Direct Simulation of the Motion of Particles in Flowing LiquidsApplicationsFundamental DynamicsStudies of Local Rearrangement MechanismsThe clusters and anisotropic microstructures observed in solid-liquid flows,
such as those shown here. Particle-Particle InteractionsParticle pair interactions are fundamental mechanisms which enter strongly
into all practical applications of particulate flows. They are due to inertia
and normal stresses and they appear to be maximally different in Newtonian and
viscoelastic liquids. The principal interactions between neighboring spheres
can be described as drafting, kissing and tumbling in Newtonian
liquids. Particle-Wall InteractionsParticle-wall interactions also produce anisotropic microstructures in
particulate flows, such as clear zones near walls, and the like. If a sphere is
launched near a vertical wall in a Newtonian liquid, it will be pushed away
from the wall to an equilibrium distance at which lateral migrations stop. Direct Numerical SimulationsHere is a video animation (1.5 MB mpeg) made from an actual dynamical simulation. It shows 6 particles falling under gravity in an Oldroyd B fluid. Particles behave differently in viscoelastic fluids than they do in Newtonian fluids. In Newtonian fluids, particles draft, kiss, and tumble. In viscoelastic fluids, by contrast, particles draft, kiss, and chain. Long chains fall faster than short chains. Statistical AnalysisStatistical analysis of simulations is yet another window in which to view the fundamentals of solid-liquid flows. The time-averaged particle (or bubble) dynamics in a periodic or infinite domain can be described in terms of the number density, velocity current, and force correlations, and their Fourier transforms. The number density correlation gives the relative arrangement and motion of the particles; the velocity current correlation gives the propagation velocities of the dominant modes; and the force correlation gives the form of the forcing term driving the particle system. For a numerical solution, the above distributions can be easily obtained by recording the particles' (or bubbles') coordinates, velocities and forces at regular time intervals. Empirical CorrelationsOne of the great engineering opportunities of the present day is the use of direct numerical simulations to construct empirical correlations, of the kind usually generated from experiments. We can hope to construct correlations similar to that of Richardson and Zaki for fluidized suspensions, and to the friction factor vs. Reynolds number correlation for slurries. There are many other possibilities. However, engineering practice would not admit such numerically generated correlations without first verifying that they work in benchmark cases; therefore, experiments must be considered. Two-Fluid ModelingIn the past, solid-liquid flows were studied using continuum modeling. When done rigorously, using spatial, temporal or ensemble averaging, this leads to ``two-fluid'' models in which one of the two fluids is the solids phase. The equations are formally correct, but the terms of interactions must be modeled, and models which work for one flow may not work for another. Direct simulations can provide clues for modeling the interaction terms and a standard to judge the performance of modeling assumptions. | AEM Home | Institute of Technology | | Academics |
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