: the rotational component of velocity, the pressure, and the harmonic potential. These five fields may be readily identified in analytic solutions available in the literature. It is clear from these exact solutions that potential flow of a viscous fluid is required to satisfy prescribed conditions, like the no-slip condition at the boundary of a solid or continuity conditions across a two-fluid boundary. It can be said that equations governing the Helmholtz decomposition describe the modification of irrotational flow due to vorticity, but the analysis shows the two fields are coupled and cannot be completely determined independently.

Potential Flow of Viscous Fluids: Historical Notes. Int. J. Multiphase Flow, 32, 285-310.

abst: In this essay I will attempt to identify the main events in the history of thought about irrotational flow of viscous fluids. I am of the opinion that when considering irrotational solutions of the Navier–Stokes equations it is never necessary and typically not useful to put the viscosity to zero. This observation runs counter to the idea frequently expressed that potential flow is a topic which is useful only for inviscid fluids; many people think that the notion of a viscous potential flow is an oxymoron. Incorrect statements like “… irrotational flow implies inviscid flow but not the other way around” can be found in popular textbooks.

Though convenient, phrases like “inviscid potential flow” or “viscous potential flow” confuse properties of the flow (potential or irrotational) with properties of the material (inviscid or viscous); it is better and more accurate to speak of the irrotational flow of an inviscid or viscous fluid.

Every theorem about potential flow of perfect fluids with conservative body forces applies equally to viscous fluids in regions of irrotational flow.

Viscous potential flow analysis of stress-induced cavitation in an aperture flow. Atomization and Sprays, 16(7), 763-776.

abst: Cavitation in an aperture flow in a flat plate is studied using viscous potential flow. The maximum tension criterion for cavitation used here was proposed by Joseph [Phy. Rev. E, vol. 51, pp. 1649−1650, 1995; J. Fluid Mech., vol. 366, 367−378, 1998]: “Liquids at atmospheric pressure which cannot withstand tension will cavitate when and where tensile stresses due to motion exceed one atmosphere. A cavity will open in the direction of the maximum tensile stress which is 45° from the plane of shearing in pure shear of a Newtonian fluid.” The aperture flow is expressed using a complex potential and the stress is calculated using viscous potential flow. We find that the viscous stress is huge near the tips of the aperture, thus cavitation could be induced.

Stress-induced cavitation for the streaming motion of a viscous liquid past a sphere. J. Fluid Mech., 578, 381-411.

abst: The theory of stress-induced cavitation is applied here to the problem of cavitation of a viscous liquid in the streaming flow past a stationary sphere. This theory is a revision of the pressure theory which states that a flowing liquid will cavitate when and where the pressure drops below a cavitation threshold, or breaking strength, of the liquid. In the theory of stress-induced cavitation the liquid will cavitate when and where the maximum tensile stress exceeds the breaking strength of the liquid. For example, liquids at atmospheric pressure which cannot withstand tension will cavitate when and where additive tensile stresses due to motion exceed one atmosphere. A cavity will open in the direction of the maximum tensile stress, which is 45° from the plane of shearing in pure shear of a Newtonian fluid. This maximum tension criterion is applied here to analyse the onset of cavitation for the irrotational motion of a viscous fluid, the special case imposed by the limit of very low Reynolds numbers and the fluid flow obtained from the numerical solution of the Navier–Stokes equations. The analysis leads to a dimensionless expression for the maximum tensile stress as a function of position which depends on the cavitation and Reynolds numbers. The main conclusion is that at a fixed cavitation number the extent of the region of flow at risk to cavitation increases as the Reynolds number decreases. This prediction that more viscous liquids at a fixed cavitation number are at greater risk of cavitation seems not to be addressed, affirmed nor denied, in the cavitation literature known to us.

Lift and multiple equilibrium positions of a single particle in Newtonian and Oldroyd-B fluids, Computers and Fluids, 35, 121-146.

abst: A heavy particle is lifted from the bottom of a channel in a plane Poiseuille flow when the Reynolds number is larger than a critical value. In this paper we obtain correlations for lift-off of particles in Oldroyd-B fluids. The fluid elasticity reduces the critical shear Reynolds number for lift-off. The effect of the gap size between the particle and the wall, on the lift force, is also studied. A particle lifted from the channel wall attains an equilibrium height at which its buoyant weight is balanced by the hydrodynamic lift force. Choi and Joseph [Choi HG, Joseph DD. Fluidization by lift of 300 circular particles in plane Poiseuille flow by direct numerical simulation. J Fluid Mech 2001;438:101–128] first observed multiple equilibrium positions for a particle in Newtonian fluids. We report several new results for the Newtonian fluid case based on a detailed study of the multiple equilibrium solutions, e.g. we find that at a given Reynolds number there are regions inside the channel where no particle, irrespective of its weight, can attain a stable equilibrium position. This would result in particle-depleted zones in channels with Poiseuille flows of a dilute suspension of particles of varying densities. Multiple equilibrium positions of particles are also found in Oldroyd-B fluids. All the results in this paper are based on 2D direct numerical simulations.

abst: The cross-stream migration of a single neutrally buoyant rigid sphere in tube flow is simulated by two packages, one (ALE) based on a moving and adaptive grid and another (DLM) using distributed Lagrange multipliers on a fixed grid. The two packages give results in good agreement with each other and with experiments. A lift law $L \,{=}\, CU_s (\Omega_s-\Omega_{\hbox{\scriptsize{\it se}}})$ analogous to $L \,{=}\, \rho U\Gamma$ which was proposed and validated in two dimensions is validated in three dimensions here; $C$ is a constant depending on material and geometric parameters, $U_s$ is the slip velocity and it is positive, $\Omega_s$ is the slip angular velocity and $\Omega_{\hbox{\scriptsize{\it se}}}$ is the slip angular velocity when the sphere is in equilibrium at the Segré–Silberberg radius. The slip angular velocity discrepancy $\Omega_s-\Omega_{\hbox{\scriptsize{\it se}}acute;$ is the circulation for the free particle and it changes sign with the lift. A method of constrained simulation is used to generate data which is processed for correlation formulas for the lift force, slip velocity, and equilibrium position. Our formulae predict the change of sign of the lift force which is necessary in the Segré–Silberberg effect. Our correlation formula is compared with analytical lift formulae in the literature and with the results of two-dimensional simulations. Our work establishes a general procedure for obtaining correlation formulae from numerical experiments. This procedure forms a link between numerical simulation and engineering practice.

Numerical study of particle migration in tube and plane Poiseuille flows. Proceedings of IUTAM symposium on Computational Approaches to Disperse Multiphase Flows, Argonne National Laboratory, Argonne, IL Oct. 4-7, 2005.

abst: The lateral migration of a single spherical particle in tube Poiseuille flow is simulated by ALE scheme, along with the study of the movement of a circular particle in plane Poiseuille flow with consistent dimensionless parameters. These particles are rigid and neutrally buoyant. A lift law L = CU s(Ωs−Ωse) analogous to L=ρUΓ is validated in both two dimensions and three dimensions here; U s and Ωs are slip velocity and angular slip velocity, Ωse is the angular slip velocity at equilibrium. A method of constrained simulation is used to generate data which is processed for correlation formulas for the lift force, slip velocity, and equilibrium position. Our formulas predict the change of sign of the lift force which is necessary in the Segré—Silberberg effect. Correlation formulas are compared between tube and plane Poiseuille flows by fixing the dimensionless size of particle and the Reynolds number. Our work provides a valuable reference for a better understanding of the migration of particle in Poiseuille flows and the Segré—Silberberg effect.

abst: Tubeless and open siphons operate without conduits, in the open, supported only by extensional stresses. Here, we demonstrate that the addition of silica nanoparticles in modest concentrations (on the order of 1% by weight) to an aqueous Poly(ethylene oxide) (PEO) solution of a moderately low concentration (0.5% by weight) has a dramatic effect on the power of the siphon as well as on the ability of the siphon to completely clean substrates. These enhanced effects may have a partly fluid mechanical explanation, since they also occur when the siphon is laden with inert sub-millimetre particles (Wang & Joseph, J. Fluid Mech. vol. 480, 2003, p. 119). The extensional properties of PEO solutions are greatly enhanced when they are loaded with silica nanoparticles. The degradation of the PEO solution is suppressed by the addition of silica nanoparticles.

Purely irrotational theories of the effect of the viscosity on the decay of free gravity waves. J. Fluid Mech., 559, 461-472.

abst: It is generally believed that the major effects of viscosity are associated with vorticity. This belief is not always well founded; major effects of viscosity can be obtained from purely irrotational analysis of flows of viscous fluids. Here we illustrate this point by comparing our irrotational solutions with Lamb's 1932 exact solution of the problem of the decay of free gravity waves. Excellent agreements, even in fluids 10$^{7}$ more viscous than water, are achieved for the decay rates $n(k)$ for all wavenumbers $k$, excluding a small interval around a critical value $k_{c}$ where progressive waves change to monotonic decay.

Boundary layer analysis for effects of viscosity of the irrotational flow on the flow induced by a rapidly rotating cylinder in a uniform stream. J. Fluid Mech., 557, 167-190.

abst: We study the streaming flow past a rapidly rotating circular cylinder. The starting point is the full continuity and momentum equations without any approximations. We assume that the solution is a boundary -layerflow near the cylinder surface with the potential flow outside the boundary layer. The order of magnitude of the terms in the continuity and momentum equations can be estimated inside the boundary layer. When terms of the order of $\delta/a$ and higher are dropped, where $\delta$ is the boundary -layerthickness and $a$ is the radius of the cylinder, the equations used by M. B. Glauert (Proc. R. Soc. Lond. A, vol. 242, 1957, p. 108) are recovered. Glauert's solution ignores the irrotational rotary component of the flow inside the boundary layer, which is consistent with dropping $\delta/a$ terms in the governing equations.

We propose a new solution to this problem, in which the velocity field is decomposed into two parts. Outside the boundary layer, the flow is irrotational and can be decomposed into a purely rotary flow and a potential flow past a fixed cylinder. Inside the boundary layer, the velocity is decomposed into an irrotational purely rotary flow and a boundary -layerflow. Inserting this decomposition of the velocity field inside the boundary layer into the governing equations, we obtain a new set of equations for the boundary -layerflow, in which we do not drop the terms of the order of $\delta/a$ or higher. The pressure can no longer be assumed to be a constant across the boundary layer, and the continuity of shear stress at the outer edge of the boundary layer is enforced. We solve this new set of equations using Glauert's method, i.e. to expand the solutions as a power series of $\alpha \,{=}\, 2 U_0 /Q$, where $U_0$ is the uniform stream velocity and $Q$ is the circulatory velocity at the outer edge of the boundary layer. The pressure from this boundary -layersolution has two parts, an inertial part and a viscous part. The inertial part comes from the inertia terms in the momentum equations and is in agreement with the irrotational pressure; the viscous part comes from the viscous stress terms in the momentum equations and may be viewed as a viscous pressure correction, which contributes to both drag and lift. Our boundary -layersolution is in reasonable to excellent agreement with the numerical simulation in the companion paper by Padrino & Joseph (2006).

Pressure corrections for the effects of viscosity on the irrotational flow outside Prandtl's boundary layer. J. Fluid Mech., 557, 145-165.

abst: This work aims at understanding the viscous effects of the outer potential flow on Prandtl's boundary layer. For a body moving with a constant velocity in an otherwise quiescent liquid, the non-zero viscous dissipation of the outer potential flow gives rise to an additional drag, increasing the drag calculated from the boundary layer alone. The drag is considered in three cases here, on a two-dimensional circular gas bubble in a streaming flow, at the edge of the boundary layer around a rapidly rotating cylinder in a uniform flow, and on an airfoil in a streaming flow. The drag may be computed using the dissipation method or the viscous pressure correction of the irrotational pressure. Such a pressure correction can be induced by the discrepancy between the irrotatinal shear stress and the zero shear stress at a fluid–gas interface, or by the discrepancy between the shear stress evaluated from the boundary-layer solution and that evaluated from the outer potential flow solution at the edge of the boundary layer.

Numerical study of the steady state uniform flow past a rotating cylinder. J. Fluid Mech., 557, 191-223.

abst: Results from the numerical simulation of the two-dimensional incompressible unsteady Navier–Stokes equations for streaming flow past a rotating circular cylinder are presented in this study. The numerical solution of the equations of motion is conducted with a commercial computational fluid dynamics package which discretizes the equations applying the control volume method. The numerical set-up is validated by comparing results for a Reynolds number based on the free stream of $\hbox{\it Re}$ = 200 and dimensionless peripheral speed of $\tilde{q}$ = 3, 4 and 5 with results from the literature. After the validation stage, various pairs of $\hbox{\it Re}$ and $\tilde{q}$ are specified in order to carry out the numerical experiments. These values are $\hbox{\it Re}$ = 200 with $\tilde{q}$ = 4 and 5; $\hbox{\it Re}$ = 400 with $\tilde{q}$ = 4, 5 and 6, and $\hbox{\it Re}$ = 1000 with $\tilde{q}$ = 3. In all these cases, gentle convergence to fully developed steady state is reached. From the numerical vorticity distribution, the position of the outer edge of the vortical region is determined as a function of the angular coordinate. This position is found by means of a reasonable criterion set to define the outmost curve around the cylinder where the vorticity magnitude reaches a certain cut-off value. By considering the average value of this profile, a uniform vortical region thickness is specified for every pair of $\hbox{\it Re}$ and $\tilde{q}$.

Next, the theoretical approach of Wang & Joseph (2006a; see the companion paper) and the numerical results are used to determine two different values of the effective vortical region thickness for every pair of $\hbox{\it Re}$ and $\tilde{q}$. One effective thickness $\delta_D/a$ is obtained from the match between the additional drag on the outer edge of the vortical region according to the viscous correction of viscous potential flow (VCVPF) and the corresponding numerical profile while the other thickness $\delta_L/a$ is determined from the match between the pressure lift on the cylinder obtained from Wang & Joseph (2006a)'s simple modification of the boundary-layer analysis due to Glauert (Proc. R. Soc. Lond. A, vol. 242, 1957, p. 108) and the numerical value of the pressure lift coefficient. The values of $\delta_D/a$ and $\delta_L/a$ are used in the computation of various parameters associated with the flow, namely, the torque on the rotating cylinder, the circulatory velocity at the edge of the vortical region, which links the cylinder's angular velocity with the circulation of the irrotational flow of the viscous fluid outside this region, and the viscous dissipation. Predictions from the approaches of Glauert (1957) and Wang & Joseph (2006a) are also included for comparison. The values of both effective thicknesses, $\delta_D/a$ and $\delta_L/a$, are found to have the same order of magnitude. Then, we show that choosing $\delta_D/a$ as a unique effective thickness, the modification of Glauert's boundary-layer analysis and the VCVPF approach as proposed by Wang & Joseph (2006a) produce results which are in better general agreement with the values from numerical simulation than those from Glauert's solution.

Liquid jet in a high Mach number air stream. Int. J. Multiphase Flow, 32, 20-50.

abst: The instability of circular liquid jet immersed in a coflowing high velocity air stream is studied assuming that the flow of the viscous gas and liquid is irrotational. The basic velocity profiles are uniform and different. The instabilities are driven by Kelvin–Helmholtz instability due to a velocity difference and neckdown due to capillary instability. Capillary instabilities dominate for large Weber numbers. Kelvin–Helmholtz instability dominates for small Weber numbers. The wavelength for the most unstable wave decreases strongly with the Mach number and attains a very small minimum when the Mach number is somewhat larger than one. The peak growth rates are attained for axisymmetric disturbances (n = 0) when the viscosity of the liquid is not too large. The peak growth rates for the first asymmetric mode (n = 1) and the associated wavelength are very close to the n = 0 mode; the peak growth rate for n = 1 modes exceeds n = 0 when the viscosity of the liquid jet is large. The effects of viscosity on the irrotational instabilities are very strong. The analysis predicts that breakup fragments of liquids in high speed air streams may be exceedingly small, especially in the transonic range of Mach numbers.

Aging properties of semi-dilute aqueous solutions of polyethylene oxide seeded with silica nanoparticles. J. Rheology, 49, 1303–1316; selected for the November 7, 2005 issue of Virtual Journal of Nanoscale Science & Technology (http://www.vjnano.org).

Stability of a Liquid Jet into Incompressible Gases and Liquids: Part 2. Effects of the irrotational viscous pressure. Int. J. Multiphase Flow, 31, 1134-1154.

abst: In this paper we investigate the effects of an irrotational, viscous pressure on the stability of a liquid jet into gases and liquids. The analysis extends our earlier work (part 1) in which the stability of the viscous jet was studied assuming that the motion and pressure are irrotational and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. The liquid jet is always unstable; at high Weber numbers the instability is dominated by capillary instability; at low W the instability is dominated by Kelvin–Helmholtz (KH) waves generated by pressures driven by the discontinuous velocity. In the irrotational analysis the viscosity is important but the effects of shear are neglected. In fact a discontinuous velocity is not compatible with the continuity of the tangential components of velocity and shear stress so that KH instability is not properly posed for exact study using the no-slip condition but some of the effects of viscosity can be ascertained using viscous potential flow. The theory is called viscous potential flow (VPF). Here we develop another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by selecting viscous contributions to the irrotational pressure. These pressures generate a hierarchy of potential flows in powers of the viscosity, but only the first one, linear in viscosity, in the irrotational viscous stress, is thought to have physical significance. The tangential velocity and shear stress in an irrotational study cannot be made continuous, but the effects of the discontinuous velocity and stress in the mechanical energy balance can be removed “in the mean.” This theory with the additional viscous pressure is called VCVPF, viscous correction of VPF. VCVPF is VPF with the additional pressures. The theory here cannot be compared with an exact solution, which would not allow the discontinuous velocity and stress. In other problems, like capillary instability, in which VCVPF can be compared with an exact solution, the agreements are uniformly excellent in the wave number when one of the fluids is gas and in good but not uniform, agreement when both fluids are liquids.

Simulating the dynamics of fluid-ellipsoid interactions. Computers and Structures, 83, 463-478.

abst: We present the simulation of the dynamics of fluid–ellipsoid interactions

in a narrow channel filled with a Newtonian fluid using a Lagrange multiplier based fictitious domain methodology. As expected, a settling ellipsoid turns its broadside perpendicular to the stream main direction and the center of mass moves to the central axis of the channel. For two ellipsoid cases, we have obtained two kinds of interactions between two ellipsoid: (1) they settle side-by-side and interact with each other periodically; (2) they keep moving around each other and stay together. We also found that the length of longest axis plays an important role for these interactions.

Simulating the dynamics of fluid-cylinder interactions. J. of Zhejiang Univ. Science, 6A(2), 97-109.

abst: We present the simulation of the dynamics of fluid-cylinder interactions in a narrow three-dimensional channel filled with a Newtonian fluid, using a Lagrange multiplier based fictitious domain methodology combined with a finite element method and an operator splitting technique. As expected, a settling truncated cylinder turns its broadside perpendicular to the main stream direction and the center of mass moves to the central axis of the channel. In the case of two truncated cylinders, they first move around each other for a while and then stay together in a “T” shape. After the “T” shape has been formed for a long enough time, we found no vortex shedding behind the cylinders. When simulating the fluidization of 60 truncated cylinders, we captured the features of interactions among fluidized cylinders as observed in experiments.

Liquid jet in a high Mach number air stream. Int. J. Multiphase Flow, 32(1), 20-50.

Potential flow of a second-order fluid over a tri-axial ellipsoid. J. App. Math., 4, 341-364.

abst: The problem of potential flow of a second-order fluid around an ellipsoid is solved, and the flow and stress fields are computed. The flow fields are determined by the harmonic potential but the stress fields depend on viscosity and the parameters of the second-order fluid. The stress fields on the surface of a tri-axial ellipsoid depend strongly on the ratios of principal axes and are such as to suggest the formation of gas bubble with a round flat nose and two-dimensional cusped trailing edge. A thin flat trailing edge gives rise to a large stress which makes the thin trailing edge thinner.

Composite power law holdup correlations in horizontal pipes, Int. J. Multiphase Flow, 31(12), 1276-1303.

abst: A wide range of experimental holdup data, from different sources, are analyzed based on a theoretical model proposed in this work to evaluate the holdup in horizontal pipes. 2276 gas–liquid flow experiments in horizontal pipelines with a wide range of operational conditions and fluid properties are included in the database. The experiments are classified by mixture Reynolds number ranges and composite analytical expressions for the relationship between the liquid holdup and no-slip liquid holdup vs. the gas–liquid volumetric flow rate are obtained by fitting the data with logistic dose curves. The Reynolds number appropriate to classify the experimental data for gas–liquid flows in horizontal pipes is based on the mixture velocity and the liquid kinematic viscosity. Composite power law holdup correlations for flows sorted by flow pattern are also obtained. Error estimates for the predicted vs. measured holdup correlations together with standard deviation for each correlation are presented. The accuracy of the correlations developed in this study is compared with the accuracy of 26 previous correlations and models in the literature. Our correlations predict the liquid holdup in horizontal pipes with much greater accuracy than those presented by previous authors.

J. Wang, D.D. Joseph and T. Funada, 2005. Pressure corrections for potential flow analysis of capillary instability of viscous fluids. J. Fluid Mech.522, 383-394.

abst: Funada & Joseph (Intl J. Multiphase Flow, vol. 28, 2002, p. 1459) analysed capillary instability assuming that the flow is irrotational but the fluids are viscous (viscous potential flow, VPF). They compared their results with the exact normal-mode solution of the linearized Navier–Stokes equations (fully viscous flow, FVF) and with the irrotational flow of inviscid fluids (inviscid potential flow, IPF). They showed that the growth rates computed by VPF are close to the exact solution when Reynolds number is larger than $O(10)$ and are always more accurate than those computed using IPF. Recently, Joseph & Wang (J. Fluid Mech., vol. 505, 2004, p. 365) presented a method for computing a viscous correction of the irrotational pressure induced by the discrepancy between non-zero irrotational shear stress and the zero-shear-stress boundary condition at a free surface. The irrotational flow with a corrected pressure is called the viscous correction of VPF (VCVPF). Here we compute the pressure correction for capillary instability in cases in which one fluid is viscous and the other fluid is a gas of negligible density and viscosity. The growth rates computed using VCVPF are in remarkably good agreement with the exact solution FVF.

Viscous contributions to the pressure for potential flow analysis of capillary instability of two viscous fluids. Phys. Fluids, 17, 052105.

abst: Capillary instability of a liquid cylinder immersed in another liquid is analyzed using viscous potential flow. An effect of viscosity on the irrotational motion may be introduced by evaluating the viscous normal stress at the liquid–liquid interface on the irrotational motions. In a second approximation, the explicit effects of the discontinuity of the shear stress and tangential component of velocity which cannot be resolved pointwise in irrotational flows, can be removed in the mean from the power of traction integrals in the energy equation by the selection of two viscous corrections of the irrotational pressure. The actual resolution of these discontinuities presumably takes place in a boundary layer which is not computed or needed. We include the irrotational stress and pressure correction in the normal stress balance and compare the computed growth rates to the growth rates of the exact viscous flow solution. The agreement is excellent when one of the liquids is a gas; for two viscous liquids, the agreement is good to reasonable for the maximum growth rates but poor for long waves. Calculations show that good agreement is obtained when the vorticity is relatively small or the irrotational part is dominant in the exact viscous solution. We show that the irrotational viscous flow with pressure corrections gives rise to exactly the same dispersion relation as the dissipation method in which no pressure at all is required and the viscous effect is accounted for by evaluating the viscous dissipation using the irrotational flow.

abst: We have developed a numerical package to simulate particle motions in fluid interfaces. The particles are moved in a direct simulation respecting the fundamental equations of motion of fluids and solid particles without the use of models. The fluid–particle motion is resolved by the method of distributed Lagrange multipliers and the interface is moved by the method of level sets. The present work fills a gap since there are no other theoretical methods available to describe the nonlinear fluid dynamics of capillary attraction.

Two different cases of constrained motions of floating particles are studied here. In the first case, we study motions of floating spheres under the constraint that the contact angle is fixed by the Young–Dupr´e law; the contact line must move when the contact angle is fixed. In the second case, we study motions of disks (short cylinders) with flat ends in which the contact line is pinned at the sharp edge of the disk; the contact angle must change when the disks move and this angle can change within the limits specified by the Gibbs extension to the Young–Dupré law. The fact that sharp edged particles cling to interfaces independent of particle wettability is not fully appreciated and needs study.

The numerical scheme presented here is at present the only one which can move floating particles in direct simulation. We simulate the evolution of single heavier-than-liquid spheres and disks to their equilibrium depth and the evolution to clusters of two and fours spheres and two disks under lateral forces, collectively called capillary attraction. New experiments by Wang, Bai & Joseph on the equilibrium depth of floating disks pinned at the edge are presented and compared with analysis and simulations.

Purely irrotational theories of the effects of viscosity and viscoelastacity on capillary instability of a liquid cylinder. J. Non-Newtonian Fluid Mech., 129, 106-116.

abst: Capillary instability of a liquid cylinder can arise when either the interior or exterior fluid is a gas of negligible density and viscosity. The shear stress must vanish at the gas-liquid interface but it does not vanish in irrotational flows. Joseph and Wang [D.D. Joseph, J. Wang, The dissipation approximation and viscous potential flow, J. Fluid Mech. 505 (2004) 365] derived an additional viscous correction to the irrotational pressure. They argued that this pressure arises in a boundary layer induced by the unphysical discontinuity of the shear stress. Wang et al. [J. Wang, D.D. Joseph, T. Funada, Pressure correction for potential flow analysis of capillary instability of viscous fluids, J. Fluid Mech. 522 (2005) 383] showed that the dispersion relation for capillary instability in the Newtonian case is almost indistinguishable from the exact solution when the additional pressure contribution is included in the irrotational theory. Here we extend the formulation for the additional pressure to potential flows of viscoelastic fluids in flows governed by linearized equations, and apply this additional pressure to capillary instability of viscoelastic liquid filaments of Jeffreys type. The shear stress at the gas–liquid interface cannot be made to vanish in an irrotational theory, but the explicit effect of this uncompensated shear stress can be removed from the global equation for the evolution of the energy of disturbances. This line of thought allows us to present the additional pressure theory without appeal to boundary layers. The validity of this purely irrotational theory can be judged by comparison with the exact solutions of Navier–Stokes equations. Here we show that our purely irrotational theory is in remarkably good agreement with the exact solution in linear analysis of the capillary instability of a viscoelastic liquid cylinder.

Sedimentation of Cylindrical Particles in a Viscoelastic Liquid: Shape-Tilting. China Particuology, 2(1), 13-18. 328.

abst: Aluminum and Teflon cylindrical particles with flat ends are dropped in aqueous Polyox solutions. The terminal equilibrium orientation of the particles is characterized by the tilt angle, α, formed by the major axis of the cylinder with the horizontal. It is observed that α is a function of the aspect ratio L=L/d, where L is the length and d is the diameter of the cylinder, and that it varies continuously from a certain angle, α0, to 90°, as L increases toward a value L0. For a given shape, both α0 and L0 depend on the density of the cylinder and the properties of the liquid used. For the particles we have considered the value of L0 is of the order of 2. This “tilt-angle phenomenon” disappears as soon as the ends of the cylinder are round. Specifically, cylinders of the same density and with the same aspect ratio but with round ends, when dropped in the same polymeric solution will reach a final orientation with α=90°. Therefore, this tilt-angle phenomenon seems to be tightly related to the shape of the particle.

Ellipsoidal model of the rise of a Taylor bubble in a round tube. Int. J. Multiphase Flow, 31, 473-491.

abst: The rise velocity of long gas bubbles (Taylor bubbles) in round tubes is modeled by an ovary ellipsoidal cap bubble rising in an irrotational flow of a viscous liquid. The analysis leads to an expression for the rise velocity which depends on the aspect ratio of the model ellipsoid and the Reynolds and Eötvös numbers. The aspect ratio of the best ellipsoid is selected to give the same rise velocity as the Taylor bubble at given values of the Eötvös and Reynolds numbers. The analysis leads to a prediction of the shape of the ovary ellipsoid which rises with same velocity as the Taylor bubble.

Stability of a liquid jet into incompressible gases and liquids. Int. J. Multiphase Flow, 30, 1279-1310.

abst: We carry out an analysis of the stability of a liquid jet into a gas or another liquid using viscous potential flow. The instability may be driven by Kelvin–Helmholtz KH instability due to a velocity difference and a neckdown due to capillary instability. Viscous potential flow is the potential flow solution of Navier–Stokes equations; the viscosity enters at the interface.

KH instability is induced by a discontinuity of velocity at a gas–liquid interface. Such discontinuities cannot occur in the flow of viscous fluids. However, the effects of viscous extensional stresses can be obtained from a mathematically consistent analysis of the irrotational motion of a viscous fluid carried out here. An explicit dispersion relation is derived and analyzed for temporal and convective/absolute (C/A) instability. We find that for all values of the relevant parameters, there are wavenumbers for which the liquid jet is temporally unstable. The cut-off wavenumber and wavenumber of maximum growth are most important; the variation of these quantities with the density and viscosity ratios, the Weber number and Reynolds is computed and displayed as graphs and asymptotic formulas. The instabilities of a liquid jet are due to capillary and KH instabilities. We show that KH instability cannot occur in a vacuum but capillary instability can occur in vacuum. We present comprehensive results, based on viscous potential flow, of the effects of the ambient.

Temporally unstable liquid jet flows can be analyzed for spatial instabilities by C/A theory; they are either convectively unstable or absolutely unstable depending on the sign of the temporal growth rate at a singularity of the dispersion relation. The study of such singularities is greatly simplified by the analysis here which leads to an explicit dispersion relation; an algebraic function of a complex frequency and complex wavenumber. Analysis of this function gives rise to an accurate Weber–Reynolds criterion for the border between absolute and convective instabilities. Some problems of the applicability to physics of C/A analysis of stability of spatially uniform and nearly uniform flows are discussed.

The dissipation approximation and viscous potential flow. J. Fluid Mech., 505, 365-377.

abst: Dissipation approximations have been used to calculate the drag on bubbles and drops and the decay rate of free gravity waves on water. In these approximations, viscous effects are calculated by evaluating the viscous stresses on irrotational flows. The pressure is not involved in the dissipation integral, but it enters into the power of traction integral, which equals the dissipation. A viscous correction of the irrotational pressure is needed to resolve the discrepancy between the zero-shear-stress boundary condition at a free surface and the non-zero irrotational shear stress. Here we show that the power of the pressure correction is equal to the power of the irrotational shear stress. The viscous pressure correction on the interface can be expressed by a harmonic series. The principal mode of this series is matched to the velocity potential and its coefficient is explicitly determined. The other modes do not enter into the expression for the drag on bubbles and drops. They vanish in the case of free gravity waves.

Factors governing friction losses in selflubricated transport of bitumen froth: 1. Water release. Can. J. Chem. Eng., 82, 735-742

abst: Syncrude Canada Ltd. transports bitumen froth, a viscous intermediate product of the oil sand extraction process, 35 km via pipeline. Pipeline transport is feasible because some of the water that occurs naturally in the froth forms a thin lubricating layer around a bitumen-rich core, thereby greatly reducing friction losses and transportation costs. In this paper, the effect of froth composition (namely, water content) on the formation of the lubricating layer is reported. Tests were conducted with a 25 mm diameter pipe loop and a concentric cylinder froth rheometer. Measurements of pressure gradient and water holdup (free water fraction), along with visual observations, showed that froth containing a lower total water content yielded less free water to the lubricating layer. In the froth rheometer, the conditions for which stable, self-lubricated flow could be maintained were comparable to those required to maintain self-lubricated flow in the 25 mm pipe loop.

The maximum contact angle at the rim of a heavy floating disk. J. Colloid and Interface Sci., 279, 186-191.

abst: We give a simple mathematical argument that as the weight of a floating disk is gradually increased, the maximum contact angle at its sharp rim which is attained before the disk sinks is greater than 90°, and present numerical results which support this conclusion.

The maximum contact angle at the rim of a heavy floating disk. J. Colloid and Interface Sci., 279, 186-191.

Critical remarks about flow charting. Multiphase Science and Technology, 15, 12.

abst: In a recent paper (Mata, Pereyra, Trallero and Joseph 2002) we computed stability limits for Kelvin-Helmholtz instability of superposed gas-liquid flow, comparing theories of Jeffreys (1925, 1926), Taitel and Dukler (1976), Lin and Hanratty (1986), Barnea and Taitel (1993), and Fimada and Joseph (2001). The theories we compared with literature data on air-water flow and with new data on heavy oil. A problem encountered in the experiments is that the experimental data is presented in a plane of superficial gas and liquid velocities which do not uniquely determine the flow type. A critical view of this method of presenting results is the subject of the remarks to follow...

Opportunities for extracting correlations from numerical and real experiments using digital technology. Multiphase Science and Technology, 15, 1-4.

abst: I wrote a book called, Interrogation of Direct Numerical Simulation of Solid-Liquid Flows, which is available on www.efluids.com. The Epilogue to the book sets out the case for putting new life into the tried and true engineering approach to correlations. Excerpts from the Epilogue updated for discussion at our workshop appears below.

Acceleration of a liquid drop suddenly exposed to a high speed air stream. Int. J. Multiphase Flow., 30, 217-224.

abst: In this communication we propose a correlation for the drag coefficient on a liquid drop suddenly exposed to a high-speed airstream. The correlation is a bi-power law in the Ohnesorge and Weber numbers. The correlation predicts the acceleration of the drop in terms of known quantities.

Potential flow of a second order fluid over a sphere or an ellipse. J. Fluid Mech., 511, 201-215.

abst: We study the potential flow of a second-order fluid over a sphere or an ellipse. The normal stress at the surface of the body is calculated and has contributions from the inertia, viscous and viscoelastic effects. We investigate the effects of Reynolds number and body size on the normal stress; for the ellipse, various angles of attack and aspect ratios are also studied. The effect of the viscoelastic terms is opposite to that of inertia; the normal stress at a point of stagnation can change from compression to tension. This causes long bodies to turn into the stream and causes spherical bodies to chain. For a rising gas bubble, the effect of the viscoelastic and viscous terms in the normal stress is to extend the rear end so that it tends to the cusped trailing edge observed in experiments.

Power law and composite power law friction factor corrections for laminar and turbulent gas-liquid flow in horizontal pipelines. Int. J. Multiphase Flow, 29(10), 1605-1629.

abst: Data from 2435 gas–liquid flow experiments in horizontal pipelines, taken from different sources, including new data for heavy oil are compiled and processed for power law and composite power law friction factor correlations. To our knowledge this is the largest database so far published in the literature; it includes the widest range of operational conditions and fluid properties for two-phase friction factor correlations. Separate power laws for laminar and turbulent flows are obtained for all flows in the database and also for flows sorted by flow pattern. Composite analytical expressions for the friction factor covering both laminar and turbulent flows are obtained by fitting the transition region between laminar and turbulent flow with logistic dose curves. Logistic dose curves lead to rational fractions of power laws which reduce to the power laws for laminar flow when the Reynolds number is low and to turbulent flow when the Reynolds number is large. The Reynolds number appropriate for gas–liquid flows in horizontal pipes is based on the mixture velocity and the liquid kinematic viscosity. The definition of the Fanning friction factor for gas–liquid flow used in this study is based on the mixture velocity and density. Error estimates for the predicted vs. measured friction factor together with standard deviation for each correlation are presented. The correlations in this study are compared with previous correlations, homogeneous models and mechanistic models most commonly used for gas–liquid flow in pipelines. Since different authors use different definitions for friction factors and Reynolds numbers, comparisons of the predicted pressure drop for each and every data point in the database are presented. Our correlations predict the pressure drop with much greater accuracy than those presented by previous authors.

Drag reduction by polymer additives in a turbulent channel flow, J. Fluid Mech., 486, 213-238.

abst: Turbulent drag reduction by polymer additives in a channel is investigated using direct numerical simulation. The dilute polymer solution is expressed with an Oldroyd-B model that shows a linear elastic behaviour. Simulations are carried out by changing the Weissenberg number at the Reynolds numbers of 4000 and 20 000 based on the bulk velocity and channel height. The onset criterion for drag reduction predicted in the present study shows a good agreement with previous theoretical and experimental studies. In addition, the flow statistics such as the r.m.s. velocity fluctuations are also in good agreement with previous experimental observations. The onset mechanism of drag reduction is interpreted based on elastic theory, which is one of the most plausible hypotheses suggested in the past. The transport equations for the kinetic and elastic energy are derived for the first time. It is observed that the polymer stores the elastic energy from the flow very near the wall and then releases it there when the relaxation time is short, showing no drag reduction. However, when the relaxation time is long enough, the elastic energy stored in the very near-wall region is transported to and released in the buffer and log layers, showing a significant amount of drag reduction.

Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids, Phys. Fluids, 18(8), 2267-2278.

abst: Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids are investigated by direct numerical simulation. Previous works on this topic for Newtonian fluids show that the two-dimensional channel can be divided into alternating regions defined by the stability of the particle's equilibrium. We observe stability regions with the same pattern in flows of shear thinning fluids and study the effects of shear thinning properties on the distribution of the stability regions. Joseph and Ocando [J. Fluid Mech. 454, 263 (2002)] analyzed the role of the slip velocity Us = Uf–Up and the angular slip velocity Omega

s =

p–

f on migration and lift in plane Poiseuille flow of Newtonian fluids. They concluded that the discrepancy Omega

s–

se, where

se is the angular slip velocity at equilibrium, changes sign across the equilibrium position. In this paper we verify that this conclusion holds in shear thinning fluids. Correlations for lift forces may be constructed by analogy with the classical lift formula L = CU Gamma

of aerodynamics and the proper analogs of U and Gamma

in the present context are Us and Omega

s–

se. Using dimensionless parameters, the correlation is a power law near the wall and a linear relation (which can be taken as a power law with the power of one) near the centerline. The correlations are compared to analytical expressions for lift forces in the literature and we believe that the correlations capture the essence of the mechanism of the lift force. Our correlations for lift forces can be made completely explicit provided that the correlations relating Us and Omega

s to prescribed parameters are obtained.©

abst: The theory of viscous potential flow is applied to the problem of finding the rise velocity $U$ of a spherical cap bubble (see Davies & Taylor 1950; Batchelor 1967). The rise velocity is given by \frac{U}{\sqrt{gD}}=-\frac{8}{3}\frac{\nu(1+8s)}{\sqrt{gD^3}}+ \frac{\sqrt{2}}{3}\left[ 1-2s-\frac{16s\sigma}{\rho gD^2}+ \frac{32v^2}{gD^3}(1+8s)^2\right]^{1/2}, \nonumber where $R = D/2$ is the radius of the cap, $\rho$ and $\nu$ are the density and kinematic viscosity of the liquid, $\sigma$ is surface tension, $r(\theta) = R(1 + s\theta^2)$ and $s = r''(0)/D$ is the deviation of the free surface from perfect sphericity $r(\theta)=R$ near the stagnation point $\theta = 0$. The bubble nose is more pointed when $s < 0$ and blunted when $s > 0.$ A more pointed bubble increases the rise velocity; the blunter bubble rises slower. The Davies & Taylor (1950) result arises when $s$ and $\nu$ vanish; if $s$ alone is zero, \[\frac{U}{\sqrt{gD}}= -\frac{8}{3}\frac{\nu}{\sqrt{gD^3}}+\frac{\sqrt{2}}{3} \left[ 1+\frac{32\nu^2}{gD^3}\right]^{1/2},\] showing that viscosity slows the rise velocity. This equation gives rise to a hyperbolic drag law \[C_D =6+32/R_e,\] which agrees with data on the rise velocity of spherical cap bubbles given by Bhaga & Weber (1981).

Self-lubricated transport of aqueous foams in horizontal conduits, Int. J. Multiphase Flow, 29, 1817-1831.

abst: The flow characteristics of aqueous foams were studied in a thin flow channel and a round pipe instrumented for pressure gradient and flow rate measurements. The quality of the foam was varied by controlling the volumetric flow rate of liquid and gas, and different flow types were identified and charted. Uniform foams move as a rigid body lubricated by water generated by breaking foam at the wall. A lubrication model leading to a formula for the thickness of the lubricating layer is presented. The formula predicts a layer thickness of 6–8 μm in the channel and 10–12 μm in the pipe. The thickness depends weakly on foam quality. An overall correlation for the friction factor as a function of Reynolds number which applies to both channel and pipe is derived. This correlation is consistent with a model in which a rigid core of foam is lubricated by laminar flow of a water layer in the range of measured thickness.

Universal correlation for the rise velocity of long gas bubbles in round pipes, J. Fluid Mech., 494, 379-398.

abst: We collected all of the published data we could find on the rise velocity of long gas bubbles in stagnant fluids contained in circular tubes. Data from 255 experiments from the literature and seven new experiments at PDVSA Intevep for fluids with viscosities ranging from 1 mPa s up to 3900 mPa s were assembled on spread sheets and processed in log–log plots of the normalized rise velocity, $\hbox{\it Fr} \,{=}\,U/(gD)^{1/2}$ Froude velocity vs. buoyancy Reynolds number, $R\,{=}\,(D^{3}g (\rho_{l}-\rho_{g}) \rho_{l})^{1/2}/\mu $ for fixed ranges of the Eötvös number, $\hbox{\it Eo}\,{=}\,g\rho_{l}D^{2}/\sigma $ where $D$ is the pipe diameter, $\rho_{l}$, $\rho_{g}$ and $\sigma$ are densities and surface tension. The plots give rise to power laws in $Eo$; the composition of these separate power laws emerge as bi-power laws for two separate flow regions for large and small buoyancy Reynolds. For large $R$ ($>200$) we find \[\hbox{\it Fr} = {0.34}/(1+3805/\hbox{\it Eo}^{3.06})^{0.58}.\] For small $R$ ($<10$) we find \[ \hbox{\it Fr} = \frac{9.494\times 10^{-3}}{({1+{6197}/\hbox{\it Eo}^{2.561}})^{0.5793}}R^{1.026}.\] The flat region for high buoyancy Reynolds number and sloped region for low buoyancy Reynolds number is separated by a transition region ($10\,{<}\,R\,{<}\, 200$) which we describe by fitting the data to a logistic dose curve. Repeated application of logistic dose curves leads to a composition of rational fractions of rational fractions of power laws. This leads to the following universal correlation: \[ \hbox{\it Fr} = L[{R;A,B,C,G}] \equiv \frac{A}{({1+({{R}/{B}})^C})^G} \] where \[ A = L[\hbox{\it Eo};a,b,c,d],\quad B = L[\hbox{\it Eo};e,f,g,h],\quad C = L[\hbox{\it Eo};i,j,k,l],\quad G = m/C \] and the parameters ($a, b,\ldots,l$) are \begin{eqnarray*} &&\hspace*{-5pt}a \hspace*{-0.8pt}\,{=}\,\hspace*{-0.8pt} 0.34;\quad b\hspace*{-0.8pt} \,{=}\,\hspace*{-0.8pt} 14.793;\quad c\hspace*{-0.8pt} \,{=}\,\hspace*{-0.6pt}{-}3.06;\quad d\hspace*{-0.6pt} \,{=}\, \hspace*{-0.6pt}0.58;\quad e\hspace*{-0.6pt} \,{=}\,\hspace*{-0.6pt} 31.08;\quad f\hspace*{-0.6pt} \,{=}\, \hspace*{-0.6pt}29.868;\quad g\hspace*{-0.6pt}\,{ =}\,\hspace*{-0.6pt}{ -}1.96;\\ &&\hspace*{-5pt}h = -0.49;\quad i = -1.45;\quad j = 24.867;\quad k = -9.93;\quad l = -0.094;\quad m = -1.0295.\end{eqnarray*} The literature on this subject is reviewed together with a summary of previous methods of prediction. New data and photographs collected at PDVSA-Intevep on the rise of Taylor bubbles is presented.

abst: A tubeless siphon was created by sucking a 1% aqueous Polyox 1 solution laden with particles from a beaker into a cylinder by moving a piston. The piston speed and particle concentration were varied. At very high rates of withdrawal, all the liquid could be removed before the siphon broke. In this case, the beaker was completely cleaned without a trace of liquid. The addition of small concentrations of small, nearly neutrally buoyant particles greatly enhanced the pulling power of the liquid, reducing the threshold speed of withdrawal at which the beaker was completely cleaned. At speeds of withdrawal smaller than the threshold not all of the fluid–particle mixture is pulled out of the beaker. The amount pulled out first increases, then decreases as the particle concentration is increased.

abst: Potential flows ${\bm u} = {\bm\nabla} \phi$ are solutions of the Navier–Stokes equations for viscous incompressible fluids for which the vorticity is identically zero. The viscous term $\mu \nabla^2 {\bm u} = \mu{\bm \nabla}\nabla^2\phi$ vanishes, but the viscous contribution to the stress in an incompressible fluid (Stokes 1850) does not vanish in general. Here, we show how the viscosity of a viscous fluid in potential flow away from the boundary layers enters Prandtl's boundary layer equations. Potential flow equations for viscous compressible fluids are derived for sound waves which perturb the Navier–Stokes equations linearized on a state of rest. These linearized equations support a potential flow with the novel features that the Bernoulli equation and the potential as well as the stress depend on the viscosity. The effect of viscosity is to produce decay in time of spatially periodic waves or decay and growth in space of time-periodic waves.

In all cases in which potential flows satisfy the Navier–Stokes equations, which includes all potential flows of incompressible fluids as well as potential flows in the acoustic approximation derived here, it is neither necessary nor useful to put the viscosity to zero.

The lattice Boltzmann equation method: theoretical interpretation, numerics and implications, Int. J. Multiphase Flow, 29(1), 117-169.

abst: During the last ten years the lattice Boltzmann equation (LBE) method has been developed as an alternative numerical approach in computational fluid dynamics (CFD). Originated from the discrete kinetic theory, the LBE method has emerged with the promise to become a superior modeling platform, both computationally and conceptually, compared to the existing arsenal of the continuum-based CFD methods. The LBE method has been applied for simulation of various kinds of fluid flows under different conditions. The number of papers on the LBE method and its applications continues to grow rapidly, especially in the direction of complex and multiphase media.

The purpose of the present paper is to provide a comprehensive, self-contained and consistent tutorial on the LBE method, aiming to clarify misunderstandings and eliminate some confusion that seems to persist in the LBE-related CFD literature. The focus is placed on the fundamental principles of the LBE approach. An excursion into the history, physical background and details of the theory and numerical implementation is made. Special attention is paid to advantages and limitations of the method, and its perspectives to be a useful framework for description of complex flows and interfacial (and multiphase) phenomena. The computational performance of the LBE method is examined, comparing it to other CFD methods, which directly solve for the transport equations of the macroscopic variables.

Distributed Lagrange multiplier method for particulate flows with collisions, Int. J. Multiphase Flow, 29(3), 495-509.

abst: A modified distributed Lagrange multiplier/fictitious domain method (DLM) that allows particles to undergo collisions is developed for particulate flows. In the earlier versions of the DLM method for Newtonian and viscoelastic liquids the particle surfaces were restricted to be more than one velocity element away from each other. A repulsive body force was applied to the particles when the distance between them was smaller than this critical value. This was necessary for ensuring that conflicting rigid body motion constraints from two different particles are not imposed at the same velocity nodes.

In the modified DLM method the particles are allowed to come arbitrarily close to each other and even slightly overlap each other. When conflicting rigid body motion constraints from two different particles are applicable on a velocity node, the constraint from the particle that is closer to that node is used and the other constraint is dropped. An elastic repulsive force is applied when the particles overlap each other. In our simulations, the particles are allowed to overlap as much as one hundredth of the velocity element size. The modified DLM method is implemented for both Newtonian and viscoelastic liquids.

Our simulations show that when particles are dropped in a channel, and the viscoelastic Mach number (M) is less than one and the elasticity number (E) is greater than one, the particles form a chain parallel to the flow direction. As in experiments, the new method allows particles in the chain to approximately touch each other. The particles dropped in a Newtonian liquid, on the other hand, undergo characteristic drafting, kissing and tumbling. During the touching phase, as in experiments, the two particles touch each other. The modified method thus allows hydrodynamic forces to be fully resolved to within the tolerance of the mesh and thus the extra artificial force in a security zone outside the particle which are used in all other methods are not needed.

A Maxwell memory model for delayed weather response to solar heating, Perspectives and Problems in Nonlinear Science: A Celebratory Volume in Honor of Larry Sirovich, Jerrold E. Marsden, L. Sirovich, Katepalli R. Sreenivasan, eds, Springer-Verlag.

Viscoelastic potential flow analysis of capillary instability, J. Non-Newtonian Fluids, 111, 87-105.

abst: Analysis of the linear theory of capillary instability of threads of Maxwell fluids of diameter D is carried out for the unapproximated normal mode solution and for a solution based on viscoelastic potential flow. The analysis here extends the analysis of viscous potential flow [Int. J. Multiphase Flow 28 (2002) 1459] to viscoelastic fluids of Maxwell type. The analysis is framed in dimensionless variables with a velocity scale based on the natural collapse velocity V=γ/μ (surface tension/liquid viscosity). The collapse is controlled by two dimensionless parameters, a Reynolds number J=VDρ/μ=ργD/μ2=(Oh)2 where Oh is the Ohnesorge number, and a Deborah number Λ1=λ1V/D where λ1 is the relaxation time. The density ratio ρa/ρ and μa/μ are nearly zero and do not have a significant effect on growth rates. The dispersion relation for viscoelastic potential flow is cubic in the growth rate σ and it can be solved explicitly and computed without restrictions on the Deborah number. On the other hand, the iterative procedure used to solve the dispersion relation for fully viscoelastic flow fails to converge at very high Deborah number. The growth rates in both theories increase with Deborah number at each fixed Reynolds number, and all theories collapse to inviscid potential flow (IPF) for any fixed Deborah number as the Reynolds number tends to infinity.

Particle motion in a liquid film rimming the inside of a partially filled rotating cylinder, J. Fluid Mech., 496, 379-163

abst: Both lighter- and hydrophobic heavier-than-liquid particles will float on liquid–air surfaces. Capillary forces cause the particles to cluster in typical situations identified here. This kind of clustering causes particles to segregate into islands and bands of high concentrations in thin liquid films rimming the inside of a slowly rotating cylinder partially filled with liquid. A second regime of particle segregation, driven by secondary motions induced by off-centre gas bubbles in a more rapidly rotating cylinder at higher filling levels, is identified. A third regime of segregation of bidisperse suspensions is found in which two layers of heavier-than-liquid particles that stratify when there is no rotation, segregate into alternate bands of particles when there is rotation.

The dissipation approximation and viscous potential flow. J. Fluid Mech. 505, 365-477.

Modeling foamy oil flow in porous media II: Nonlinear relaxation time model of nucleation, Int. J. Multiphase Flow, 29(9), 1489-1502.

abst: In a previous communication, hereafter called Part I, we presented a model of the flow of foamy oil in porous media in situations in which the bubbles do not coalesce to produce the percolation of free gas so that the gas moves with the oil as it evolves. A central role in that theory is an equation of state, called the solubility isotherm, which describes an equilibrium between the fraction of dispersed gas ε and the pressure below the bubble point pressure. A rate equation governing the return to equilibrium was postulated and it requires a value for the relaxation constant multiplying ε. The theory developed in Part I was applied to experimental data and good agreements were achieved except for sharp transients at early times such as those that occur for sudden drops of pressure at the open end of the closed sand pack. In the present theory we introduce two rates and two relaxation times to describe the dynamics of relaxation of the system to an equilibrium state; one rate for ε and the other for the pressure p as was suggested already in Part I. However, we found that constant relaxation times could not be found to fit all the available data. We interpret this in terms of bubbles nucleating more slowly at initial drawdowns, and more rapidly as gas and vapor is released when the pressure is held below the bubble point. This feature has been more or less successfully addressed by the introduction of two relaxation functions of the gas fraction ε which allows us to describe the low rates of evolution of ε when ε is zero or close to it. The relaxation functions were fit to one rate of depletion in a depletion experiment in which oil is pulled out of a closed sand pack at a constant rate. With this selection of the relaxation function established, the set of governing PDEs is fixed and may be used to predict the results of other experiments. The prediction of the pressure profiles for other greatly different rates of depletion is satisfactory. Moreover, the experimental results processed in Part I, are improved by the new theory with the same fitting.

Direct simulation of the motion of settling ellipsoids in Newtonian fluid, Proceedings of 14th International Conf. on Domain Decomposition Methods, Mexico (Janauary).

Modeling Foamy Oil Flow in Porous Media, Int. J. Multiphase Flow, 28(10), 1659-1686.

abst: Certain heavy oils which foam under severe depressurization give rise to increased recovery factor and an increased rate of production under solution gas drive. These oils not only stabilize foam, but also stabilize dispersion of gas bubbles at lower volume ratios. The way this phenomenon is related to the chemistry of the oil and its viscosity is presently not understood. We present here a mathematical model of reservoir flow of foamy oil which depends only on the velocity through Darcy’s law, the pressure and the dispersed gas fraction. The theory governs only in situations in which the bubbles do not coalesce to produce the percolation of free gas. In this theory the bubbles move with the oil as they evolve. The main empirical content of the theory enters through the derivation of solubility isotherms which can be obtained from PVT data; modeling of nucleation, coalescence, bubble drag laws and transfer functions are avoided. The local pressure difference and dispersed gas fraction are in equilibrium on the solubility isotherm. In a pressure drawdown the time taken for the system to return to equilibrium is described by a rate law characterized by an empirical relaxation time (rate constant). The resulting systems of equations can be reduced to a coupled pair of non-linear PDEs for the dispersed gas fraction and pressure difference, which can further be reduced in the equilibrium case to a second order evolution equation for the pressure difference. This system of equations can also be derived from usual theory of two-phase flow in a porous media based on relative permeability under the assumption that the bubbles and oil move in lock step. We propose a reformulation of the conventional theory in which the concept relative permeability of the porous media is replaced with the more familiar concept of an effective phase viscosity. The equations of our relaxation theory are solved numerically, and the mixture viscosity function and relaxation time are selected to match the sandpack experiments.

Power law correlations for sediment transport in pressure driven channel flows, Int. J. Multiphase Flow, 28(8), 1269-1292.

abst: Lift forces acting on particles play a central role in many cases, such as sediment transport, proppant transport in fractured reservoirs, removal of drill cuttings in horizontal drill holes and cleaning of particles from surfaces. We study the problem of lift using 2D direct numerical simulations and experimental data. The lift-off of single particles and many particles in horizontal flows follow laws of similarity, power laws, which may be obtained by plotting simulation data on log–log plots. Data from slot experiments for fractured reservoirs is processed (for the first time) on log–log plots. Power laws with a parameter dependent power emerge as in the case of Richardson–Zaki correlations for bed expansion by drag.

abst: The lift force on a circular particle in plane Poiseuille flow perpendicular to gravity is studied by direct numerical simulation. The angular slip velocity Ωs=Ωp+½γ[dot above], where −½γ[dot above] is the angular velocity of the fluid at a point where the shear rate is γ[dot above] and Ωp is the angular velocity of the particle, is always positive at an equilibrium position at which the hydrodynamic lift balances the buoyant weight. The particle migrates to its equilibrium position and adjusts Ωp so that Ωs > 0 is nearly zero because Ωp [approximate] −1/2γ[dot above] No matter where the particle is placed, it drifts to an equilibrium position with a unique, slightly positive equilibrium angular slip velocity. The angular slip velocity discrepancy defined as the difference between the angular slip velocity of a migrating particle and the angular slip velocity at its equilibrium position is positive below the position of equilibrium and negative above it. This discrepancy is the quantity that changes sign above and below the equilibrium position for neutrally buoyant particles, and also above and below the lower equilibrium position for heavy particles. The existence and properties of unstable positions of equilibrium due to newly identified turning-point transitions and those near the centreline are discussed.

The long particle model of Choi & Joseph (2001) that gives rise to an explicit formula for the particle velocity and the velocity profile across the channel through the centreline of the particle is modified to include the effect of the rotation of the particle. In view of the simplicity of the model, the explicit formula for Up and the velocity profile are in surprisingly good agreement with simulation values. The value of the Poiseuille flow velocity at the point at the particle's centre when the particle is absent is always larger than the particle velocity; the slip velocity is positive at steady flow.

Orientation of symmetric bodies falling in a second-order liquid at nonzero Reynolds number, Math. Models Methods Appl. Sci., 12(11), 1653-1690.

abst: We study the steady translational fall of a homogeneous body of revolution around an axis a, with fore-and-aft symmetry, in a second-order liquid at nonzero Reynolds (Re) and Weissenberg (We) numbers. We show that, at first order in these parameters, only two orientations are allowed, namely, those with a either parallel or perpendicular to the direction of the gravity g. In both cases the translational velocity is parallel to g. The stability of the orientations can be described in terms of a critical value E[SUBc] for the elasticity number E = We/Re, where E[SUBc] depends only on the geometric properties of the body, such as size or shape, and on the quantity (ψ[SUBl] + ψ[SUB2])/ψ[SUB1], where ψ[SUBl] and ψ[SUB2] are the first and second normal stress coefficients. These results are then applied to the case when the body is a prolate spheroid. Our analysis shows, in particular, that there is no tilt-angle phenomenon at first order in Re and We.

Normal stresses on the surface of a rigid body in an Oldroyd-B fluid. J. Fluid Engrg-ASME, 28(3), 409-425.

F. Viana, R. Pardo, R. Yánez, J. L. Trallero, D.D. Joseph 2003.
Universal Correlation for the Rise Velocity of Long Gas Bubbles in Round Pipes, J. Fluid Mech., 494, 379-398.

abst: We collected all of the published data we could find on the rise velocity of Taylor bubbles in stagnant fluids. Data from 255 experiments from the literature and 7 new experiments collected at PDVSA Intevep for fluids with viscosities ranging from 1 mPas up to 3900 mPas were assembled on spread sheets and processed in log-log plots of the normalized rise velocity, Fr =U/(gD)^1/2 Froude velocity vs. Reynolds number, R = (D³g (rho_l - rho_g) rho_l)^1/2/mu for fixed ranges of the Eötvös number, Eö = g rho_l D²/sigma where D is the pipe diameter, rho_l , rho_g and sigma are densities and surface tension. The plots give rise to power laws in Eö; the composition of these separate power laws emerge as bi-power laws for two separate flow regions for large and small Reynolds.

abst: In a previous communication (Jospeh, Kamp and Bai 2002, hereafter called Part I) we presented a model of the flow of foamy oil in porous media in situations in which the bubbles do not coalesce to produce the percolation of free gas so that the gas moves with the oil as it evolves. A central role in that theory is an equation of state, called the solubility isotherm,

J. Wang, D.D. Joseph, N.A. Patankar, M. Conway and B. Barree, 2002.
Bi-power law correlations for sedimentation transport in pressure driven channel flows,
Int. J. Multiphase Flow,,29(3), 475-494.

abst: New data from slot experiments for fractured reservoir were collected ... Those correlations can be used as predictive tools in the fracturing industry but they are in implicit form. In this paper we find correlations for bed load transport of slurries as a composition of bi-power laws in the proppant and fluid Reynolds number with exponents and prefactors expressed as logarithmic functions of dimensionless sedimentation numbers...

T. Ko, H. G. Choi, R. Bai and D. D. Joseph, 2002.
Finite element method simulation of turbulent wavy core-annular flows using a k-w turbulence model method,
Int. J. Multiphase Flow, 28(7), 1205-1222.

abst: A numerical simulation of wavy core flow was carried out by Bai, Kelkar and Joseph. (1996). ... In our present simulation, the SST (shear stress transport) turbulence model is used to solve the turbulent kinetic energy and dissipation rate equations and a splitting method is used to solve Navier-Stokes equations for the wave shape, pressure gradient and the profiles of velocity and pressure in turbulent wavy core flows.

T. Funada and D.D. Joseph, 2002.
Viscous Potential Flow Analysis of Capillary Instability .
Int. J. Multiphase Flow, 28(9), 1459-1478.

abst: Capillary instability of a viscous fluid cylinder of diameter D surrounded by another liquid is determined by a Reynolds number J=V D rho_l/mu_l, a viscosity ratio m=mu_a/mu_l and a density ratio l=rho_a/rho_l. Here V=gamma/mu_l is the capillary collapse velocity based on the more viscous liquid...

C. Mata, E. Pereyra, J.L. Trallero, D.D. Joseph, 2002.
Stability of stratified gas-liquid flows
Int. J. Multiphase Flow, 28(8), 1249-1268.

abst: We have computed stability limits for Kelvin Helmholtz instability of superposed gas-liquid flow, comparing theories of Taitel and Dukler (1976), Lin and Hanratty (1986), Barnea and Taitel (1993) and Funada and Joseph (2001). The theories are compared with literature data on air-water flow and with new data from a 0.0508 m I.D. flow loop at PDSVA-Intevep, using a 0.480 Pa.s oil and air.

T.W. Pan, D.D. Joseph, R. Bai, R. Glowinski, V. Sarin, 2002.
Fluidization of 1204 spheres: simulation and experiment,
J. Fluid Mech., 451, 169-191.

abst:

In this paper we study the fluidization of 1204 spheres at Reynolds numbers in the thousands using the method of distributed Lagrange multipliers. The results of the simulation are compared with a real experiment.

D.D. Joseph, A.M. Kamp, R. Bai, 2002.
Modeling Foamy Oil Flow in Porous Media,
Int. J. Multiphase Flow , 28(10), 1659-1686.

D.D. Joseph, K.R. Sreenivasan, 1995.
A Maxwell memory model for delayed weather response to solar heating,
Perspectives and Problems in Nonlinear Science: A Celebratory Volume in Honor of Larry Sirovich, Jerrold E. Marsden, L.Sirovich, Katepalli R. Sreenivasan, eds, Springer-Verlag,.

abst: A linear Maxwell-type viscoelastic model, relating seasonal variations of temperature at any given place on the Earth to variations in the length of the day, is proposed. Comparison with observations shows excellent agreement for mid-latitudes, and the

D.D. Joseph, A.M. Kamp, R. Bai, 2002.
Foamy Oil Flow in Porous Media,
IMA Volumes in Mathematics and its Applications, Volume 131: Resource Recovery, Confinement, and Remediation of Environmental Hazards, J. Chadam, A. Cunningham, R.E. Ewing, P. Ortoleva, M.F. Wheeler, eds. Springer-Verlag, 81-113.

D.D. Joseph, G.S. Beavers, T. Funada, 2002.
Rayleigh-Taylor instability of viscoelastic drops at high Weber numbers,
J. Fluid Mech., 453, 109-132.

abst: Movies of the breakup of viscous and viscoelastic drops in the high speed airstream behind a shock wave in a shock tube have been reported by Joseph, Belanger and Beavers 1999. A Rayleigh-Taylor stability analysis for the initial breakup of a drop of Newtonian liquid was presented in that paper. The movies, which may be viewed at http://www.aem.umn.edu/research/Aerodynamic_Breakup, show that for the conditions under which the experiments were carried out the drops were subjected to initial accelerations of orders 10⁴ to 10⁵ times the acceleration of gravity.

R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, J. Periaux, 2001.
A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow,
J. Comput. Phys., 169, 363-426.

abst:

In this article we discuss a methodology allowing the direct numerical simulation of incompressible viscous fluid flow past moving rigid bodies. The simulation methods rest essentially on the combination of: 1) Lagrange multiplier based FDM 2) finite element approximations 3) Time discretizations

T.W. Pan, D.D. Joseph, R. Glowinski, 2001.
Modeling Rayleigh-Taylor instability of a sedimenting suspension of several thousand circular particles in direct numerical simulation,
J. Fluid Mech., 434, 23-37.

abst: In this paper we study the sedimentation of several thousand circular particles in 2D using the method of distributed Lagrange multipliers for solid-liquid flow. The simulation gives rise to fingering which resembles Rayleigh-Taylor instabilities.

| Full abstract |

T. Funada, D.D. Joseph, 2001.
Viscous potential flow analysis of Kelvin-Helmholtz instability in a channel,
J. Fluid Mech., 445, 263-283.

abst: We study the stability of stratified gas-liquid flow in a horizontal rectangular channel using viscous potential flow.The analysis leads to an explicit dispersion relation in which the effects of surface tension and viscosity on the normal stress are not neglected but the effect of shear stresses are neglected. Formulas for the growth rates, wave speeds and neutral stability curve are given in general and applied to experiments in air-water flows.

abst:

In direct simulation the fluid motion is resolved numerically and the forces which move the particles are computed rather than modeled. This procedure opens new windows for understanding and modeling. Numerical methods are discussed based on body fitted moving unstructured grids and another on a fixed grid in which the portions of the fluid occupied by solids are forced to move as a rigid body by a distribution of Lagrange multipliers. Animation of the fluidization of 1204 spheres in 3D will be compared with experiments and the concept of fluidization of slurries in conduits by lift rather than drag will be framed in animation by direct simulation. Correlation for lift-off of single particles and the bed height of slurries fluidized by lift are obtained by processing data from numerical experiments.

N.A. Patankar, D.D. Joseph, 2001.
Lagrangian numerical simulation of particulate flows,
Int. J. Multiphase Flow, 27(10), 1685-1706.

abst:

The Lagrangian numerical simulation (LNS) scheme presented in this paper is motivated by the multiphase particle-in-cell (MP-PIC). In this numerical scheme we solve the fluid phase continuity and momentum equations on an Eulerian grid. The particle motion is governed by Newton's law thus following the Lagrangian approach. Momentum exchange from the particle to fluid is modeled in the fluid phase momentum equation. Forces acting on the particle include drag from the fluid, body force and force due to interparticle stress.

N.A. Patankar, D.D. Joseph, 2001.
Modeling and numerical simulation of particulate flows by the Eulerian-Lagrangian approach,
Int. J. Multiphase Flow, 27(10), 1659-1684.

abst:

In this paper we present an Eulerian-Lagrangian numerical simulation (LNS) scheme for particulate flows. The overall algorithm in the present approach is a variation of the scheme presented earlier by N. Patankar and Joseph (1999). In this numerical scheme we solve the fluid phase continuity and momentum equations on an Eulerian grid. The particle motion is governed by Newton's law thus following the Lagrangian approach. | Full Abstract |

T. Ko, N.A. Patankar, D.D. Joseph, 2001.
Lift-off of a single particle in an Oldroyd-B fluid,
Int. J. Multiphase Flow, Submitted.

abst:

In this note we study the lift force on a circular particle near a wall in a plane Poiseuille flow of an Oldroyd-B fluid. Two-dimensional numerical simulations are performed.

N.A. Patankar, T. Ko, H.G. Choi, D.D. Joseph, 2001.
A correlation for the lift-off of many particles in plane Poiseuille flows of Newtonian fluids,
J. Fluid Mech., 445, 55-76.

abst:

Choi & Joseph (2000) reported a two-dimensional numerical investigation... We perform similar simulations. Particles heavier than the fluid are initially placed in a closely packed ordered configuration at the bottom of a periodic channel.

T.W. Pan, D.D. Joseph, R. Bai, R. Glowinski, V. Sarin, 2001.
Fluidization of 1204 spheres: simulation and experiment,
J. Fluid Mech., 451, 169-191.

abst: In this paper we study the fluidization of 1204 spheres at Reynolds numbers in the thousands using the method of distributed Lagrange multipliers. The results of the simulation are compared with a real experiment.

H.G. Choi, D.D. Joseph, 2001.
Fluidization by lift of 300 circular particles in plane Poiseuille flow by direct numerical simulation,
J. Fluid Mech., 438, 101-128.

abst: We study the transport of a slurry of heavier than liquid circular particles in a plane pressure driven flow in a direct simulation. The flow is calculated in a periodic domain containing 300 circular particles. The study leads to the concept of fluidization by lift in which all the particles are suspended by lift forces against gravity perpendicular to the flow. The study is framed as an initial value problem in which a closely packed cubic array of particles resting on the bottom of the channel are lifted into suspension. All the details of the flow are resolved numerically without model assumptions. | Full Abstract |

D.D. Joseph, D. Ocando, 2002.
Slip velocity and lift,
J. Fluid Mech., 454, 263-286.

abst:

The lift force on a circular particle in plane Poiseuille flow perpendicular to gravity is studied by direct numerical simulation. The angular slip velocity Omega_s=gamma/2-Omega_p, where gamma/2 is the angular velocity of the fluid at a point where the shear rate is gamma and Omega_p is the angular velocity of the particle, is always positive at an equilibrium position at which the hydrodynamic lift balances the buoyant weight.

N.A. Patankar, P.Y. Huang, T. Ko, D.D. Joseph, 2001.
Lift-off of a single particle in Newtonian and viscoelastic fluids by direct numerical simulation,
J. Fluid Mech., 438, 67-100.

abst:

In this paper we study the lift-off to equilibrium of a single circular particle in Newtonian and viscoelastic fluids by direct numerical simulation. A particle heavier than the fluid is driven forward on the bottom of a channel by a plane Poiseuille flow.

M. Di Lorenzo, H.T.M. Vinagre, D.D. Joseph, 2001.
Adsorption of Intan-100 at the Bitumen/Aqueous Solution Interface Studied by Spinning Drop Tensiometry
Colloids and Surfaces A, Physicochemical and Engineering Aspects, 180(1-2), 121-130.

abst: We present an experimental study on the adsorption behaviour of Intan-100, a non-ionic surfactant, at the bitumen/water interface when the density difference between the two phases is increased by diluting the crude oil with 10% Xylene by weight or using

C. Mata, M.S. Chirinos, M.E. Gurfunkel, T.A. Nunez, D.D. Joseph, 2001.
Pipeline transport of highly concentrated oil in water emulsions,
Soc. Pet. Eng., Annual Tech. Conf. New Orleans, , -To appear.

D.D. Joseph, 2001.
Power law correlations for lift from direct numerical simulation of solid-liquid flow,
Int. J. Multiphase Fluids, , Accepted.

abst: Lift forces acting on a fluidized particle plays a central role in many important applications, such as the removal of drill cuttings in horizontal drill holes, sand transport in fractured reservoirs, sediment transport and cleaning of particles from surfaces. The problem of lift is studied using direct numerical simulations. Lift formulas which respect the fact that the lift must change sign on either side of the "Segré-Silberberg" radius are discussed. An accurate analytical expression for the slip velocity of circular particles in Poiseuille flow is derived. We show that the lift-off of single particles and many particles in horizontal flows follow laws of similarity, power laws, which may be obtained by plotting simulation data in 2D on log-log plots. Data from slot experiments on bed erosion for fractured reservoirs is processed (for the first time) in log-log plots. Power laws with a parameter dependent power emerge as in the case of Richardson-Zaki correlations for bed expansion. •

D.D. Joseph, 2001.
Lift correlations from direct numerical simulation of solid-liquid flow,
Proc. of Caribbean Congress of Fluid Mechanics (LACAFLUM 2001).

abst: Lift forces acting on a fluidized particle play a central role in many important applications, such as the removal of drill cuttings in horizontal drill holes, sand transport in fractured reservoirs, sediment transport and cleaning of particles from surfaces. The problem of lift is studied using direct numerical simulations. Lift formulas which respect the fact that the lift must change sign on either side of the "Segré-Silberberg" radius are discussed. An accurate analytical expression for the slip velocity of circular particles in Poiseuille flow is derived. We show that the lift-off of single particles and many particles in horizontal flows follow laws of similarity, power laws, which may be obtained by plotting simulation data on log-log plots.

N.A. Patankar, D.D. Joseph, J. Wang, R.D. Barree, M. Conway, M. Asadi, 2002.
Power law correlations for sediment transport in pressure driven channel flows,
Int. J. Multiphase Flow, 28(8), 1269-1292.

abst:

Lift forces acting on particles play a central role in many cases, such as sediment transport, proppant transport in fractured reservoirs, removal of drill cuttings in horizontal drill holes and cleaning of particles from surfaces. We study the problem of lift using 2D direct numerical simulations and experimental data. The lift-off of single particles and many particles in horizontal flows follow laws of similarity, power laws, which may be obtained by plotting simulation data on log-log plots. Data from slot experiments for fractured reservoirs is processed (for the first time) in log-log plots. Power laws with a parameter dependent power emerge as in the case of Richardson-Zaki correlations for bed expansion by drag.

D.D. Joseph, G.S. Beavers, T. Funada. 2002.
Rayleigh-Taylor Instability of Viscoelastic Drops at High Weber Numbers,
J. Fluid Mech., 453, 109-132.

abst: Movies of the breakup of viscous and viscoelastic drops in the high speed airstream behind a shock wave in a shock tube have been reported by Joseph, Belanger and Beavers [1999]... Here we construct a Rayleigh-Taylor stability analysis for an Oldroyd-B fluid using measured data for acceleration, density, viscosity and relaxation time lambda1. The most unstable wave is a sensitive function of the retardation time lambda2 which fits experiments when ...

R.R. Nourgaliev, T.G. Theofanous, D.D. Joseph, 2003.
The lattice Boltzmann equation method: theoretical interpretation, numerics and implications,
Int. J. Multiphase Flow, , 29(1). 117-169.

abst: The Lattice Boltzmann Equation (LBE) method is reviewed and analyzed. The focus is on the fundamental principles of the approach; its `pros' and `cons' in comparison to other methods of the computational uid dynamics (CFD); and its perspectives as a competitive alternative computational approach for uid dynamics. An excursion into the history, physical background and details of the theory and numerical implementation is made, with special attention paid to the method's advantages, limitations and perspectives to be a useful framework to incorporate molecular interactions for description of complex interfacial phenomena; effiency and simplicity for modeling of hydrodynamics, comparing it to the methods, which directly solve for transport equations of macroscopic variables (\traditional CFD").

G.P. Galdi, M. Pokorny, A. Vaidya, D.D. Joseph, J. Feng, 2001.
Orientation of symmetric bodies falling in a second-order liquid at nonzero Reynolds number,
J. Non-Newtonian Fluid Mech., 12(11), 1653-1690.

abst: We study the steady translational fall of a homogeneous body of revolution around an axis a, with fore-and-aft symmery, in a second-order liquid at nonzero Reynolds (Re) and Weissenberg (We) numbers. We show that, at first order in these parameters, only

P. Singh, T.I. Hesla, D.D. Joseph, 2001.
A modified distributed Lagrange multiplier/fictitious domain method for particulate flows with collisions,
Int. J. Multiphase Flow, , submitted.

D.D. Joseph, A. Kamp, R. Bai, 2001.
Modeling Foamy Oil Flow in Porous Media,
Int. J. Multiphase Flow, , In preparation.

A. Pereira, G. McGrath, D.D. Joseph, 2001.
Flow and stress induced cavitation in a journal bearing with axial throughput,
J. Tribology, 123, 742-754.

abst: The problem of predicting flow between rotating eccentric cylinders with axial throughput is studied. The system models a device used to test the stability of emulsions against changes in drop size distribution. The analysis looks for the major variation

P. Singh, T.I. Hesla, D.D. Joseph, 2001.
Distributed Lagrange Multiplier Method for Particulate Flows with Collisions,
Int. J. Multiphase Flow,, submitted.

abst: A modified distributed Lagrange multiplier/fictitious domain method (DLM) that allows particles to undergo collisions is developed for particulate flows ... In the modified DLM method the particles are allowed to come arbitrarily close to each other and even slightly overlap each other.

R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, J. Periaux, 2000.
A distributed Lagrange multiplier/fictitious domain method for the simulation of flows around moving rigid bodies: Application to particulate flow,
Comput. Methods Appl. Mech. Engrg., 184(2-4), 241-267.

abst:

In this article we discuss the application of a Lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modeled by the Navier-Stokes equations around moving rigid bodies; the rigid body motion is due...

R. Bai, D.D. Joseph, 2000.
Steady flow and interfacial shapes of a highly viscous dispersed phase,
Int. J. Multiphase Flow, 26, 1469-1491.

abst: A perturbation theory for the steady flow of immiscible liquids is developed when the dispersed phase is much more viscous than the continuous phase, as is the case in emulsions of highly viscous bitumen in water and in water lubricated pipelines of heavy

P.Y. Huang, D.D. Joseph, 2000.
Effects of shear thinning on migration of neutrally buoyant particles in pressure driven flow of Newtonian and viscoelastic fluids,
J. Non-Newtonian Fluid Mech., 90, 159-185.

abst:

The pattern of cross streaming migration of neutrally buoyant particles in a pressure driven flow depends strongly on the properties of the suspending fluid. These migration effects have been studied by direct numerical simulation in planar flow.

N.A. Patankar, P. Singh, D.D. Joseph, R. Glowinski, T.-W. Pan, 2000.
A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows,
Int. J. Multiphase Flow, 26(9), 1509-1524.

abst:

A Lagrange-multiplier-based fictitious-domain method (DLM) for the direct numerical simulation of rigid particulate flows in a Newtonian fluid was presented previously. An important feature of this finite element based method is that the flow in the particle domain is constrained to be a rigid body motion by using a well-chosen field of Lagrange multipliers. The constraint of rigid body motion is represented by u=U+ omega × r; u being the velocity of the fluid at a point in the particle domain;

C. Verdier, H.T.M. Vinagre, M. Piau, D.D. Joseph, 2000.
High temperature interfacial tension measurements of PA6/PP interfaces compatibilized with copolymers using a spinning drop tensiometer,
Polymer, 41(17), 6683-6689.

abst: Interfacial tension measurements of polyamide/polypropylene (PA6/PP) interfaces are reported at high temperature, using a spinning drop tensiometer, especially adopted to the study of the effects of copolymers. Copolymers in different amounts are included

P. Singh, D.D. Jospeh, 2000.
Sedimentation of a sphere near a wall in an Oldroyd-B fluid,
J. Non-Newtonian Fluid Mech., 94(2-3), 179-203.

abst:

A code based on the distributed Lagrange multiplier/fictitious domain method (DLM) is used to study the motion of a sphere sedimenting in a viscoelastic liquid near a vertical wall. The viscoelastic liquid is assumed to be shear thinning and modeled by a shear-thinning Oldroyd-B model. Our simulations show that when the Deborah number based on the sphere velocity is O(1) and its initial position is sufficiently close to the wall, it moves towards the wall.

P. Singh, D.D. Joseph, T.I. Hesla, R. Glowinski, T.W. Pan, 2000.
A distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows,
J. Non-Newtonian Fluid Mech., 91, 165-188.

abst:

A distributed Lagrange multiplier/fictitious domain method (DLM) is developed for simulating the motion of rigid particles suspended in the Oldroyd-B fluid. This method is a generalization of the one described in [--IJMF 1998, 25, 755-794] where the motion of particles suspended in a Newtonian fluid was simulated. In our implementation of the DLM method, the fluid-particle system is treated implicitly using a combined weak formulation in which the forces and moments between the particles and fluid cancel. The governing equations for the Oldroyd-B liquid are solved everywhere, including inside the particles.

T. Hall, D.D. Joseph, 2000.
Rotating cylinder drag balance with application to riblets,
Experiments in Fluids, 29(3), 215-227.

abst: Experimental results are reported and discussed for a rotating cylinder drag balance designed to predict drag reduction by surfaces like riblets. The apparatus functions by measuring the torque applied to the inner cylinder by a fluid, such as water, ..

R. Glowinski, T.W. Pan, D.D. Joseph 2000.
Fictitious domain methods for particulate flow in two and three dimensions,
The Mathematics of Finite Elements and Applications X, (MAFELAP 1999) J.R. Whiteman, ed., Elsevier, Amsterdam, , 1-28.

abst:

In this article we discuss a methodology for undertaking the direct numerical simulation of the flow of mixtures of rigid solid particles and incompressible viscous fluids, possibly non-Newtonian. The simulation methods are essentially combinations of (a) Lagrange multiplier based fictitious domain methods... b) Finite element approximations of the Navier-Stokes equations... c) Time discretizations by operator splitting schemes...

D.D. Joseph, R. Bai, 1999.
Interfacial shapes in the steady flow of a highly viscous dispersed phase,
Fluid Dynamics of Interfaces, Wei Shyy, Ranga Narayanan, Cambridge University Press, UK, , 254-261.

C. Mata, D.D. Joseph, 1999.
Foam control using a fluidized bed of hydrophobic particles,
Int. J. Multiphase Flow, 25, 63-85.

abst: Applications of foams and foaming are found in many industries like the flotation of minerals, enhanced oil recovery, drilling in oil reservoirs, insulation, construction and refining processes such as Vacuum distillation and Delay-Coker reactors. However, foaming and defoaming are not yet understood. Foams trap gas and are not wanted in many applications... Hydrophobic particles appear to break, and not only to suppress, foam; and they may have a greater application.

D.D. Joseph, R. Bai, C. Mata, K. Sury, C. Grant, 1999.
Self-lubricated transport of bitumen froth,
J. Fluid Mech., 386, 127-148.

abst: Bitumen froth is produced from the oil sands of Athabasca using the Clark's Hot Water Extraction process. When transported in a pipeline, water present in the froth is released in regions of high shear; namely, at the pipe wall. This results in a lubricating layer of water that allows bitumen froth pumping at greatly reduced pressures and hence the potential for savings in pumping energy consumption. Experiments establishing the features of the self lubrication phenomenon were carried out...

R. Glowinski, T.-W. Pan, T.I. Hesla, D.D. Joseph, 1999.
A distributed Lagrange multiplier/fictitious domain method for particulate flows,
Int. J. Multiphase Flow, 25(5), 755-794.

abst:

A new Lagrange-multiplier based fictitious-domain method is presented for the direct numerical simulation of viscous incompressible flow with suspended solid particles. The method uses a finite- element discretization in space and an operator-splitting technique for discretization in time. The linearly constrained quadratic minimization problems which arise from this splitting are solved using conjugate-gradient algorithms.

H.H. Hu, D.D. Joseph, 1999.
Lift on a sphere near a plane wall in a second-order fluid,
J. Non-Newtonian Fluid Mech., 88, 173-184.

abst: In this paper, we examine the lift on a sphere moving very close to an infinite plane wall in a shear flow of a second-order fluid. The sphere is allowed to both translate and rotate along the plane. We focus on the limit when the sphere touches the wall.

D.D. Joseph, J. Belanger, G.S. Beavers, 1999.
Breakup of a liquid drop suddenly exposed to a high-speed airstream, *

Int. J. Multiphase Flow, 25, 1263-1303.

abst: The breakup of viscous and viscoelastic drops in the high speed airstream behind a shock wave in a shock tube was photographed with a rotating drum camera giving one photograph every 5 us. From these photographs we created movies of the fragmentation...

R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, J. Periaux, 1999.
A distributed Lagrange multiplier/fictitious domain method for flows around moving rigid bodies: application to particulate flow,
Int. J. Numer. Meth. Fluids, 30, 1043-1066.

abst:

This article discusses the application of a Lagrange multiplier-based fictitious domain method to the numerical simulation of incompressible viscous flow modeled by the Navier-Stokes equations around moving rigid bodies; the rigid body motions are due...

R. Glowinski, T.-W. Pan, T.I. Hesla, D.D. Joseph, J. Periaux, 1998.
A fictitious domain method with distributed Lagrange multipliers for the numerical simulation of particulate flow,
Contemporary Mathematics, 218, 121-137.
Also published in Domain Decomposition Methods 10, J. Mandel, C. Farhat, and X.-C. Cai eds., AMS, Providence, RI, 121-137 (1998).

abst:

The main goal of this article, which generalizes [Glowinski et al 1997] considerably, is to discuss the numerical simulation of particulate flow for mixtures of incompressible viscous fluids and rigid particles. Such flow occurs in liquid/solid fluidized

G.A. Nunez, H.J. Rivas, D.D. Joseph, 1998.
Drive to produce heavy crude prompts variety of transportation methods,
Oil & Gas Journal, , 59-68.

abst: Increasing oil demand has been driving development of the world's large resources of heavy oil and bitumen, more than 70% of which are in Canada and Venezuela. Moving these heavy crudes and bitumens to market requires alternative pipeline transportation

J. Guitian, D.D. Joseph, 1998.
How bubbly mixtures foam and foam control using a fluidized bed,
Int. J. Multiphase Flow, 24(1), 1-16.

abst: In hydrocracking and other foaming reactors, the foam rises to the top because it has a higher gas fraction than the bubbly mixture from which it comes. The high gas hold-up in foams is undesirable in chemical reactors because it strongly decreases ...

P.Y. Huang, H.H. Hu, D.D. Joseph, 1998.
Direct simulation of the sedimentation of elliptic particles in Oldroyd-B fluids,
J. Fluid Mech., 362, 297-325.

abst: Cross-stream migration and stable orientations of elliptic particles falling in an Oldroyd-B fluid in a channel are studied. We show that the normal component of the extra stress on a rigid body vanishes; lateral forces and torques are determined by the pressure. Inertia turns the longside of the ellipse across the stream and elasticity turns it along the stream; tilted off-center falling is unstable.

abst: The problem of the inception of cavitation is formulated in terms of a comparison of the breaking strength or cavitation threshold at each point of a liquid sample with the principal stresses there. A criterion of maximum tension is proposed which unifies the theory of cavitation...

M. Cloitre, T. Hall, C. Mata, D.D. Joseph, 1998.
Delayed-die swell and sedimentation of elongated particles in wormlike micellar solutions,
J. Non-Newtonian Fluid Mech., 79, 157-171.

abst: It has been recently proposed that the combined action of inertia and non-linear viscoelasticity may be the origin of very peculiar behaviors with dramatic changes of flow type. Two examples are the problem of delayed die swell and the orientation of elon

T.W. Pan, R. Glowinski, T.I. Hesla, D.D. Joseph, J. Periaux, 1998.
Numerical simulation of the Rayleigh-Taylor instability for particulate flow,
Proceedings of the 10th International Conference on Finite Elements in Fluids, M. Hafez, J.C. Heinrich eds., January 5-8, Tucson, 217-222.

abst: In this article we briefly discuss, first, a distributed Lagrange multiplier based, fictitious domain method for the numerical simulation of incompressible viscous flow, modelled by the Navier-Stokes equations, around moving rigid bodies. Then we apply the above method to simulate the sedimentation of densely and regularly packed solid particles, initially at rest and located on top of a lighter fluid. The simulation clearly shows that a Rayleigh-Taylor instability takes place at the beginning of the sedimentation phenomenon.

D.D. Joseph, 1998.
Lubricated transport of viscous materials,
Lecture at IUTAM Symposium on Lubricated Transport of Viscous Materials, Tobago, Jan 7, 1997, H. Ramkissoon, ed., , 1-24.

abst: 1. Phase arrangements. In two phase flows the dynamic response is tied to the way thephases are arranged. Many configuratons are realized in practice; these are often described by flow charts for a) Liquid-liquid b) Gas-liquid c) Liquid-solid. 2. Types of

C. Mata, R. Bai, D.D. Joseph, 1998.
Levitation of core flows,
IUTAM Symposium on Lubricated Transport of Viscous Materials, H. Ramkissoon, ed., , 65-84.

abst: A simple model is proposed for a 2D horizontal core annular flow in which the effect of gravity due to the difference in the densities of the two fluids is the eccentricity of the core. We split the domain through the center of the core; we characterized

D.D. Joseph, R. Bai, K.P. Chen, Y.Y. Renardy, 1997.
Core-annular flows,
Annu. Rev. Fluid Mech., 29, 65-90.

abst: This paper gives an overview of the issues posed by the science and technology of transporting heavy oils in a sheath of lubricating water. It touches on measures of energy efficiency, industrial experience, fouling, stability, models of levitation, ...

D.D. Joseph, 1997.
Technical Forum- Questions in fluid mechanics: Understanding foams and foaming,
J. Fluids Engineering, 119, 497-498.

abst: Foams are common, complex, and not well understood. Most of the common foams are a two-phase medium of gas and liquid with a particular structure consisting of gas pockets trapped in a network of thin liquid films and Plateau borders.

T.Y. Liao, D.D. Joseph, 1997.
Sidewall effects in the smoothing of an initial discontinuity of concentration,
J. Fluid Mech., 342, 37-51.

abst: The velocity field of a binary mixture of incompressible miscible liquids is non-solenoidal when the densities of the two liquids are different. If the mixture density is linear in the volume fraction, as in the case of simple (ideal) mixtures or...glycer

abst: This paper gives a brief overview of the issues posed by the science and technology for transporting heavy oils in a sheath of lubricating water. It touches on measures of energy efficiency, industrial experience, fouling, models of levitation, and future

P.Y. Huang, J. Feng, H.H. Hu, D.D. Joseph, 1997.
Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids,
J. Fluid Mech., 343, 73-94.

abst:

This paper reports the results of direct numerical simulation of the motion of a two-dimensional circular cylinder in Couette flow and in Poiseuille flow of an Oldroyd-B fluid. Both neutrally buoyant and non-neutrally buoyant cylinders are considered.

D.D. Joseph, 1997.
Steep wave fronts on extrudates of polymer melts and solutions: lubrication layers and boundary lubrication,
J. Non-Newtonian Fluid Mech., 70, 187-203.

abst: Steep wave fronts tend to develop in many regimes of lubricated, slipping flows in which waves appear. Problems of slip, spurt, fracture and extrudate distortion can be framed in terms of lubrication theory with paradigms arising from the lubrication ...

R. Glowinski, T. Hesla, D.D. Joseph, T.W. Pan, J. Periaux, 1997.
Distributed Lagrange multiplier methods for particulate flows,
in Computational Science for the 21st Century, M.-O. Bristeau, G. Etgen, W. Fitzgibbon, J.L. Lions, J. Periaux, M.F. Wheeler eds. John Wiley & Sons, Chichester, England, , 270-279.

abst: In this article we discuss the application of a Lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modeled by the Navier-Stokes equations around moving bodies. The solution method combines finite element approximations, time discretization by operator splitting and conjugate gradient algorithms for the solution of the linearly constrained quadratic minimization problems coming from the splitting method. The results of numerical experiments for two sedimenting cylinders in a two-dimensional channel are presented.

M.S. Arney, G.S. Ribeiro, E. Guevara, R. Bai, D.D. Joseph, 1996.
Cement-lined pipes for water lubricated transport of heavy oil,
Int. J. Multiphase Flow, 22(2), 207-221.

abst: This paper presents different strategies for preventing oil from fouling the walls of core-annular flow pipelines and also for recovery from an unexpected pipeline shut-down. The most promising of these strategies is to use cement-lined pipes. Experiments presented here show that hydrated cement-lined pipes are highly oleophobic and therefore resist oil fouling for long term.

D.D. Joseph, 1996.
Flow induced microstructure in Newtonian and viscoelastic fluids,
Proc. of the 5th World Congress of Chemical Engineering, Second Particle Technology Forum, San Diego, July 14-18, 1996 AIChE New York, Keynote presentation (paper 95a), Particle Technology Track 6, 3-16.

abst:

Pair interactions between neighboring particles and turning couples on long bodies formed from touching bodies give rise to flow induced microstructures. In Newtonian fluids, pair interactions in a fluidized suspension lead to dispersions with particles..

J. Feng, D.D. Joseph, P.Y. Huang, 1996.
The motion and interaction of solid particles in viscoelastic liquids,
Rheology and Fluid Mechanics of Nonlinear Materials, 1996 ASME Int. Mechanical Engineering Congress and Exposition, D.A. Siginer, S.G. Advani, eds, 217, 123-133.

abst: In this paper we present numerical and experimental results on the motion and interaction of solid particles in polymeric fluids. The two-dimensional numerical work investigates the viscoelastic effects on the sedimentation of a particle in the presence..

D.D. Joseph, A. Huang, H.H. Hu, 1996.
Non-solenoidal velocity effects and Korteweg stresses in simple mixtures of incompressible liquids,
Physica D, 97, 104-125.

J. Feng, D.D. Joseph, 1996.
The motion of a solid sphere suspended by a Newtonian or viscoelastic jet,
J. Fluid Mech., 315, 367-385.

abst: This paper describes experimental observations of a solid sphere suspended by a vertical or inclined jet. A laminar Newtonian jet is able to suspend a sphere only through viscous entrainment at low Reynolds numbers (Re~10). A turbulent Newtonian jet (Re~10⁴) attracts a sphere that is sufficiently large but rejects smaller ones. The Coanda effect is responsible for steady suspension of solid spheres even in highly slanted jets. .

D.D. Joseph, A. Huang, G.V. Candler, 1996.
Vaporization of a liquid drop suddenly exposed to a high-speed airstream,
J. Fluid Mech., 318, 223-236.

abst: Many studies of fragmentation of liquid drops at supersonic Mach numbers report the appearance of large amounts of mist. Photographs from other studies, which do not mention mist at all, strongly suggest that copious amounts of mist are formed at the earliest stages of fragmentation. In this paper, we present arguments and calculations which indicate that this mist is formed from condensed vapour arising from the flash vaporization of the hot and low-pressure liquid on the leeside of the drop.

R. Bai, K. Kelkar, D.D. Joseph, 1996.
Direct simulation of interfacial waves in a high-viscosity-ratio and axisymmetric core-annular flow,
J. Fluid Mech., 327, 1-34.

abst: A direct numerical simulation of spatially periodic wavy core flows is carried out under the assumption that the densities of the two fluids are identical and that the viscosity of the oil core is so large that it moves as a rigid solid which may nevertheless be deformed by pressure forces in the water.

G.A. Nunez, M. Briceno, C. Mata, H. Rivas, D.D. Joseph, 1996.
Flow characteristics of concentrated emulsions of very viscous oil in water,
J. Rheol., 40(3), 405-423.

abst: This paper advances ideas and presents experiments on the flow characteristics of concentrated emulsions of Venezuelan bitumen in water plus surfactant. These emulsions are studied under a variety of flow conditions, namely between rotating cylinders, ..

J. Feng, P.Y. Huang, D.D. Joseph, 1996.
Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid,
J. Non-Newtonian Fluid Mech., 63, 63-88.

abst:

In this paper we present a two-dimensional numerical study of the viscoelastic effects on the sedimentation of particles in the presence of solid walls or another particle. The Navier-Stokes equations coupled with an Oldroyd-B model are solved using a ...

J. Feng, D.D. Joseph, 1996.
The motion of solid particles suspended in viscoelastic liquids under torsional shear,
J. Fluid Mech., 324, 199-222.

abst: This paper presents an experimental study of the behavior of single particles and suspensions in polymer solutions in a torsional flow. Four issues are investigated in detail: the radial migration of a spherical particle; the rotation and migration of..

D.D. Joseph, A.C. Bannwart, Y.J. Liu, 1996.
Stability of annular flow and slugging,
Int. J. Multiphase Flow, 22(6), 1247-1254.

abst: In this work we propose an effective viscosity criterion for the stabilitization of annular gas-liquid and liquid-particle flows and an inertial mechanism which drives waves into slugs in slugging gas-liquid flows. Annular flow is stable when the fluid..

L. Preziosi, D.D. Joseph, G.S. Beavers, 1996.
Infiltration of initially dry, deformable porous media,
Int. J. Multiphase Flow, 22(6), 1205-1222.

abst: The present paper studies the infiltration of an incompressible liquid in an initially dry (or partially dry), deformable spongeous material made of an incompressible constituent in the slug-flow approximation having in mind the application to some industrial processes involving flow through spongeous materials and, in particular, some composite materials manufacturing processes. The resulting initial-boundary value problem is of Stefan type, with suitable interface conditions and evolution equations describing the position of the interfaces delimiting the saturated region within the porous material. Different models are then suggested in the saturated region, depending on the importance of the inertial terms and on the constitutive equation for the stress. Comparison of the simulation with known experimental results is satisfactory. •

D.D. Joseph, Y.J. Liu, 1996.
Letter to the Editor: Steep wave fronts on extrudates of polymer melts and solutions,
J. Rheol., 40(2), 317-320.

abst: It seems to us that the shape of the extrudate of polymers and polymer melts is very much like the wavy shapes one sees in core-annular flows of heavy oils in water. These flows are lubricated by the water and can be said to give rise to slip.

Extended Summary: the shape of the extrudate of polymers and polymer melts, The shape of the extrudate of polymers and polymer melts is very much like the wavy shapes one sees in core-annular flows of heavy oils in water.

D.D. Joseph, J. Feng, 1996.
A note on the forces that move particles in a second-order fluid,
J. Non-Newtonian Fluid Mech., 64, 299-302.

abst: In this note we show that the normal stresses on a solid body in plane flow of a second-order fluid are compressive and such as to turn long bodies into the stream and to cause circular particles to aggregate and chain.

D.D. Joseph, Y.J. Liu, 1995.
Motion of particles settling in a viscoelastic fluid,
Proc. 2nd International Conference on Multiphase Flow '95 Kyoto, April 3-7, 1995, Kyoto, Japan, , PD1_1-8.

abst: In this paper, we will attempt to extract some principles concerning the flow-induced anistotropy which develops in the settling of particles in Newtonian and viscoelastic fluids. Our point of view is that the local microstructure, which is determined by

D.D. Joseph, R. Bai, T.Y. Liao, A. Huang, H.H. Hu, 1995.
Parallel Pipelining,
J. of Fluids Engineering, 117, 446-449.

abst: The use of water as a libricant to reduce friction in pipelining of heavy crude oil is an old idea which has been use sporadicaly over the past half century (Joeph and Renardy, 1992). The essence of lubrication is that water forms an annulus around oil

J. Feng, D.D. Joseph, R. Glowinski, T.W. Pan, 1995.
A three-dimensional computation of the force and torque on an ellipsiod settling slowly through a viscoelastic fluid,
J. Fluid Mech., 283, 1-16.

abst: The orientation of an ellipsoid falling in a viscoelastic fluid is studied by methods of perturbation theory. For small fall velocity, the fluid's rheology is described by a second-order fluid model. The solution of the problem can be expressed by a dual

P. Singh, D.D. Joseph, 1995.
Dynamics of fluidized suspensions of spheres of finite size,
Int. J. Multiphase Flow, 21(1), 1-26.

abst: We propose a one-dimensional theory of fluidized suspensions in which the fluids and solids momentum equations are decoupled by using a new mean drag law for the particles. Our mean drag law differs from the standard drag laws frequently used in that...

J.J. Nelson, A.E. Alving, D.D. Joseph, 1995.
Boundary layer flow of air over water on a flat plate,
J. Fluid Mech., 284, 159-169.

abst: A non-similar boundary layer theory for air blowing over a water layer on a flat plate is formulated and studied as a two-fluid problem in which the position of the interface is unknown. The problem is considered at large Reynolds number (based on x) ..

A. Huang, D.D. Joseph, 1995.
Stability of eccentric core-annular flow,
J. Fluid Mech., 282, 233-245.

abst: Perfect core-annular flows are two-phase flows, for example of oil and water, with the oil in a perfectly round core of constant radius and the water outside. Eccentric core flows can be perfect, but the centre of the core is displaced off the centre ...

J. Feng, P.Y. Huang, D.D. Joseph, 1995.
Dynamic simulation of the motion of capsules in pipelines,
J. Fluid Mech., 286, 201-227.

abst:

In this paper we report results of two-dimensional simulations fo the motion of elliptic capsules carried by a Poiseuille flow in a channel. The numerical method allows computation of the capsule motion and the fluid flow around the capsule, and accurate

M. Poletto, R. Bai, D.D. Joseph, 1995.
Propagation of voidage waves in a two-dimensional liquid-fluidized bed,
Int. J. Multiphase Flow, 21(2), 223-239.

abst: Digital video recordings were used to obtain voidage distribution in a narrow fluidized bed with a small gap slightly larger than three particle diameters. From these recordings we determined auto-corrections and power spectra in spatial and temporal..

D.D. Joseph, J. Feng, 1995.
The negative wake in a second-order fluid (Short Communication),
J. Non-Newtonian Fluid Mech., 57, 313-320.

abst: To investigate the origin of negative wakes in viscoelastic fluid, we used a perturbation method to calculate the flow induced by a solid sphere falling slowly through a viscoelastic fluid in a vertical column of square cross-section.

D.D. Joseph, 1995.
Cavitation in a flowing liquid,
Physical Review E, 51(3), R1649-1650.

abst: In this paper, I propose that the cavitation threshold in a flowing liquid could be associated with the maximum tension that the fluid can sustain before undergoing cohesive fracture at a certain point. My criterion is not isotropic; I am thinking that a liquid will break if the tension in one direction exceeds a threshold, independent of the value of the other principal stresses. The other thought is that if a liquid breaks, it is a cohesive fracture in which the liquid molecules disassociate into vapor and recondense as mist.

Y.J. Liu, T.Y. Liao, D.D. Joseph 1995.
A two-dimensional cusp at the trailing edge of an air bubble rising in a viscoelastic liquid,
J. Fluid Mech., 304, 321-342.

abst: When an air bubble rises in a viscoelastic fluid there is a critical capillary number for cusping and jump in velocity: when the capillary number is below critical, which is about 1 in our data, there is no cusp at the tail of a (smooth) air bubble.

M. Poletto, D.D. Joseph, 1995.
Effective density and viscosity of a suspension,
J. Rheol., 39(2), 323-343.

abst: This paper presents results of a series of experiments on the settling velocity of spheres in two-component solid-liquid suspensions. Particular emphasis has been given to the effective values of density and viscosity of the mixture which allows us to describe the settling of the spheres in the mixture using appropriate modifications of the equations valid for the settling of spheres in pure fluids.

J. Feng, D.D. Joseph, 1995.
The unsteady motion of solid bodies in creeping flows,
J. Fluid Mech., 303, 83-102.

abst: In treating unsteady particle motions in creeping flows, a quasi-steady approximation is often used, which assumes that the particle's motion is so slow that it is composed of a series of steady states. In each of these states, the fluid is in a steady...

D.D. Joseph, T.Y. Liao, 1994.
Viscous and viscoelastic potential flow,
Trends and Perspectives in Applied Mathematics, Applied Mathematical Sciences, Sirovich, Arnol'd, eds, Springer-Verlag, 100, 1-54. Also in Army HPCRC preprint 93-010.

abst: Potential flows of incompressible fluids admit a pressure (Bernoulli) equation when the divergence of the stress is a gradient as in inviscid fluids, viscous fluids, linear viscoelastic fluids and second-order fluids. We show that the equation balancing drag and acceleration is the same for all these fluids independent of the viscosity or any viscoelastic parameter and that the drag is zero in steady flow. The unsteady drag on bubbles in a viscous (and possibly in a viscoelastic) fluid may be approximated ...

D.D. Joseph, 1994.
Interrogation of numerical simulation for modeling of flow induced microstructure,
ASME FED (Liquid-Solid Flows), 189, 31-40.

abst: This paper summarizes our recent efforts using direct numerical simulations to determine microstructural properties of fluidized suspensions of a few particles. We have been studying the motions of a few particles in a viscous fluid by direct numerical simulation at moderate values of the Reynolds number in the 100's. From these simulations, we find the mechanisms which give rise to lateral migration of particles and turn the broad side of long bodies perpendicular to the stream.

D.D. Joseph, T.Y. Liao, 1994.
Potential flow of viscous and viscoelastic fluids,
J. Fluid Mech., 265, 1-23.

abst: Potential flows of incompressible fluids admit a pressure (Bernoulli) equation when the divergence of the stress is a gradient as in inviscid fluids, viscous fluids, linear viscoelastic fluids and second-order fluids. We show that in potential flow without boundary layers the equation blancing drag and acceleration is the same for all these fluids, independent of the viscosity or any viscoelastic parameter, and that the drag is zero when the flow is steady. But,if the potential flow is viewed as an approximation to the actual flow field, the unsteady drag on bubbles ...

J. Feng, H.H. Hu, D.D. Joseph, 1994.
Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid, Part 1, Sedimentation,
J. Fluid Mech., 261, 95-134.

abst: This paper reports the result of direct simulations of fluid-particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and ellipitical particles in a vertical channel. The fluid motion is computed from ...

D.D. Joseph, Y.J. Liu, M. Poletto, J. 1994.
Aggregation and dispersion of spheres falling in viscoelastic liquids,
J. Non-Newtonian Fluid Mech., 54, 45-86.

abst: This paper focuses on the settling on one sphere near another or near a wall. We find maximum differences between Newtionan and viscoelastic liquids, with repulsion between nearby bodies in the Newtonian case and attraction in the viscoelastic case.

T.Y. Liao, H.H. Hu, D.D. Joseph, 1994.
White-Metzner models for rod climbing in A1,
J. Non-Newtonian Fluid Mech., 51, 111-124.

abst: Measurements of rod climbing in A1 give rise to an apparent linear relation between the height rise h and the angular velocity Omega of the rod. We use a White-Metzner model to fit the data & we find that the height rise on the rod deviates from the quadr

A. Huang, C. Christodoulou, D.D. Joseph, 1994.
Friction factor and holdup studies for lubricated pipelining-- II. Laminar and k-epsilon models of eccentric core flow,
Int. J. Multiphase Flow, 20(3), 481-491.

abst: A model of core-annular flow in which the oil core is a pefect cylinder with generators parallel to the pipe wall, but off-center, is studied in laminar and turbulent flow to asses the effects of eccentricity and the volume flow rate ratio on ...

P.Y. Huang, J. Feng, D.D. Joseph, 1994.
The turning couples on an elliptic particle settling in a vertical channel,
J. Fluid Mech., 271, 1-16.

abst: We do a direct two-dimensional finite-element simulation of the Navier-Stokes equations and compute the forces which turn an ellipse settling in a vertical channel of viscous fluid in a regime in which the ellipse oscillates under the action of a vortex..

G.A. Nunez, G.S. Ribeiro, M.S. Arney, J. Feng, D.D. Joseph, 1994.
Rod climbing and normal stresses in heavy crude oils at low shears,
J. Rheol., 38(5), 1251-1270.

abst: This paper gives the results of a study of the nonlinear viscoelastic behavior of three heavy crude oils from California and Venezuela. A linear combination of normal stress coefficients at zero shear is expressed in terms of the quantity (climbing const

J. Feng, H.H. Hu, D.D. Joseph, 1994.
Direct simulation of initial value problems for the motion of solid bodies in a Netwonian fluid, Part 2, Couette and Poiseuille flows,
J. Fluid Mech., 277, 271-301.

abst: This paper reports the results of a two-dimensional finite element simulation of the motion of a circular particle in a Couette and a Poiseuille flow. The size of the particle and the Reynolds number are large enough to include fully nonlinear inertial..

H.H. Hu, D.D. Joseph, 1994.
Evolution of a liquid drop in a spinning drop tensiometer,
J. Colloid and Interface Sci., 162(2), 331-339.

abst: To obtain desired material properties, a blend of two mostly incompatible polymers is often used. The blend morphology developed during the mixing process of molten polymers is strongly influenced by interfacial tension between the polymers. A spinning drop tensiometer is commonly used to measure the interfacial tension between two polymeric liquids.

D.D. Joseph, T.Y. Liao, H.H. Hu, 1993.
Drag and moment in viscous potential flow,
Eur. J. Mech. B/Fluids, 12(1), 97-106.

abst: We consider solutions of the Navier-Stokes equations in which the velocity is given by the gradient of a potential. We show that the drag on bodies and bubbles is the same in viscous and inviscid potential flow. The lift on two-dimensional bodies is given by the usual Kutta condition but the moment about the origin of the stresses acting on the body is given by M₁+2mu Gamma where mu is the viscosity, Gamma is the circulation and M₁ is the usual moment for an inviscid fluid.

T.I. Hesla, A.Y. Huang, D.D. Joseph, 1993.
A note on the net force and moment on a drop due to surface forces,
J. Colloid Interface Sci., 158(1), 255-257.

abst: It is shown that the net force and moment on a smooth drop or bubble due to surface forces are zero. The net force and moment due to the jump in traction are also zero.

D.D. Joseph, 1993.
Non-solenoidal velocity effects and Korteweg stresses in simple mixtures of incompressible liquids, *
Proc. of the Symposium on Applied Mathematics at the Turn of the Century, Universidad Complutense, Cursos de Verano, Almeria, Spain, July 5-10, 1993, , 1.

abst: (see note below)

A. Huang, D.D. Joseph, 1993.
Stability of liquid-vapor flow down an inclined channel with phase change,
Int. J. Heat Mass Transfer, 36(3), 663-672.

abst: We study the stability of a two-phase flow between heated inclined plates. The temperature of the bottom plate is held below the vaporization temperature and the top plate is hotter than the vaporization temperature. A water film is on the cold wall ...

M.S. Arney, R. Bai, E. Guevara, D.D. Joseph, K. Liu, 1993.
Friction factor and holdup studies for lubricated pipelining - I,
Int. J. Multiphase Flow, 19(6), 1061-1076.

abst: Results from new experiments on the lubricated pipelining of emulsified waxy crude oil and No. 6 fuel oil are presented and compared with other sources of literature. A correlation forumla which estimates the holdup fraction is introduced and evaluated..

Y.J. Liu, D.D. Joseph, 1993.
Sedimentation of particles in polymer solutions,
J. Fluid Mech., 255, 565-595.

abst: In this paper, we present detailed and systematic experimental results on the sedimentation of solid particles in aqueous solutions of polyox and polyacrylamide. The tilt angles of long cylinders falling in these viscoelastic liquids were measured.

D.D. Joseph, Y.J. Liu, 1993.
Orientation of long bodies falling in a viscoelastic liquid,
J. Rheol., Bingham Award Lecture-1993, 37(6), 961-983.

abst: New experiments on the orientation of a cylinder settling in viscoelastic and pseudoplastic fluids are described in an attempt to identify the main mechanisms which control the orientation of the cylinder as it falls.

Y.J. Liu, J. Nelson, J. Feng, D.D. Joseph, 1993.
Anomalous rolling of spheres down an inclined plane,
J. Non-Newtonian Fluid Mech., 50, 305-329.

abst: A sphere in air will roll down a plane which is tilted away from the vertical. The only couple acting about the point of contact between the sphere and the plane is due to the component of the weight of the sphere along the plane, provided that air friction

D.D. Joseph, C. Christodoulou, 1993.
Independent confirmation that delyed die swell is a hyperbolic transition,
J. Non-Newtonian Fluid Mech., 48, 225-235.

abst: We measured shear wave speeds in the same aqueous Xanthan solutions used to study delayed die swell by Allain, Cloitre, Perrot and Quemada 1993. They reported delayed die swell for solutions of 500, 1000, 2000 and 4000 ppm Xanthan in water when the shear

D.D. Joseph, H.H. Hu, 1992.
Non-solenoidal velocity effects and Kortweg stresses in simple mixtures of incompressible liquids,
AHPCRC Report, preprint 91-03,
Also in Chapter 10: Fundamentals of Two-Fluid Dynamics, Springer 1992.

abst: We study some basic problems of fluid dynamics of two incompressible miscible liquids modeled as a simple mixture in which the volume of the mixture does not change on mixing. In general, the expansion Delta=divu in these problems does not vanish. The velocity in such a mixture can be decomposed into a solenoidal and an expansion part. The expansion velocity is induced by diffusion which is proportional to the gradient of the expansion volume fraction in a simple mixture. The expansion can be large at certain times and places.

D.D. Joseph, 1992.
Chapter 10, Finite Size Effects in Fluidized Suspension Experiments,
Particulate Two-Phase Flow, M.C. Roco, ed., NSF and Univ. of Kentucky, , 300-324.

abst: 'Two fluid' equations for fluidized suspensions of solid particles can be rigorously formulated as ensemble averages (Joseph & Lundgren 1990). Even though these equations have a rigorous foundation they are not useful unless the interaction forces are correctly modeled. Modeling, the framing of constitutive hypotheses, is basically a guess about the solutions of the equations of motion. A constitutive hypothesis is when you guess what the solution of a problem of dynamics might be without actually obtaining the solution.

D.D. Joseph, M. Arney, G. Ma, 1992.
Upper and lower bounds for interfacial tension using spinning drop devices,
J. Colloid Interface Sci., 148(1), 291-294.

abst: In this note we show how to use spinning drop devices to determine lower and upper bounds for interfacial tension between immiscible liquids. We like the idea of upper and lower bounds because the equilibrium tension is not a robust function and depends..

N. Baumann, D.D. Joseph, P. Mohr, Y. Renardy, 1992.
Chapter IX. Vortex rings of one fluid in another in free fall,
Physics of Fluids A, 4(3), 567-580.

abst: Experiments in which vortex rings of one immiscible liquid are created in another from drops falling from rest under gravity are presented and interpreted. These rings are associated with circulations generated by viscosity and, unlike classical vortex rings which occur in miscible liquids at high Reynolds numbers, they can exist even at very low Reynolds numbers. Since the rings do not diffuse, they are well-defined. Nonetheless, there are many similarities in the dynamics of formation and flow of miscible and immiscible rings. Parameters are identified which appear to correlate the authors’ observations and photographs of some of the more interesting events are shown.

D.D. Joseph, T.Y.J. Liao, J.C. Saut 1992.
Kelvin-Helmholtz mechanism for side branching in the displacement of light with heavy fluid under gravity,
Eur. J. Mech. B/Fluids, 11(3), 253-264.

abst: The problem of stability of smooth fingering motions which may develop from the Rayleigh-Taylor instability when the initial data is analytic is considered. A second-order ordinary linear differential equation with time-dependent coefficients is derived..

D.D. Joseph, H.H. Hu, 1992.
Chapter 10, Interfacial tension between miscible liquids,
Fundamentals of Two-Fluid Dynamics: Part 1 and 2, DD Joseph and YY Renardy, eds., .

D.D. Joseph, 1992.
The tilt angle transition and potential flow,
Proceedings of the Plenary Lecture at the 1st International Syposium of the Grenoble Mechanics Federation, May 19-21, , .

abst: The natural orientation of a long body is the key to understanding flow induced structures of spherical bodies. The natural orientation of a long body falling in a viscous liquid is broadside-on; the body will always turn its long side perpendicular ...

D.D. Joseph, J. Nelson, H.H. Hu, Y.J. Liu, 1992.
Competition between inertial pressures and normal stresses in the flow induced anisotropy of solid particles,
Theoretical and Applied Rheology, Proc. XI-th Int. Congress on Rheology, Brussels, Belgium, August 17-21, 1992, P. Moldenaers, R. Keunings, eds., , 60-64.

abst: It is well known that a long body settling in a viscous liquid will turn its broadside to the stream. The same long body settling in a viscoelastic liquid will turn its broadside parallel to the stream at small speeds, but heavier long bodies which fall faster again turn broadside. Sedimenting spheres in a fluid filled channel will arrange themselves so that the line of centers between neighboring spheres is across the stream in a viscous liquid and parallel to the stream ...

D.D. Joseph, A. Huang, M. Arney, 1992.
A discussion on the aerodynamic dissemination of simulant released at high altitude,
Proc. 1992 US Army Chemical Research Development & Engineering Center, Scientific Conference on Chemical Defense Research, November 18, 1992, , .

R. Bai, K. Chen, D.D. Joseph, 1992.
Lubricated pipelining: stability of core-annular flow. Part 5, Experiments and comparison with theory,
J. Fluid Mech., 240, 97-132.

abst: Results are given for experiments on water-lubricated pipelining of 6.01 P cylinder oil in a vertical apparatus in up- and downflow in regimes of modest flow rates, less than 3 ft/s. Measured values of the flow rates, holdup ratios, pressure gradients...

A. Huang, D.D. Joseph, 1992.
Instability of the equilibrium of a liquid below its vapour between horizontal heated plates,
J. Fluid Mech., 242, 235-247.

abst: We study the stability of a motionless liquid below its vapour between heated horizontal plates. The temperature of the bottom plate is held below the vaporization temperature and the top plate is hotter than the vaporization temperature. A water film...

K.P. Chen, D.D. Joseph, 1992.
Elastic short wave instability in extrusion flows of viscoelastic liquids,
J. Non-Newtonian Fluid Mech., 42, 189-211.

abst: An analysis of the stability to short waves of the flow of concentric coextruded polymeric liquids modeled by upper convected Maxwell models is presented. The flow can be unstable to short waves under various conditions on the elastic parameter.

H.H. Hu, D.D. Joseph, M.J. Crochet, 1992.
Direct simulation of fluid particle motions,
J. Theoret. Comput. Fluid Dynamics, 3, 285-306.

abst: Continuum models of two-phase flows of solids and liquids use constitutive assumptions to close the equations. A more fundamental approach is a "molecular dynamic" simulation of flowing "big" particles based on reliable macroscopic equations for both...

D.D. Joseph, M.S. Arney, G. Gillberg, H.H. Hu, D. Hultman, C. Verdier, T.M. Vinagre, 1992.
A spinning drop tensioextensometer,
J. Rheology, 36(4), 621-662.

abst: We examine some theoretical and experimental aspects of the measurement of interfacial tension, stress relaxation in elongational flow, and yield stresses in organic liquids, blends of polymer melts, and liquid crystal polymers. ..is based on instrument..

D.D. Joseph, 1992.
Understanding cusped interfaces,
J. Non-Newtonian Fluid Mech., 44, 127-148.

abst: The good progress made on the recently opened problem of two-dimensional cusped interfaces in Newtonian and non-Newtonian fluids is reviewed. Some new results are presented and open problems are discussed.

D.D. Joseph, 1992.
Bernoulli equation and the competition of elastic and inertial pressures in the potential flow of a second-order fluid,
J. Non-Newtonian Fluid Mech., 42, 385-389.

abst: A Bernoulli equation for potential flow of a second order fluid is derived. This equation is used to form an expression for normal extensional stresses at points of stagnation, in which elastic and inertial pressures compete.

H.H. Hu, D.D. Joseph, 1992.
Miscible displacement in a Hele-Shaw cell,
Zfangew Math Phys (ZAMP), 43, 626-644.

abst: We formulated a theory of simple mixtures of incompressible miscible liquids in terms of the mass averaged velocity u and the solenoidal volume averaged velocity W. We derived simplified equations for miscible displacement in a Hele-Shaw cell.

H.H. Hu, D.D. Joseph, A.F. Fortes, 1992.
Experiments and direct simulations of fluid particle motions,
Int. Video J. Engineering Research, 2, 17-24.

abst: This paper and the accompanying video segment show how the motions of sedimenting particles may be simulated by direct computations based on the Navier-Stokes equations and the equations of particle motion. Sedimenting and fluidized particles are confined

P. Galdi, D.D. Joseph, L. Preziosi, S. Rionero, 1991.
Mathematical problems for miscible, incompressible fluids with Korteweg stresses,
Eur. J. Mech. B/Fluids, 10(3), 253-267.

abst: It is shown that the equations governing the motion and diffusion of miscible liquids can be reduced to a form like the Navier-Stokes equations when the equation of state is for the density of a simple mixture. In particular, in this case, W=Cu+D psi ...

A.F. Fortes, D.D. Joseph, 1991.
Wake Architecture in two-dimensional fluidization of spheres. Part 1, Experiments and phenomenogical description,
Proceedings of Joint DOE/NSF workshop on fliow of particulates and fluids, Worcester MA, October 22-24, , 1-12.

abst: The structure of a shear flow past freely suspended spheres at low Reynolds numbers (based on the diameter of the spheres and mean fluid velocity) is visualized employing sheets of hydrogen bubbles illuminated by laser light as well as tungsten halogen...

P. Singh, D.D. Joseph, 1991.
Finite size effects in fluidized beds,
FED, Liquid Solid Flows, M.C. Roco, T. Magasume, eds., 118, 77-86.

abst: We consider a one-dimensional theory of fluidized beds in which the fluids and solids equations are decoupled and the system is closed with a momentum equation for the particles alone. The simplest theory, based on the Foscolo-Gibilaro force law, ..

C. Christodoulou, K.N. Liu, D.D. Joseph, 1991.
Combined effects of riblets and polymers on drag reduction in pipes,
Phys. Fluids A, 3(5), 995-996.

abst: In the present Brief Communication, experiments are reported establishing superposition of drag reduction due to riblets on drag reduction due to polymers, in fully developed turbulent flow of dilute aqueous solutions of polymers (2-50ppm) through 25.4mm

D.D. Joseph, J. Nelson, M. Renardy, Y. Renardy, 1991.
Two-dimensional cusped interfaces,
J. Fluid Mech., 223, 383-409.

abst: Two-dimensional cusped interfaces are line singularities of curvature. We create such cusps by rotating a cylinder half immersed in liquid. A liquid film is dragged out of the reservoir on one side and is plunged in at the other, where it forms a cusp...

K. Chen, D.D. Joseph, 1991.
Lubricated pipelining: stability of core-annular flow. Part 4, Ginzburg-Landau equations,
J. Fluid Mech., 227, 587-615.

abst: Nonlinear stability of core-annular flow near points of the neutral curves at which perfect core-annular flow loses stability is studied using the Ginzburg-Landau equations. Most of the core-annular flows are always unstable. Therefore the set of core-ann

K.P. Chen, D.D. Joseph, 1991.
Long wave and lubrication theories for core-annular flow,
Phys. Fluids A, 3(11), 2672-2679.

abst: Different nonlinear amplitude equations for long waves in core-annular flow are compared. Each equation has its own limits of validity that can be critically assessed by comparing the linearization of approximate and exact theories.

P. Singh, P. Mohr, D.D. Joseph, 1991.
Application of binary sequences to problems of chaos,
International Video Journal of Engineering Research, 1, 107-114.

abst: Oil and water in equal proportion are set into motion between horizontal concentric cylinders when the inner one rotates. In a range of speeds where the water is Taylor unstable and the oil Taylor stable, we get Taylor cells. The main focus of this paper is the mathematical description of the apparently chaotic trajectory of a small oil bubble moving between an eddy pair in a single Taylor cells trapped between the oil bands of a banded Couette flow.

D.D. Joseph, J.C. Saut, 1990.
Short-wave instabilities and ill-posed initial-value problems,
Theoret. Comput. Fluid Dynamics, 1, 191-227.

abst: We characterize ill-posed problems as catastrophically (Hadamard) unstable to short waves. The growth rate tends to infiinity as the wavelength tends to zero. The mathematical description of ill-posed problems is framed in terms of instability.

K.N. Liu, C. Christodoulou, O. Riccius, D.D. Joseph, 1990.
Drag reduction in pipes lined with riblets,
AIAA Journal, 28(10), 1697-1698.

abst: In the present paper, experiments are reported establishing a maximum drag reduction of 5-7% in fully developed turbulent flow of water through 25.4- and 50.8-mm-diam. pipes lined with a film of grooved equilaterial triangles of base 0.11 mm.

D.D. Joseph, 1990.
Mathematical problems associated with the elasticity of liquids,
Problems Involving a Change of Type, D. Kirchgassner, ed., 99-111, 22-50.

abst: The mathematical theory of hyperbolicity and change of type is associated with models with an instantaneous elastic response. Basically, this means there is no Newtonian-like part of the constitutive equation. The underlying quasilinear system gives rise

D.D. Joseph, L. Preziosi, 1990.
Addenum to the paper "Heat waves",
Reviews of Modern Physics, 62(2), 375-391.

abst: Since the appearance of our paper on heat waves [Rev. Mod. Phys. 61, 1989], certain papers which should have been cited have come to our attention. It appears that our effort to write a relatively complete chronology of thought about heat waves fell somew

D.D. Joseph, 1990.
Fluid dynamics of two miscible liquids with diffusion and gradient stresses,
Eur. J. Mech. B/Fluids, 9(6), 565-596.

abst: The density of incompressible fluids can vary with concentration phi and and temperature, but not with pressure. The velocity field u of such incompressible fluids is not in general solenoidal, div u not-equal 0. A conservation form for the left hand side of the diffusion equation which differs from the usual substantial derivative of phi by the addition of phi div u, is implied by requiring that the mass per unit total volume of one liquids in a material volume is conserved in the absence of diffusion.

abst: Two liquids of different viscosities will stratify with the heavy liquid below, when stationary. But when these stratified liquids are made to flow down a pipe, the less viscous liquid will tend to encapsulate the more viscous liquid, even lubricating...

D.D. Joseph, 1990.
Fluid Dynamics of Viscoelastic Liquids,
Springer Applied Math Series, 84, 755 pages.

abst: This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models. The major emphasis of the book is on the mathematical and physical consequences of the elasticity of liquids; seventeen of twenty chapters are devoted to this. Constitutive models which are instantaneously elastic can lead to some hyperbolicity in the dynamics of flow, waves of vorticity into rest (known as shear waves), to shock waves of vorticity or velocity, to steady flows of transonic type or to short wave instabilities which lead to ill-posed problems. Other kinds of models, with small Newtonian viscosities, give rise to perturbed instantaneous elasticity, associated with smoothing of discontinuities as in gas dynamics.

K.P. Chen, D.D. Joseph, 1990.
Application of the singular value decomposition to the numerical computation of the coefficients of amplitude equations and normal forms,
Applied Numerical Mathematics, 6, 425-430.

abst: The Fredholm alternative is a standard procedure by which one generates the coefficients of amplitude equations and normal forms. The alternative requires that the inhomogeneous terms in the underlying systems of differential equations, which contain...

D.D. Joseph, P. Singh, K. Chen, 1990.
Couette flows, rollers, emulsions, tall Taylor cells, phase separation and inversion, and a chaotic bubble in Taylor-Couette flow of two immiscible liquids,
Proceedings of NATO Advanced Research Workshop on Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems, 1989 in Streitberg, FR Germany, F.H. Busse, L. Kramer, 225(Series B: Physics), 169-189.

abst: Oil and water in equal proportion are set into motion between horizontal concentric cylinders when the inner one rotates. Many different flows are realized and described. In one regime many large bubbles of oil are formed. In a range of speeds where...

D.D. Joseph, 1990.
Generalization of the Foscolo-Gibilaro analysis of dynamic waves,
Chemical Engineering Science, 45(2), 411-414.

abst: A new expression for the particle phase pressure in a fluidized bed, generalizing the one used by Foscolo and Gibilaro, is derived. In the new theory uniform fluidization is always unstable.

D.D. Joseph, T.S. Lundgren, R. Jackson, D.A. Saville, 1990.
Ensemble averaged and mixture theory equations for incompressible fluid-particle suspensions,
Int. J. Multiphase Flow, 16(1), 35-42.

abst: Two-fluid equations for flowing composites of solid particles in a liquid have been given by mixture theory and by ensemble averaging. The mixture theory equations are postulated and the ensemble averaged equations are derived.

K. Chen, R. Bai, D.D. Joseph, 1990.
Lubricated pipelining; Part 3, Stability of core-annular flow in vertical pipes,
J. Fluid Mech., 214, 251-286.

abst: The stability of core-annular flow in vertical pipes is analysed using the linearized theory of stability. In previous studies instabilities due to interfacial friction, interfacial tension and Reynolds stresses in the bulk fluid were indentified and...

H.H. Hu, O. Riccius, K.P. Chen, M. Arney, D.D. Joseph, 1990.
Climbing constant, second-order correction of Trouton's viscosity, wave speed and delayed die swell for M1,
J. Non-newtonian Fluid Mech., 35, 287-307.

abst: Measurements of wave speed c in M1 imply a fast time lambda=mu/rho c^2 of relaxation. This and the delayed die-swell measuremnts suggest that M1 is not very elastic. Extensive and very reliable values of the climbing constants show that M1 has weak...

P. Singh, D.D. Joseph, 1990.
One-dimensional, particle bed models of fluidized suspensions,
Two Phase Flows and Waves, IMA Volumes in Mathematics and Its Applications, D.D. Joseph, D. Schaeffer, eds., Springer-Verlag, 26, 1-20.

abst: One-dimensional unsteady models of a fluidized suspension based on modeling the forces that the fluid exerts on the particles are considered. Four different theories are discussed. The first, by Foscolo and Gibilaro 1984,1987 gives a criterion for...

H.H. Hu, D.D. Joseph, 1990.
Numerical simulation of viscoelastic flow past a cylinder,
J. Non-Newtonian Fluid Mech., 37, 347-377.

abst: The flow of an upper-convected Maxwell fluid past a circular cylinder is simulatd numerically using the algorithm SIMPLER, which is based on a finite volume discretization on a staggered grid of the governing equations and an iterative solution to ...

H.H. Hu, T.S. Lundgren, D.D. Joseph, 1990.
Stability of core-annular flow with a small viscosity ratio,
Physics of Fluids A, 2(11), 1945-1954.

abst: It is known that the stability problem for core-annular flow of very viscous crude oil and water is singular, the water annulus appears to be inviscid with boundary layers at the pipe wall and at the interface.

D.D. Joseph, L. Preziosi, 1989.
Heat waves,
Reviews of Modern Physics, 61(1), 41-73.

abst: The concept of transmission of heat by waves is reviewed and interpreted. The notion of an effective thermal conductivity, an effective heat capacity, and relaxation functions for heat and energy is introduced along lines used recently to describe ...

L. Preziosi, K. Chen, D.D. Joseph, 1989.
Lubricated pipelining: stability of core-annular flow,
J. Fluid Mech., 201, 323-356.

abst: The stability of core-annular flow (CAF) in pipes is analyzed using the linear theory of stability. Attention is confined to the potentially stable case of lubricated pipelining with the less viscous liquid, say water, in the annulus. The effects of surface tension and density is included, but gravity is excluded. We find upper and lower branches of the neutral curve in a Reynolds number (R) vs. wave number (Œ) plane. A window of parameters is identified in which CAF is stable to small disturbances.

H.H. Hu, D.D. Joseph, 1989.
Lubricated pipelining: stability of core-annular flow; Part 2.,
J. Fluid Mech., 205, 359-396.

abst: In this paper, we study the linearized stability of three symetric arrangements of two liquids in core-annular Poiseuille flow in round pipes. Deferring to one important application, we say oil and water when we mean more viscous and less viscous liquids.

P. Singh, PH. Caussignac, A.F. Fortes, D.D. Joseph, T. Lundgren, 1989.
Stability of periodic arrays of cylinders across the stream by direct simulation,
J. Fluid Mech., 205, 553-571.

abst: We treat the problem of the stability of an infinite horizontal array of cylinders, spaced periodically, by a direct numerical simulation of the Navier-Stokes equations for steady flow at Reynolds numbers less than or equal to 100. We find that the only stable configuration for the array is one with equal spacing between cylinders and all cylinders lying on a line perpendicular to the flow. The array is found to be stable under displacements of the cylinders perpendicular and parallel to the array. We say a perturbation is stable when it gives rise to a force which acts to restore the original stable configuration. Our results are consistent with experiments in which spheres were confined by the sidewalls of a fluidized bed to move in two dimensions. As a secondary issue we consider the variation with parameters of the length and width of wakes behind cylinders. •

C. Verdier, D.D. Joseph, 1989.
Change of type and loss of evolution of the White-Metzner model,
J. Non-Newtonian Fluid Mech., 31, 325-343.

abst: In this paper a mathematical study of the White-Metzner model is presented. This model gives rise to systems of first order nonlinear (not quasilinear) partial differential equations. The unsteady case is studied first to determine if the Cauchy problem..

C. Verdier, D.D. Joseph, 1989.
Similarity solutions that give rise to hyperbolicity and change of type in steady flow of a viscoelastic fluid,
J. Non-Newtonian Fluid Mech., 31, 301-323.

abst: Similarity solutions have proved to be a very useful tool for the study of flows of viscoelastic fluids since they allow us to check numerical computations against them. We compute here hyperbolic regions of the vorticity for an upper convected Maxwell..

P. Singh, D.D. Joseph, 1989.
Autoregressive methods for chaos on binary sequences for the Lorenz attractor,
Physics Letters A, 135(4,5), 247-253.

abst: A binary sequence is defined for the Lorenz attractor. This binary sequence contains some information about the original system. To extract this information we have used autoregressive methods from the theory of signal processing. The binary sequences...

D.D. Joseph, 1989.
Remarks on inertial radii, persistent normal stresses, secondary motions, and non-elastic extensional viscosities,
J. Non-Newtonian Fluid Mech., 32, 107-114.

abst: In this note I discuss some consequences of the balance of inertia and normal stresses in nearly steady slow motions. I argue that the fluid's elasticity cannot be determined from its extensional viscosity. A formula is given for the extensional viscosity

H.H. Hu, D.D. Joseph, 1989.
Stability of core-annular flow in a rotating pipe,
Phys. Fluids A, 1(10), 1677-1685.

abst: The linear stability of core-annular flow in rotating pipes is analyzed. Attention is focused on the effects of rotating the pipe and the difference in density of the two fluids. Both axisymmetric and nonaxisymmetric disturbances are considered.

L. Preziosi, D.D. Joseph, 1988.
The run-off condition for coating and rimming flows,
J. Fluid Mech., 187, 99-113.

abst: A layer of liquid can be supported on the inside or outside of a horizontal rotating cylinder if the viscous forces pulling the liquid around with the cylinder are large enough to overcome the force of gravity. If there are places on the cylnder where...

P. Than, L. Preziosi, D.D. Joseph, M. Arney, 1988.
Measurement of interfacial tension between immiscible liquids with the spinning rod tensiometer,
J. Colloid and Interface Sci., 124(2), 552-559.

abst: A spinning rod interfacial tensiometer (US patent 4,644,782) is described and compared with spinning drop tensiometers. The rod pierces the drop and can help to stabilize the rotating bubble, reducing spin up time and drift. The effects of contact..

D.D. Joseph, K. Chen, 1988.
Anomalous elongational flows and change of type,
J. Non-Newtonian Fluid Mech., 28, 47-60.

abst: Anomalous effects on elongational flows at high rates of elongation reported by Ferguson et al 1987 are here treated as a change of type. Analysis predicts that the vorticity near the drum is hyperbolic, elliptic away from the drum under the supercritical

D.D. Joseph, 1988.
Hyperboliicity, change of type, wave speeds and related matters,
MISSING PUBLICATION INFO, , 107-122.

abst: In this paper I will review some consequences of instantaneous elasticity for the numerical analysis of flows of viscoelastic liquids. I will consider situations which are associated with hyperbolic waves of vorticity. T vorticity equation may change type in steady and unsteady flow. In the latter case we get instability to short waves, ill-posedness, and, in the former, transonic flow. The two types of change are related. The regularizing effect of an effective Newtonian viscosity and the physical origins of viscosity are briefly reviewed. •

C. Guillope, D.D. Joseph, K. Nguyen, F. Rosso, 1987.
Nonlinear stability of rotating flow of two fluids,
J. Theoretical Applied Mech., 6(5), 619-645.

abst: The stability of Couette flow between concentric cylinders of two immiscible fluids with different viscosities and different densities is studied. Two approaches are proposed, both based on the energy method. The first one consists in decomposing the solution at time t into a steady solution defined on the evolution configuration plus a disturbance... The second approach is possible only when an explicit solution is known.

P.T. Than, F. Rosso, D.D. Joseph, 1987.
Instability of Poiseuille flow of two immiscible liquids with different vicosities in a channel,
Int. J. Engng. Sci., 25(2), 189-204.

abst: We study the stability of plane Poiseuille flow of two immiscible liquids of different viscosities and equal densities. The problem is like one considered by C.S. Yih who found that flow in two layers of equal thickness was always unstable.

D.D. Joseph, A.F. Fortes, T.S. Lundgren, P. Singh, 1987.
Nonlinear mechanics of fluidization of spheres, cylinders and disks in water,
SIAM Advances in Multiphase Flow and Related Problems, G. Papanicolau, ed, , 101-122.

abst: Experiments on fluidization with water of spherical particles falling against gravity in columns of rectangular cross section are described. All of them are dominated by inertial effects associated with wakes. Two local mechanisms are involved: drafting &

D.D. Joseph, A.F. Fortes, T.S. Lundgren, P. Singh, 1987.
Nonlinear mechanics of fluidization of spheres, cylinders and disks in water,
Physics of Fluids, Gallery of Fluid Motion special ed., 30(9), 2599.

abst: In all the figures, particles fluidized by water are held in place by a balance of weight and drag. In all the figures except Figs. 1 and 6, the parataicles are constrained by closely spaced side walls to motion in two dimensions. The motion of particles is dominated by wakes and turning couples. Wakes are important in the first part of the scenario we call drafting, kissing, and tumbling.

O. Riccius, D.D. Joseph, M. Arney, 1987.
Shear-wave speeds and elastic moduli for different liquids; Part 3, Experiments update,
Rheo. Acta, 26, 96-99.

abst: Tables of values of shear-wave speeds, shear moduli and relaxation times for 18 new liquids are presented, supplementing the tables for 51 liquids given in Part 2. A brief discussion of errors and analysis of the oscilloscope traces is presented.

D.D. Joseph, 1987.
Hyperbolic dynamics in the flow of elastic liquids,
IMA, Proceedings of Amorphous Polymers Workshop, March 5-8, 1985 at Inst. for Mathematics and its Applications, Dafermos, J.L. Ericksen, D. Kinderlehrer, eds. Springer Verlag, 6, 57-88.

abst: In this paper I discuss concepts of viscosity, elasticity, hyperbolicity, Hadamard instability and change of type in the flow of viscoelastic fluids.

A.F. Fortes D.D., Joseph T.S., Lundgren 1987.
Nonlinear mechanics of fluidization of beds of spherical particles,
J. Fluid Mech., 177, 467-483.

abst: Experiments on fluidization with water of spherical particles falling against gravity in columns of rectangular cross-section are described. All of them are dominated by inertial effects associated with wakes. Two local mechanisms are involved: drafting &

L. Preziosi, D.D. Joseph, 1987.
Stokes' first problem for viscoelastic fluids,
J. Non-Newtonian Fluid Mech., 25, 239-259.

abst: The theory given in this paper is based on a generalization of Boltzmann's equation of linear viscoelasticity in which the presence of a Newtonian viscosity is acknowledged. The solution of Stokes' first problem for this kind of fluid, with a viscosity

D.D. Joseph, J.E. Matta, K. Chen, 1987.
Delayed die swell,
J. Non-Newtonian Fluid Mech., 24, 31-65.

abst: The experiments reported here establish that there is a general critical condition associated with die swell which we called delayed die swell. This condition is defined by a critical speed which is the area-averaged velocity, the extrusion velocity...

M. Ahrens, Y.J. Yoo, D.D. Joseph, 1987.
Hyperbolicity and change of type in the flow of viscoelastic fluids through pipes,
J. Non-Newtonian Fluid Mech., 24, 67-83.

abst: We consider the steady flow of an upper convected Maxwell fluid through a pipe with wavy walls. The analysis is an extension to round pipes of the methods introduced by Yoo and Joseph 1985 to study the same problem in plane channels.

D.D. Joseph, L. Preziosi, 1987.
Stability of rigid motions and coating films in bicomponent flows of immiscible liquids,
J. Fluid Mech., 185, 323-351.

(photos)

abst: We consider the problem of global stability of the rigid rotation of two fluids. The realized interfacial configurations minimize a potential. We derive the most general form of the potential in which the working of the contact line may be expressed as..

D.D. Joseph, 1986.
Two fluids heated from below,
Proceedings of the Conference on Energy, Stability, Theory and Convection, Capri, May 20-28, 1986, , 364-382.

abst: We consider the problem of stability of the conduction solution of two fluids in two layers heated from below. This is the classical Benard problem, but for two fluids. The two fluid problem is never self-adjoint. We compute the adjoint. The computation..

D.D. Joseph 1986.
Recent results on the stability of rotating flows of two fluids,
Rend. Sem. Mat. Univ. Politec. Torino, 44(2), 173-206.

abst: Flows of two fluids are important and interesting because they are commonplace, they lend themselves to technological application and they introduce new phenomena without counterpart in the flow of one fluid. Many configurations of flow of two fluids are possible. We see layers, slugs, rollers, sheets, bubbles, drops and dynamic emulsions and foams. These structures are often topologically different from the rest confiurations from which they arise.

D.D. Joseph, K. Nguyen, G.S. Beavers, 1986.
Rollers,
Phys. Fluids, Gallery of Fluid Motion, special ed., 29(9), 2771.

abst: High-viscosity liquids hate to work. Low-viscosity liquids are the victims of the laziness of high-viscosity liquids because they are easy to push around. The arrangement of components in two fluid flows is typicaly nonunique. There is a problem of places and a problem of shapes.

M. Renardy, D.D. Joseph, 1986.
Hopf bifurcation in two component flow,
SIAM J. Math. Anal., 17(4), 894-910.

abst: The stability of viscosity-stratified bicomponent flow has been studied by long wave asymptotics, by short wave asymptotics and numerically. These studies have shown that interfacial instabilities arise from the viscosity difference between th two fluids.

D.D. Joseph, A. Narain, O. Riccius, 1986.
Shear-wave speeds and elastic moduli for different liquids; Part 1, Theory,
J. Fluid Mech., 171, 289-308.

abst: In this paper we develop a theory for a rheometrical device for measuring the speed of shear waves into a region at rest. The device is a Couette apparatus with a narrow gap. The outer cylinder is moved impulsively and a time of transit is measured.

D.D. Joseph, O. Riccius, M. Arney, 1986.
Shear-wave speeds and elastic moduli for different liquids; Part 2, Experiments,
J. Fluid Mech., 171, 309-338.

abst: In this paper we describe the experimental apparatus that we use to measure transit speeds. Tables of measured values of transit speeds and the corresponding values of the shear modulus are presented. The criteria we use to determine if a transit speed is a shear-wave speed are described and applied to the data. The main criteria are that transit speeds should be independent of the gap size and the corresponding value of the shear modulus should be consistent with independent rheometrical measurements. ...

D.D. Joseph, 1986.
Historical perspectives on the elasticity of liquids,
J. Non-Newtonian Fluid Mech., 19, 237-249.

abst: The existence of normal stresses, shear thinning and recoil in polymeric solutions and undiluted polymers (melts) makes it impossible to believe that every liquid is Newtonian. There are recurrent arguments starting with Poisson 1829, stimulated by Maxwel

D.D. Joseph, J.C. Saut, 1986.
Change of type and loss of evolution in the flow of viscoelastic fluids,
J. Non-Newtonian Fluid Mech., 20, 117-141.

abst: In this paper we discuss concepts associated with viscosity, elasticity, hyperbolicity, Hadamard instability and ill posedness of Cauchy problems in the flow of viscoelastic fluids. We frame the analysis in terms of vorticity and develop relations between change of type in steady flow and the ill posedness of the unsteady problem. We also consider the problem of regularizing Hadamard instabilities by the addition of Newtonian contributions to the constitutive equations.

D.D. Joseph, Appendix by Marshall Slemrod 1985.
Hyperbolic phenomena in the flow of viscoelastic fluids,
Viscoelasticity and Rheology, A. Lodge, J. Nohel, M. Renardy, eds. Academic Press, , 235-321.

abst: This paper treats the problem of hyperbolicity, change of type and nonlinear wave propagation in the flow of viscoelastic fluids. Rate equations for fluids with and without instataneous elasticity are derived and discussed. ...

Y. Renardy, D.D. Joseph, 1985.
Couette flow of two fluids between concentric cylinders,
J. Fluid Mech., 150, 381-394.

abst: We consider the flow of two immiscible fluids lying between concentric cylinders when the outer cylinder is fixed and the inner one rotates. The interface is assumed to be concentric with the cylinders, and gravitational effects are neglected. We present a numerical study of the effect of different viscosities, different densitities and surface tension on the linear stabilitity of the Couette flow. Our results indicate that, with surface tension, a thin layer of the less-viscous fluid next to either cylinder is linearly stable and that it is possible to have stability with the less dense fluid lying outside. The stable configuration ...

D.D. Joseph, Y. Renardy, M. Renardy, K. Nguyen, 1985.
Stability of rigid motions and rollers in bicomponent flows of immiscible liquids,
J. Fluid Mech., 153, 151-165.

abst: We consider the motion of two rings of liquids with different viscosities and densities lying between concentric cylinders that rotate with the same angular velocity [omega]. Gravity is neglected and interfacial tension is included. We show that rigid motions are globaly stable and that the shape of the interface which separates the two fluids is determined by a minimizing problem for a potential P defined as the negative of the sum of the kinetic energies of two rigid motions plus the surface energy of the interface. ...

J.Y. Yoo, M. Ahrens, D.D. Joseph, 1985.
Hyperbolicity and change of type in sink flow,
J. Fluid Mech., 153, 203-214.

abst: We consider the problem of steady fast flow of a family of Oldroyd fluids into a hole, and show that the field of flow is partitioned into elliptic (subcritical) and hyperbolic (supercritical) regions. We analyse the characteristics and show that the vort

D.D. Joseph, M. Renardy, J.-C. Saut, 1985.
Hyperbolicity and change of type in the flow of viscoelastic fluids,
ARMA, 87(3), 213-251.

abst: The equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators. Propagation of singularities is discussed and conditions for a change of type are investigated. The vorticity equations for steady flow can change type when a critical condition involving speed and stresses is satisfied. This leads to a partitioning of the field of flow into subcritical and supercritical regions, as in the problem of transonic flow.

Y. Renardy, D.D. Joseph, 1985.
Oscillatory instability in a Benard problem of two fluids,
Phys. Fluids, 28(3), 788-793.

abst: A linear stability analysis for a Benard problem with two layers is considered. The equations are not self-adjoint. The system can lose stability to time-periodic disturbances. For example, it is shown numerically that when the viscosities and coefficient

D.A. Nield, D.D. Joseph, 1985.
Effects of quadratic drag on convection in a saturated porous medium,
Phys. Fluids, 28(3), 995-997.

abst: The effects of inertia (involving a drag which is quadratic in velocity) on convection in a fluid-saturated porous medium are considered. It is shown that the effect of quadratic drag is physically significant for natural convection, at realistic

J.Y. Yoo, D.D. Joseph, 1985.
Hyperbolicity and change of type in the flow of viscoelastic fluids through channels,
J. Non-Newtonian Fluid Mech., 19, 15-41.

abst: We consider steady flow of an upper convected Maxwell fluid through a channel with wavy walls. The vorticity of this flow will change type when the velocity in the center of the channel is larger than a critical value defined by the propagation of shear..

D.D. Joseph, G.S. Beavers, A. Cers, C. Dewald, A. Hoger, P.T. Than, 1984.
Climbing constants for various liquids,
J. Rheol, 28(4), 325-345.

abst: In this article we present tables of values of the climbing constant \hat beta=3alpha_1 + 2alpha_2, where alpha_1 and alpha_2 are the parameters of the second-order approximation to the stress in a slow, slowly varying flow of any simple non-Newtonian...

M. Ahrens, D.D. Joseph, M. Renardy, Y. Renardy, 1984.
Remarks on the stability of viscometric flow,
Rheol. Acta, 23, 345-354.

abst: We study the stability of viscometric flow using the type of short memory introduced by Akbay, Becker, Krozer and Sponagel. The instability found by these researchers is recognized as a "change of type" leading to non-evolutionary character of the governing equations. We also address the question of justification for the short memory assumption and find that it cannot be justified for some of the more popular rheological models.

J. Dunwoody, D.D. Joseph, 1984.
Systematic linearization for stability of shear flows of viscoelastic fluids,
ARMA, 86, 65-84.

abst: The phenomenon of melt fracture occuring in the process of polymer extrusion (see Tordella, 1963) has attracted the attention of research workers in the past two decades. In order to understand the mechanisms which might give rise to this phenomenon, ...

A. Narain, D.D. Jospeh, 1984.
Classification of linear viscoelastic solids based on a failure criterion,
J. of Elasticity, 14, 19-26.

abst: An isotropic, incompresible linear viscoelastic solid subjected to a step shear displacement fails if the relaxation function G(s) is such that 0<G(0)< infty and -infty<G'(0)<=0. In this case, the discontinuity in displacement propagates into ...

H.A. Tieu, D.D. Joseph, G.S. Beavers, 1984.
Interfacial shapes between two superimposed rotating simple fluids,
J. Fluid Mech., 145, 11-70.

abst: The interfacial shape of two immiscible simple fluids in a vertical cylinder which oscillates about its axis is investigated using the theory of domain perturbations. The perturbation stresses are expressed by integrals over the history of the deformation. At first order the azimuthal velocity field satisfies the requirements of continuity in velocity and shear stresses across the interface. At second order the solution consists of a mean part and a time-periodic part varying at twice the frequency of the cylinder. the mean problem is inverted for the mean secondary flow, pressure and interfacial shape. Experimental data for two polymeric oils (TLA227 and STP) show qualitative agreement with theoretical predictions for the mean interfacial shapes.

D.D. Joseph, M. Renardy, Y. Renardy, 1984.
Instability of the flow of two immiscible liquids with different viscosities in a pipe,
J. FLuid Mech., 141, 309-317.

abst: We study the flow of two immiscible fluids of different viscosities and equal density through a pipe under a pressure gradient. This problem has a continuum of solutions corresponding to arbitrarily prescribed interface shapes. The question therefore...

D.D. Joseph, K. Nguyen, G.S. Beavers, 1984.
Non-uniqueness and stability of the configuration of flow of immiscible fluids with different viscosities,
J. Fluid Mech., 141, 319-345.

(with 8 color plates)

abst: High-viscosity liquids hate to work. Low-viscosity liquids are the victims of the laziness of high-viscosity liquids because they are easy to push around. The arrangement of components in steady flow of immiscible liquids is typically non-unique. The problem of selection of arrangements is defined here and is studied by variational methods under the hypothesis that the realized arrangements are the ones that maximize the speed on exterior boundaries for prescribed boundary tractions, or the ones that minimize the tractions for prescribed speeds.

abst: Fading memory expresses the intuitive idea that the recent rather than the remote history of deformation of a material body should have a greater effect on the present stress. The problem of fading memory is to give a useful mathematical formulation...

A. Narain, D.D. Joseph, 1983.
Remarks about the interpretation of impulse experiments in shear flows of viscoelastic liquids,
Rheol. Acta, 22, 528-538.

abst: The effect of inertia in three popular impulse experiments in shear flows of viscoelastic liquids is considered. Dynamics of the flow is used to evaluate the stress observables such as the shear stress and the first normal stress difference at the walls.

A. Narain, D.D. Joseph, 1983.
Linearized dynamics of shearing deformation perturbing rest in viscoelastic materials,
Lecture Notes in Mathematics, Equadiff 82. Proceedings Worzburg 1982, Springer, 1017, 476-507 (1983).
Also in Transactions of 28th Conference of Army Mathematicians, ARO Report, 83-1.

abst: This paper extends our earlier work on the propagation of jumps in velocity and displacement for shearing deformations imposed impulsively at the boundary of viscoelastic fluids and solids obeying constitutive equations in integral form with arbitrary...

D.D. Joseph, M. Renardy, J.-C. Saut, 1983.
Examples and significance of change of type in viscoelasticity,
Transactions of the 39th Conference of Army Mathematicians, , 1-6.

abst: The equations governing the flow of viscoelastic fluids are classified according to the symbol of their differential operators. Conditions for a change of type in steady two-dimensional flows are derived for a three-constant Oldroyd model. ...

D.D. Joseph, 1983.
Stability and bifurcation theory (course 5),
Chaotic Behavior of Deterministic Systems, , 1.

abst: In this lecture we consider the theory of singular points of plane curves. And to these considerations we add the study of stability...]

D.D. Joseph, K. Nguyen, J.E. Matta, 1983.
Jets into liquid under gravity,
J. Fluid Mech., 128, 443-468.

abst: We study the flow of a heavy, viscous, possibly non-Newtonian axisymmetric jet of liquid of density rho falling under gravity g into a lighter liquid of density ~-rho. If the change in the momentum of the entrained lighter liquid is neglected the jet...

H.A. Tieu, D.D. Joseph, 1983.
Extrudate swell for a round jet with large surface tension,
J. Non-Newtonian Fluid Mech., 13, 203-222.

abst: The problem of extrudate swell of a viscoelastic fluid from a round pipe is studied by the method of domain perturbations. The perturbation problems are solved by a finite-element method through second-order in the flow rate parameter

for small flow rates. The analysis extends the work of Sturges on swelling in two-dimensional channels to round capillary tubes.

D.D. Joseph, L.D. Sturges, W.H. Warner, 1982.
Convergence of biorthogonal series of biharmonic eigenfunctions by the method of titchmarsh,
ARMA, 78(3), 223-274.

abst: Canonical edge problems for the biharmonic equation can be solved by separating variables. The eigenvalues and eigenvectors arising in this separation are derived from a reduced system of ordinary differential equations along lines suggested in...RCSmith

D.D. Joseph, D.A. Neild, G. Papanicolaou, 1982.
Nonlinear equation governing flow in a saturated porous medium,
Water Resources Research, 18(4), 1049-1052.

abst: It is argued that the appropriate generalization of Darcy's law when inertia effects are included takes the form nabla p=-(mu/k) V -( rho c/k^[1/2])|V|V, div V=0, where k is the permeability of the medium and the 'form drag constant' c is a coeff...

A. Narain, D.D. Joseph, 1982.
Linearized dynamics for step jumps of velocity and displacement of shearing flows of a simple fluid,
Rheol. Acta, 21, 228-250.

abst: We consider linearized dynamics associated with step jumps in the velocity or displacement of the boundary of a fluid in a shearing motion. The discontinuity will propagate into the interior with a speed C=sqrt[G(0)/rho], (rho is the density) if...

D.D. Joseph, 1982.
The application of bifurcation theory to physical problems,
Proceedings of 9th US National Congress of Applied Mechanics, Held at Cornell Univ, Ithaca, NY June 21-25, 1982, Y.H. Pao, et al, , 433-436.

abst: I am going to start my lecture with a citation by James Lighthill 1982. He says "There is one great complicating feature that introduces major difficulties into mechanics, physics, chemistry, engineering, astronomy and biology. This complicating feature..

P. Dixit, D.D. Joseph, 1982.
The shape of stress-free surfaces on a sheared block,
SIAM J. Appl. Math., 47(3), 653-677.

abst: We obtain solutions for the shape of the free surface on the upper and lower boundaries of an initially rectangular, incompressible linearly viscoelastic block when the block is sheared at the vertical sidewall. To solve the problem when the vertical...

S.A. Trogdon, D.D. Joseph, 1982.
Matched eigenfunction expansions for slow flow over a slot,
J. Non-Newtonian Fluid Mech., 10, 185-213.

abst: We solve the problem of plane flow of a second-order fluid over a rectangular slot when inertia is neglected by matching biorthogonal eigenfunction expansions in different regions of flow. The method appears to be cheaper and more accurate than direct num

D.D. Joseph, 1981.
Hydrodynamic stability and bifurcation,
Topics in Applied Physics, Hydrodynamic Instabilities and the Transition to Turbulence, H.L. Swinney, J.P. Gollub, eds., 45, 27-76.

abst: The goal of hydrodynamics is to describe and predict the motions of fluids under applied forces. For incompressible Navier-Stokes fluids, in many circumstances, these forces scale with the Reynolds number. When the Reynolds number is small...

D.D. Joseph, 1981.
Instability of the rest state of fluids of arbitrary grade greater than one,
ARMA, 75(3), 251-256.

abst: I am going to prove that the rest state of fluids of grade n, any n?1, is unstable in the spectral sense of linearized theory when the ratio of the coefficients of A_n and A_(n-1) in the constitutive equation is negative. Negative ratios, and only ...

P.M. Dixit, A. Narain, D.D. Joseph, 1981.
Free surface problems induced by motions perturbing the natural state of simple solids,
ARMA, 77(3), 199-261.

abst: We develop a perturbation theory for solids along the lines which have been used to treat the motions of fluids which perturb states of rest or rigid motion. The perturbation theory for fluids does not assume special rheological models; it defines its own

D.D. Joseph, 1981.
Mathematics, Mechanics, and Engineering: an essay on the contribution of applied mechanics to engineering and applied science,
ASME-SMAC Forum, J. Fong, ed., , .

D.D. Joseph, 1981.
Lectures on bifurcation from periodic orbits,
Dynamical Systems and Turbulence, Warwick 1980; Proceedings of a Symposium Held at Univ. of Warwick, 1979/80, D.A. Rand, L.-S. Young, eds.; Springer Lecture Notes in Mathematics, 898, 1-12.

abst: These lectures are about bifurcations from a periodic orbit of an evolution equation with periodic forcing. The analysis applies to equations in an arbitrary Hilbert space, not just to finite dimensional problems. The results described here are joint...

S.A. Trogdon, D.D. Joseph, 1981.
The stick-slip problem for a round jet; II, Small surface tension,
Rheol. Acta, 20(1), 1-13.

abst: The stick-slip problem for a round jet studied in Part I gives a good approximation for the swell of a low speed jet when the surface tension is large but it fails when the surface tension is small. In this paper a new stick-slip problem II is defined..

J. Sanders, D.D. Joseph, G.S. Beavers, 1981.
Rimming flow of a viscoelastic liquid inside a rotating horizontal cylinder,
J. Non-Newtonian Fluid Mech., 9, 269-300.

abst: The flow of a simple liquid coating the inside of a horizontal, steadily rotating cylinder is investigated. The theory, in combination with the experiments, allows us to determine the complex viscosity eta*(Omega) of the liquid, characterizing its ...

J. Sanders, V. O'Brian, D.D. Joseph, 1980.
Stokes flow in a driven sector by two different methods,
J. Applied Mech., 87, 482-484.

abst: A biorthogonal series expansion and a numerical finite-difference approximation are applied to the problem of steady Stokes flow in a driven sector of 10 deg total angle, providing mutual support of the theoretical techniques. For this problem the method

B.E.D. Kolpin, G.S. Beavers, D.D. Joseph, 1980.
Free surface on a simple fluid betwen cylinders undergoing torsional oscillations; IV, Oscillating Rods,
J. Rheol., 24(6), 719-739.

abst: In earlier papers(Parts 1 and 2) we gave the perturbation analysis for the prediction of the free surface on a simple fluid near an oscillating rod and presented the results of a preliminary experiment involving a single rod in one sample of simple fluid.

P.M. Dixit, D.D. Joseph, 1980.
Motions pertubing states of rest of viscoelastic solids,
Transactions of the 25th Conference of Army Mathematicians, 80(1), 503-584.

abst: Our goal is to derive the canonical forms of the stress and equations of motion governing the motions which perturb the rest state (of elastostatic deformation) and the natural (unstressed and undeformed) state of viscoelastic solids. In this theory...

G. Iooss, D.D. Joseph, 1980.
The behaviour of solutions lying on an invariant 2-Torus arising from the bifurcation of a periodic solution,
Proceedings of a Conference on Bifurcation Theory at Bielefeld, Germany, October 1979, H. Amann, N. Bayley, K. Kirchgasser, eds., Pitman Pub., , 92-114.

abst: We are going to consider the problem of bifurcation of a periodic solution into an invariant two-dimensional torus, for the following autonomous differential equation in R^k : dV/dt=F(mu,V), where F is as smoth as we wish and mu is a real parameter.

D.D. Joseph, 1980.
An integral invariant for jets of liquid into air,
ARMA, 79, 389-393.

abst: A liquid is forced to move from left to right (x increasing) down a round pipe of length L by high pressure imposed at the entrance x=-L of the pipe. The flow is assumed to be axisymmetric but the pressure and velocity which is prescribed at ...

D.D. Joseph, 1980.
Bifurcation in fluid mechanics,
Proceedings of IUTAM Toronto, North Holland, 1980, , 295-305.

abst: A broad discursive review of bifurcation theory in fluid mechanics is given. The review delineates the assumptions, methods and potential for application of bifurcation theory. The problem of sequential bifurcation of flows into other flows...

D.D. Joseph, 1981.
Bifurcation of periodic solutions,
Recent Methods in Nonlinear Analysis and Applications, SAFA IV - Int'l Meeting, Napoli, Italy, March 21-28, 1980. Ed. A. Canfora, et al. Pub. Liguori Editore, p 89-98.

abst: I consider the problem du/dt = f(t,mu,u), f(t,•,•)=f(t+T,•,•), f(t,mu,0)=mu[element of] I_0, where I_0 is an interval containing mu=0, u is a vector in R^n, or more generally, in a Hilbert space. The problem (1) can arise when there is a forced T-periodic motion which is subtracted off the governing problem leading to the local form given by (1) in which u=0 is a solution. The analysis given here is taken from Chap. X of the forthcoming book "Elementary Stability and Bifurcation Theory" by G. Iooss and D. Joseph which is to appear in 1980 as a Springer Undergratuate Textbook in Mathematics.

G.S. Beavers, J.Y. Yoo, D.D. Joseph, 1980.
The free surface on a liquid between cylinders rotating at different speeds; Part III,
Rheol. Acta, Dietrich Steinkopff, Verlag, Darmstadt, 19, 19-31.

abst: When a viscoelastic fluid is sheared between two concentric cylinders undergoing differential rotation the free surface on the fluid is deformed as a consequence of the normal stresses induced in the fluid by the shearing motion. ..

L.D. Sturges, D.D. Joseph, 1980.
A normal stress amplifier for the second normal stress difference,
J. Non-Newtonian Fluid Mech., 6, 325-331.

abst: When a viscoelastic fluid flows down a tilted trough, the free surface bulges upward in the middle. The amount of bulge is proportional to the second normal stress difference of the fluid. Wineman and Pipkin 1966 were the first to suggest that ...

S.A. Trogdon, D.D. Joseph, 1980.
The stick-slip problem for a round jet; I. Large surface tension,
Rheol. Acta, 19, 404-420.

abst: A jet of fluid is extruded from a round pipe at low speed with gravity and wind shear neglected. The fluid must adjust from a fully developed flow in the pipe to a uniform flow far downstream. At low speeds this adjustment appears to require that ...

D.D. Joseph, 1980.
Boundary conditions for thin lubrication layers,
Phys. Fluids 23(12), 2356-2358.

abst: In certain circumstances, the effects of a thin lubrication layer may be accommodated by a slip flow boundary condition with the gradient of the tangential component of the velocity at the wall proportional to the square of the tangential component there.

D.D. Joseph, 1979.
A new separation of variables theory for problems of Stokes flow and elasticity,
2nd Symposium on Trends in Applications of Pure Mathematics to Mechanics, London; Pitman Publishing, , 129.

abst: Some classes of fourth-order boundary-value problems arising in the theory of Stokes flow and elasticity are solved by the method of biorthogonal series. The eigenfunctions are formed from separable solutions when the separation constants (eigenvalues)..

D.D. Joseph, 1979.
Factorization theorems and repeated branching of solutions at a simple eigenvalue,
Annals of the New York Academy of Sciences, 316, 150-167.

abst: In this paper I prove factorization theorems which show that, under certain typical hypotheses, the stability of steady and time-periodic solutions can change only at a turning point or at a point of bifurcation.

D.D. Joseph, 1979.
Direct and repeated bifurcation into turbulence,
Approximation Methods for the Navier-Stokes Equations, Springer Lecture Notes in Mathematics, R. Rautmann, ed., 771, 249-271.

abst: This lecture is a review of the applications of the theory of bifurcation to the problem of transition to turbulence. Most of the material in this lecture can be found in detail in my recent review, in other reviews in the same volume and in the monograph

J. Yoo, D.D. Joseph, G.S. Beavers, 1979.
Higher-order theory of the Weissenberg effect,
J. Fluid Mech., 92(3), 529-590.

abst: The higher-order theory of the Weissenberg effect is developed as a perturbation of the state of rest. The perturbation is given in powers of the angular frequency Omega of the rod and the solution is carried out to O(Omega^4). The perturbation induces ..

D.D. Joseph, 1979.
Perturbation of state of rest and rigid motion of simple fluids and solids,
J. Non-Newtonian Fluid Mech., 5, 13-31.

abst: In the lecture I advocate perturbing states of rest and rigid motion with arbitrary motions. This procedure leads to general expressions for the relation between stress and deformation and defines the parameters which must be measured in order to ...

G.S. Beavers, D.D. Joseph, 1979.
Experiments on free surface penomena,
J. Non-Newtonian Fluid Mech., 5, 323-352.

abst: This paper reviews an experimental program in which predictions from domain perturbation theory for motions which perturb the rest state are used in conjunction with experimental measurements on free surface deformations associated with Weissenberg effect

D.D. Joseph, 1978.
Hydrodynamic stability and bifurcation,
Fluid Dynamics Transactions (Arch. Mechaniki Stosovanej), Proceedings of XIIIth Biennial Fliud Dynamics Symposium, Olztyn-Kortowo, Poland Sept 5-10, 1977, 9, 177-228.

abst: Our understanding of hydrodynamic stability has been greatly enriched by recent developments in the mathematical theory of bifurcation. Bifurcation theory brings the theory of stability closer to physics and leads to simple criteria by which one can judge

J.Y. Yoo, D.D. Joseph, 1978.
Stokes flow in a trench between concentric cylinders,
SIAM J. Appl. Math., 34(2), 247-285.

abst: In this paper we develop a separation of variables theory for solving problems of Stokes flow in annular trenches bounded by horizontal parallel planes and concentric vertical cylinders. The theory leads to a new set of Stokes flow eigenfunctions, ...

D.D. Joseph, L. Sturges, 1978.
The convergence of biorthogonal series for biharmonic and Stokes flow edge problems: Part II,
SIAM J. Appl. Math., 34(1), 7-26.

abst: Sufficient conditions are established for the convergence of the biorthogonal series solving edge problems which arise in elasticity and in Stokes flow in cavities. These conditions and those given in Part I, (D.D.Joseph,vol.33,1977,pp337-347) include...

C.H. Liu, D.D. Joseph, 1978.
Stokes flow in conical trenches,
SIAM J. Appl. Math., 34(2), 286-296.

abst: In this paper we develop a separation of variables theory for solving problems of Stokes flow in cone-shaped trenches formed as the intersection of a cone of circular cross-section and a spherical shell centered at the vertex of the cone. The theory leads

D.D. Joseph, 1978.
Constitutive equations and free surfaces,
Contemporary Developments in Continuum Mechanics and Partial Differential Equations, G.M. de La Penha, L.A. Medeiros, , 254-283.

abst: The general theory of perturbations of rigid body motions of simple fluids with applications to fre surface problems is discussed. The general theory is utilized to explain phenomena exhibited in the movie "Novel Weissenberg Effects" by G.S. Beavers & DDJ

L.D. Sturges, D.D. Joseph, 1977.
The free surface on a simple fluid between cylinders undergoing torsional oscillations. Part III, Oscillating planes,
ARMA, 64(3), 245-267.

abst: In Part I (Joseph 1976a) of this paper in three parts, a recently developed algorithm (Joseph 1976b) for computing the motions of a simple fluid of integral type which perturb the state of rest was applied to the problem of finding the shape of the free..

D.D. Joseph, 1977.
Perturbations of the rest state of a simple fluid: the Weissenberg effect induced by torsional oscillation of a rod,
Proceedings of VII-th International Congress on Rheology, , 242-243.

abst: A rod of small diameter (2a) is partially immersed in a vat of simple fluid. The rod is set into torsional osscillation with an angular frequency Omega equal to epsilon sin wt. An analysis of this problem based on a newly developed theory of ...

D.D. Joseph, G.S. Beavers, 1977.
Free surfaces induced by the motion of viscoelastic fluids,
Proceedings of ASME Symposium on Viscoelastic Fluids, R.S. Rivlin, Yale, , 59.

abst: Free surfaces are sensitive to the state of stress in fluids. The striking variations in the shape of free surfaces induced by the motion of viscoelastic fluids chart the competing effects of elasticity, normal stresses and inertia in the fluid.

D.D. Joseph, 1977.
The convergence of biorthogonal series for biharmonic and stokes flow edge problems, Part I,
SIAM J. Appl. Math., 33(2), 337.

abst: Sufficient conditions are established for the convergence of the biorthogonal series solving edge problems which arise in elasticity and in Stokes flow in cavities. These conditions greatly improve those stated in the excellent work of R.C.T Smith 1952.

abst: In this paper I derive iterative procedures for the sequential computation of velocity fields and strain histories of motions of incompressible simple fluids driven by arbitrary, time-dependent prescribed data. The arbitrary data is a small perturbation..

D.D. Joseph, 1977.
The bifurcation of T-periodic solutions into nT-periodic solutions and Tori,
Proceedings of International Workshop on Synergetics at Schloss Elmau, Bavaria, May 2-7, 1977, H. Haken, ed., , .

abst: My lecture on bifurcation and stability of solutions which branch from forced T-periodic solutions is based on the recent work of G. Iooss and myself [ARMA 66(2) 1997, 135-172] and on my forthcoming paper on factorization theorems [ARMA 66(2) 1997, 99-118]. In general, forced T-periodic solutions bifurcate into subharmonic solutions with a fixed period tau(tau=nT; n=1,2,3,4) independent of the amplitude or into a torus [1,3,4,5,6] containing solutions whose analytic properties are not yet fully understood. The subharmonic bifurcating solutions with n=1 are the T-periodic equivalent of a symmetry-breaking bifurcation of steady solutinos with other steady solutions. The symmetry breaking ...

D.D. Joseph, 1977.
Factorization theorems, stability and repeated birucation,
ARMA, 66(2), 99-118.

abst: In this paper I prove theorems about the stability of bifurcating solutions without restricting the study to small amplitudes. I do not even always require that the solutions which I call 'bifurcating' form connected branches; they may be isolated ...

G. Iooss, D.D. Joseph, 1977.
Bifurcation and stability of nT-periodic solutions branching from T-periodic solutions at points of resonance,
ARMA, 66(2), 135-172.

abst: We shall study solutions which bifurcate from forced, T-perodic solutions of evolution equations of the Navier-Stokes type. Our principal interest is in subharmonic bifurcating solutions, n T-periodic solutions with n>=1.

G.S. Beavers, D.D. Joseph, 1977.
Novel Weissenberg effects,
J. Fluid Mech., 81(2), 265-272.

abst: We have observed two novel manifestations of the Weissenberg effect in viscoelastic liquids which are set into motion by the rotation of a circular rod. In thefirst exeriment we floated a layer of STP on water. The STP climbs up the rod into the air...

C.H. Liu, D.D. Joseph, 1977.
Stokes flow in wedge-shaped trenches,
J. Fluid Mech., 80(3), 443-463.

abst: In this paper we develop a separation of variables theory for solving problems of Stokes flow in wedge-shaped trenches bounded by radial lines and concentric circles centered at the vertex of the wedge. The theory leads to a set of Stokes flow eigenfuncti

D.D. Joseph, G.S. Beavers, 1977.
Free surface problems in rheological fluid mechanics,
Rheol. Acta, Dr. Dietrich Steinkopff, ed., 16, 169-189.

D.D. Joseph, 1976.
Factorization theorems for the stability of bifurcating solutions,
Proceedings of Conference, Turbulence and Navier Stokes Equations, University of Paris-Sud, Orsay, June 12-13, 1975, Roger Temam, ed., 565, 85-93.

abst: The theory of bifurcation at a simple complex eigenvalue, developed for ordinary differential equations by Hopf 1942 and extended to partial differential equations, like the Navier-Stokes equations, by Joseph and Sattinger 1972, using Hopf's methods...

D.D. Joseph, B.S. Beavers, 1976.
The free surface on a simple fluid between cylinders undergoing torsional oscillations,
ARMA, 62(4), 323-352.

abst: In a recent work (Joseph 1976), ideas from the theory of domain perturbations were used to develop an algorithm for the computation of unsteady motions of a simple fluid. In this algorithm, the rest state is perturbed with an unsteady motion.

L. Sturges, D.D. Joseph, 1975.
Slow motion and viscometric motion, Part V: the free surface on a simple fluid flowing down a tilted trough,
ARMA, 59(4), 359-387.

abst: This paper is a contribution to the theory of viscometry of slow steady motions of a simple fluid and is presented as Part V of the work on slow motion and viscometric motion which formed the subject of the paper in four parts of Joseph 1974.

D.D. Joseph, D.A. Nield, 1975.
Stability of bifurcating time-periodic and steady solutions of arbitrary amplitude,
ARMA, 58(4), 369-380.

D.D. Joseph, L. Sturges, 1975.
The free surface on a liquid filing a trench heated from its side,
J. Fluid Mech., 69(3), 565-589.

abst: In this paper we compute the motion and the shape of the free surface on a liquid in a trench heated from its side. The analysis is based on Joseph's Lagrangian theory of domain perturbations, which is developed in general and through simple examples...

G.S. Beavers, D.D. Joseph, 1975.
The rotating rod viscometer,
J. Fluid Mech., 69(3), 475-511.

abst: This paper reports the development of paractical methods of viscometry to characterize non-Newtonian fluids in slow flow. It is shown that measurements of the free surface near rods rotating in STP and polyacrylamide are accurate, reproducible, and in...

D.D. Joseph, 1974.
Response curves for plane Poiseuille flow,
Adv. Applied Mech., 14, 241-277.

abst: A response function for a fluid motion can be defined as a scalar function that measures the response of the flow to the external forces which induce the motion. For example, in problems of thermal convection, the response function can be taken as ...

D.D. Joseph, 1974.
Repeated supercritical branching of solutions arising in the variational theory of turbulence,
ARMA, 53(2), 101-130.

abst: In the variational theory of statistically stationary turbulence one seeks bounds on the difference between the response of laminar and turbulent flow when the steady external forces driving the flow are specified. For example, the difference between ...

G.S. Beavers, D.D. Joseph, 1974.
Tall Taylor cells in polyacrylamide solutions,
Physics of Fluids, 17(3), 650-651.

abst: The behavior of Taylor cells in a polyacrylamide solution contained between rotating cylinders is described. As the rotational speed increases, the cell aspect ratio changes from about 1 to 4. Hysteresis of the 4-cell configuration is observed.

D.D. Joseph, T.S. Chen, 1974.
Friction factors in the theory of bifurcating Poiseuille flow through annular ducts,
J. Fluid Mech., 66(1), 189-207.

abst: The objective of this paper is to show how to formulate a bifurcation theory for pipe flows in terms of the friction factor. We compute the slope of the friction factor vs. Reynolds number curve and the frequency change for the time periodic solution ...

D.D. Joseph, 1974.
Slow motion and viscometric motion; stability and bifurcation of the rest state of a simple fluid,
ARMA, 56, 99-157.

abst: This paper is divided into four loosely connected parts whose common thread is the study of slow steady motion of a simple fluid. The motions to be considered are those which can be constructed as a perturbation series pivoted about a state of rest. ...

D.D. Joseph, 1973.
Remarks about bifurcation and stability of quasi-periodic solutions which bifurcate from periodic solutions of the Navier Stokes equations,
Nonlinear Problems in Physical Science and Engineering, Joseph, Sattinger, Stakgold, eds., Springer Lecture Notes in Mathematics, , 1-30.

abst: L.D. Landau (1944) and E. Hopf (1948) have conjectured that the transition to turbulence may be described as repeated branching of quasi-periodic solutions into quasi-periodic solutions with more frequencies. The simplest case is the bifurcation of ...

D.D. Joseph, T.S. Lundgren, 1973.
Quasilinear Dirichlet problems driven by positive sources,
ARMA, 49(4), 241-269.

abst: We study the problem (r^(n-1)u')' + lambd r^(n-1) F(u)=0 where F(u)>0 when u>=0. Our main concern is with functions F(u)=(1+alpha u)^beta, alpha beta>0 and with F(u)=e^u. The last secton... deals with solutions of (I.1) when F(u) is Lipschitz continuous..

D.D. Joseph, 1973.
Domain perturbations: The higher order theory of infinitesimal water waves,
ARMA, 51(4), 295-303.

abst: The higher order theory of infinitesimal water waves refers to a perturbation theory which represents solutions to problems in the theory of nonlinear water waves as a power series in the amplitude of the wave. The infinitesimal wave appears in this theor

T.S. Chen, D.D. Joseph, 1973.
Subcritical bifurcation of plane Poiseuille flow,
J. Fluid Mech., 58(2), 337-351.

abst: We apply the perturbation theory which was recently developed and justified by Joseph & Sattinger (1972) to determine the form of the time-periodic solutions which bifurcate from plane Poiseuille flow. The results at lowest significant order seem to be in

D.D. Joseph, R.L. Fosdick, 1973.
The free surface on a liquid between cylinders rotating at different speeds; Part I,
ARMA, 49(5), 321-380.

abst: When a liquid in a vessel rotates as a rigid body, the free surface on top of the liquid is shaped by the requirements of a balance of forces arising from centripetal accelerations, gravity, and surface tension. In the absence of relative internal motion,

D.D. Joseph, G.S. Beavers, R.L. Fosdick, 1973.
The free surface on a liquid between cylinders rotating at different speeds; Part II,
ARMA, 49(5), 381-401.

abst: Chapt IV. The rise of fluid on a rod rotating in a large vat. The detailed agreement between theory and experiment which we shall display here leaves open the possibility that standard experiments on climbing can be so designed to determine accurately ...

V.P. Gupta, D.D. Joseph, 1973.
Bounds for heat transport in a porous layer,
J. Fluid Mech., 57(3), 491-514.

abst: Strongly nonlinear heat transport across a porous layer is studied using Howard's (1963) variational method. The analysis explores a bifurcation property of Busse's (1969) multi-alpha solution of this variational problem and complements the 1972 study ...

D.D. Joseph, 1972.
Energy stability of hydromagnetic flow,
Proceedings of Conference on Mathematical Topics in Stability Theory, March 29-31, 1971 at Washington State Univ., , 1-12.

abst: The governing equations of motion for a viscous fluid with constant density rho and finite conductivity sigma flowing in a magnetic field are dU/dt=1/(rho mu) B.nablaB - .., dB/dt=B.nabla U + 1/(sigma mu) .., and nabla.U=nabla.B=0 where B is the magnetic

D.D Joseph, D.H. Sattinger, 1972.
Bifurcating time periodic solutions and their stability,
ARMA, 45(2), 79-109.

abst: Equilibrium configurations of mechanical systems are often characterized by stability parameters, such as the Reynolds number R in fluid mechanics. When R is small, the equilibrium configuration is stable; but when R is raised to a certain critical value

W.L. Hung, D.D. Joseph, B.R. Munson, 1972.
Global stability of spiral flow; Part 2,
J. Fluid Mech., 51(3), 593-612.

abst: The stability of spiral flow between rotating and sliding cylinders is considered. In the limit of narrow gap, a 'modified' energy theory is constructed. This theory exploits the consequences of assuming the existence of a preferred spiral direction ...

F.H. Busse, D.D. Joseph, 1972.
Bounds for heat transport in a porous layer,
J. Fluid Mech., 54(3), 521-543.

abst: Bounds on the heat transport in a porous layer are derived using the variational method of Howard 1963 and Busse 1969b. The relatively simple structure of the variational problem in the case of prorous convection allows one to formulate the theory ...

D.D. Joseph, 1971.
On the place of energy methods in a global theory of hydrodynamic stability,
Instability of Continuous Systems, IUTAM Symposium September 1969, , 132-142.

abst: The point of departure for the global theory to be described is the system of the nonlinear Boussinesq equations (1,2) governing the disturbance of some given motion. For simplicity, let (U,T,Gamma) be a basic steady velocity, temperature and concen' ...

D.D. Joseph, W. Hung, 1971.
Contributions to the nonlinear theory of stability of viscous flow in pipes and between rotating cylinders,
ARMA, 44(1), 1-22.

abst: Three component disturbance vector fields of the title flows, which are constant along a distinguished directin, imply the existence of a component of disturbance velocity which is not driven by disturbance pressure. This fact implies the existence of two

D.D. Joseph, 1971.
Stability of convection in containers of arbitrary shape,
J. Fluid Mech., 47(2), 257-282.

abst: When a container of fluid of arbitrary shape is heated from below and the temperature gradient exceeds a critical value (R_c²) the conduction solution with no motion becomes unstable and is replaced by convection. The convection may have two forms: one with 'upflow' at the centre of the container and one with 'downflow' there. Here we study the stability of the two forms of convection.

B.R. Munson, D.D. Joseph, 1971.
Viscous incompressible flow between concentric rotating spheres; Part 1, Basic flow,
J. Fluid Mech., 49(2), 289-303.

abst: The steady motion of a viscous fluid contained between two concentric spheres which rotate about a common axis with different angular velocities is considered. A high-order analytic perturbation solution, through terms of order Re^7, is obtained for low R

B.R. Munson, D.D. Joseph, 1971.
Viscous incompressible flow between concentric rotating spheres; Part 2, Hydrodynamic stability,
J. Fluid Mech., 49(2), 305-318.

abst: The energy theory of hydrodynamic stability is applied to the viscous incompressible flow of a fluid contained between two concentric spheres which rotate about a common axis with prescribed angular velocities. The critical Reynolds number is calculated..

D.D. Joseph, E.M. Sparrow, 1970.
Nonlinear diffusion induced by nonlinear sources,
Quarterly J. Applied Math., 28, 327-342.

abst: In the published literature dealing with a number of diverse scientific and technological problems, one encounters the mathematical system nabla^2psi+lambda g(x)Phi(psi)=0 in R, ...

D.D. Joseph, 1970.
Global stability of the conduction-diffusion solution,
ARMA, 36(4), 285-292.

abst: This paper continues and, to a degree, completes the working out of an energy-stability theory for the thermosolutal conduction-diffusion solution of the Boussinesq equations [1,2,3]. The Boussinesq equations allow a steady conduction-diffusion solution..

T.S. Fu, D.D. Joseph, 1970.
Linear instability of asymmetric flow in channels,
Physics of Fluids, 13(2), 217-221.

abst: A study of the linear stability of asymmetric channel flows is presented. Three one-parameter families of basic velocity which possess, respectively, no, one, and two inflection points are treated. The cmopeting effects of stabilizing asymmetry and destab

D.D. Joseph, B.R. Munson, 1970.
Global stability of spiral flow,
J. Fluid Mech., 43(3), 545-575.

abst: Energy and linear limits are calculated for the Poiseuille-Couette spiral motion between concentric cylinders which rotate rigidly and rotate and slide relative to one another. The addition of solid rotation can bring the linear limit down ...

P.C. Fife, D.D. Joseph, 1969.
Existence of convective solutions of the generalized Benard problem which are analytic in their norm,
ARMA, 33(2), 116-138.

abst: The generalized nonlinear Benard problem defined below, like the standard Benard problem itself, possesses a unique, motionless, conduction-solution when the parameters lie within a restricted range. This solution, however, bifurcates at certain ...

D.D. Joseph, 1969.
Uniqueness criteria for the conduction-diffusion solution of the Boussinesq equations,
ARMA, 35(3), 169-177.

abst: Energy stability theory gives sufficient conditions for the exponential stability of basic fluid motions [1]. If the basic motion is steady, the energy criterion is also sufficient for uniqueness [2]. However, since it is sufficient to guarantee ...

D.D. Joseph, S. Carmi, 1969.
Stability of Poiseuille flowin pipes, annuli, and channels,
Quarterly J. Applied Math., 26(4), 575-599.

abst: The value of R=180 which has been given by Orr [1] as a limit for sure stability of Hagen-Poiseuille flow is incorrect. A lower value, R=82.88, can be associated with an eigenfunction possessing a first mode azimuthal variation (N=1) and no streamwise var

D.D. Joseph, 1969.
Eigenvalue bounds for the Orr-Sommerfeld equation; Part 2,
J. Fluid Mech., 36(4), 721-734.

abst: Rigorous estimates of amplification rates, wave speeds and sufficient conditions for linear stability are derived for the manifold of solutions of the Orr-Sommerfeld problem governing parallel motion in the boundary layer and in round pipes. ...
7

C.C. Shir, D.D. Joseph, 1968.
Convective instability in a temperature and concentration field,
ARMA, 30(1), 38-80.

abst: In chemically homogeneous fluids, density differences induced by thermal gradients can drive fluid motions. If, in addition, there is a concentration gradient, e.g., a salt gradient or a gradient of water vapor in air, then the density variations ...

J.E. Mott, D.D. Joseph, 1968.
Stability of parallel flow between concentric cylinders,
Physics of Fluids, 11(10), 2065-2073.

abst: The linear stability of parallel flow in a concentric annulus to infinitesimal, axially symmetric disturbances in considered. First, the Poiseuille flow in annular cylinders is studied with the ratio k of the outer to inner cylinder as a parameter...

D.D. Joseph, R.J. Goldstein, D.J. Graham, 1968.
Subcritical instability and exchange of stability in a horizontal fluid layer,
Physics of Fluids, 11(4), 903-904.

abst: Rayleigh numbers calculated from linear and energy theories do not coincide when internal heat sources are present. For free boundaries exchange of stability applies, but energy theory nonetheless deems possible the existence of subcritical instabilities.

D.D. Joseph, 1968.
Eigenvalue bounds for the Orr-Sommerfeld equation,
J. Fluid Mech., 33(3), 617-621.

abst: Estimates of the eigenvalues C belonging to the manifold of solutions of the Orr-Sommerfeld equation are constructed by application ofelementary isoperimetric inequalities. The inequalities also lead to a considerable improvement on the estimate of (a-R)

D.D. Joseph, 1967.
Parameter and domain dependence of eigenvalues of elliptic partial differential equations,
ARMA, 24(5), 325-351.

abst: It is our purpose in this paper to exploit the technique of parameter differentiation for studying the calculus of eigenvalues. The study of the domain dependence of eigenvalues is emphasized, but not exclusively, and dependence of eigenvalues on other parameters of the generating boundary-value problem is also considered.

D.D. Joseph, W.H. Warner, 1967.
Parameter values excluded by existence conditions for buoyant dissipative motions in vertical channels,
Quarterly J. Applied Math., 25(2), 163-173.

abst: The nonexistence of steady, fully-developed solutions for frictionally heated buoyant flow in vertical channels is established analytically. Explicit bounds on the values of parameters beyond which solutions to this nonlinear problem cannot exist are ...

G.S. Beavers, D.D. Joseph, 1967.
Boundary conditions at a naturally permeable wall,
J. Fluid Mech., 30(1), 197-207.

abst: Experiments giving the mass efflux of a Poiseuille flow over a naturaly permeable block are reported. The efflux is greatly enhanced over the value it would have if the block were impermeable, indicating the presence of a boundary layer in the block. ...

C.C. Shir, D.D. Joseph, 1966.
Lubrication of a porous bearing -- Reynolds' solution,
J. Applied Mech., 33, 761-167.

abst: The problem of lubrication of a journal in a porous bearing is considered. A Reynolds equation modified to accommodate mass transfer with the fluid-saturated bearing is solved, and the influence of the permeability and radius ratio of the bearing is exami

D.D. Joseph, L.N. Tao, 1966.
Lubrication of a porous bearing -- Stokes' solution,
J. Applied Mech., 33, 753-761.

abst: Coupling of flows induced by the rotation of an infinite cylinder in an eccentric cylinderical hole in a fluid-saturated porous space is investigated in the context of a coupled boundary-value problem in which the Stokes flow outside porous regions and

D.D. Joseph, 1966.
Bounds on lambda for positive solutions of nabla^2 psi + lambda f(r) {psi + G(psi)}=0,
Quarterly J. Applied Math., 23(4), 349-354.

abst: We shall show that when G(psi) >=G(0)=1 and psi satisfies typical conditions on the closed (sufficiently smooth) boundary S of an open n dimsional region v, the values of lambda > 0 for shiwh the title equation has positive solutions...

D.D. Joseph, 1966.
Nonlinear stability of the Boussinesq equations by the method of energy,
ARMA, 22(3), 163-184.

abst: The linear theory of hydrodynamic stability suffers from the defect that one cannot, in principle make judgements regarding the growth potential of finite disturbances. Thus, one cannot say for certain that a given flow will remain stable if disturbed..

D.D. Joseph, C.C. Shir, 1966.
Subcritical convective instability; Part 1, Fluid layers,
J. Fluid Mech., 26(4), 753-768.

abst: This paper elaborates on the assertion tha energy methods provide an always mathematically rigorous and a somes physically precise theory of subcritical convective instability. The general theory, without explicit solutions, is used to deduce that ..

D.D. Joseph, S. Carmi, 1966.
Subcritical convective instability; Part 2. Spherical shells,
J. Fluid Mech., 26(4), 769-777.

abst: In this paper we consider the effect of internal heat generation and a spatial variation of the gravity field on the onset of thermal convection in spherical shells. If the temperature gradient and gravity fields have the same spatial variation, ...

T.S. Chen, D.D. Joseph, E.M. Sparrow, 1966.
Evaluation of Tietjens function in stability calculations,
Physics of Fluids, 9(12), 2519-2520.

abst: The Tietjens function is re-expressed as a ratio of raidly converging power series of its (complex) argument which may be utilized to replace tables or graphs in the calculation of critical Reynolds numbers from asymptotic theory.

D.D. Joseph, 1965.
Note on steady flow induced by rotation of a naturally permeable disc,
Quarterly J. Mech. Applied Math., 18(3), .

abst: Coupled flow induced by the steady rotation of a fluid saturated, naturally permeable and infinite disk is compared with the flow induced by the rotation of an otherwise impermeable disk over which a uniform suction has been prescribed. The coupled proble

D.D. Joseph, 1965.
On the stability of the Boussinesq equations,
ARMA, 20(1), 59-71.

abst: In this paper we generalize the method of energy to discuss the stability of thermally-driven convective flows governed by the Boussinesq equations. The energy method as applied to non-convective flows has the striking advantage that it may be applied to

D.D. Joseph, 1965.
Stability of frictionally-heated flow,
Physics of Fluids, 8(12), 2195-2200.

abst: Extended results relative to the existence of a critical stress (a finite shear stress or pressure gradient above which fully-developed steady solutinos do not exist) in Couette and Poiseuille motions are reported. The results apply to liquids under gener

D.D. Joseph, L.N. Tao, 1965.
Unsteady Free and Forced Convection in Vertical Annular and Annular Sector Tubes,
Developments in Mechanics, Proceedings of the 8th Midwestern Mechanics Conference at Case Institute of Technology, April 1-3, 1963, , 403-404.

abst: In this investigation solutions to the problem of unsteady laminar forced and free convection in coaxial sector tubes in the presence of a constant axial temperature gradient have been developed. The solutions admit phenomena of oscillation and resonance which are not usually present in flows in which the dissipative mechanisms of heat conduction and viscosity are important. Several numerical examples are constructed and used to discuss the "dashpot" features of the solutions.

D.D. Joseph, 1965.
Non-linear heat generation and stability of the temperature distribution in conducting solids,
Int. J. Heat Mass Transfer, 8, 281-288.

abst: The effect of non-linear dependence of resistance on temperature on the Joulean production of heat in electrically conducting systems is investigated. The theory is compared with well-known linear theories. In common conducting materials there exists...

D.D. Joseph, L.N. Tao, 1965.
Ground flow induced by a moving cylinder,
Physics of Fluids, 8(8), 1438.

abst: Ground flow induced by rotation and translation of a solid cylinder is investigated in the context of a coupled boundary-value problem in which the Stokes flow outside porous regions and the arcy flow inside porous regions are connected by the continuity

D.D. Joseph, 1964.
Incompatibility of Beltrami Flow with Viscous Adherence,
Physics of Fluids, 7(5), 648-651.

abst: Boundary conditions on the vorticity are deduced to infer conditions under which Beltrami flows of a viscous fluid are possible. The inconsistency of steady and unsteady Beltrami flow with adherence to rigid surfaces is established for a broad class of rigid motions of the bounding surfaces. The implications of isochoric motions are explored, and the possibility of an isochoric Beltrami motion of a Newtonian fluid is eliminated for rigid translatory motions of the boundary surface. The inconsistency of Beltrami Blows of any fluid with rotation about an axis of geometric symmetry is also established. It is shown that the adherence condition implies either a vanishing or infinite vorticity at boundary surfaces for certain kinematically possible types of Beltrami motions.

D.D. Joseph, L.N. Tao, 1964.
The Effect of Permeability on the Slow Motion of a Porous Sphere in a Viscous Liquid,
Zeitschrift AMM, 44(8), 361-364.

abst: A technique is suggested by which the effects of permeable materials on the low Reynolds number flow of viscous liquids may be evaluated. In particular, we show that Darcy's law and the asymptotic equations (Re->0) of Stokes may be used to formulate boundary value problems generating solutions valid for both porous and non-porous regions and matched at common boundaries. The coupled problem of the streaming of a viscous liquid past a permeable sphere is considered and closed solutions which depend simply on the permeability on the sphere are derived. The drag on a permeable sphere is shown to be the same as the drag on an impermeable sphere of reduced radius.

D.D. Joseph, 1964.
Variable Viscosity Effects on the Flow and Stability of Flow in Channels and Pipes,
Physics of Fluids, 7(11), 1761-1771.

abst: Variable viscosity and frictionally heated channel and pipe flows are investigated. The solutions are bounded and improved estimates of the critical stress (beyond which there are no steady solutions) developed. The stress first increases, then decreases, with increasing maximum temperature. At this stress maximum there is a neutral solution and neighboring unstable solutions to an associated stability problem. Points of inflection in the velocity profile can develop in Poiseuille flows and must develop in Couette flows. The Poiseuille profiles which develop are inviscidly unstable in channels but stable in pipes.

D.D. Joseph, L.N. Tao, 1963.
Transverse Velocity Components in Fully Developed Unsteady Flows,
J. Applied Mech., , 147-148.

abst: It is known that if an incompressible fluid is confined to straight pipe or channel, and if the axial velocity is steady and fully developed, then, under certain very general conditions, no transverse velocity components can exist. This conclusion is not valid for unsteady flows, and it is the purpose of this note to develop the appropriate restrictions for the unsteady case.

L.N. Tao, D.D. Joseph, 1962.
Fluid flow between porous rollers,
J. Applied Mech., 29, 1-5.

abst: The problem of fluid flow between two porous rollers with a small gap is investigated. Solutions for both large and small values of the porosity of the minimum gap distance are derived. It is found tht increasing porosity will decrease the maximum suction and shift its position away from the origin.