# University of Minnesota

Aerospace Engineering and Mechanics

**Fall 2000 Seminar Series**

*Viscous Heating and the Stability of Newtonian and
Non-Newtonian Taylor-Couette Flow*

*Abstract*

**Viscoelastic forces are well-known to
produce instabilities which are absent in Newtonian fluids and which may impose
significant limitations on polymer processing operations such as extrusion or
fiber spinning. Such instabilities are also present in the model problem of
rotational shearing flow between concentric cylinders (Taylor-Couette flow).
Our recent experimental work has focused on the Taylor-Couette problem both as
a model for instabilities in polymer processing flows and as a test of
constitutive equations for polymeric liquids. The isothermal Taylor-Couette
system has long been a paradigm for studies of stability and transitions for
Newtonian fluids; here, as the rotation rate of the inner cylinder is
increased, the purely azimuthal base flow becomes unstable at a critical
Reynolds number and is replaced by a stationary, axisymmetric vortex flow. This
instability is driven by centrifugal forces and thus does not occur if the
inner cylinder is held fixed and the outer cylinder is rotated. In the case of
viscoelastic fluids, e.g. dilute solutions of polymers, a purely elastic
instability occurs at vanishing Re. Here the flow is predicted to become
unstable to an oscillatory, non-axisymmetric vortex flow at a critical value of
fluid elasticity. Since the elastic instability is unrelated to centrifugal
forces, it occurs for both rotation of the inner and rotation of the outer
cylinder. While a purely elastic instability has been documented experimentally
in a range of polymer solutions, and is indeed independent of which cylinder is
rotated, there remain a number of discrepancies between experiments and
predictions. Recent experiments have revealed that viscous heating in
***Newtonian* fluids drives a transition to a new, oscillatory mode of
instability at a critical Reynolds number which is significantly below that at
which the isothermal, centrifugal transition is predicted and observed. A
similar destabilization of viscoelastic modes through viscous heating may
explain the discrepancies between the observed and predicted spatial and
temporal symmetry of the disturbance flow and the critical conditions.

###

### Friday,
October 13, 2000

209 Akerman
Hall

2:30-3:30 p.m.

### Refreshments served after the seminar in
227 Akerman Hall.

Disability accomodations provided upon request.

Contact Kristal Belisle, at (612)
625-8000.