Instabilities In Shear Flow Of Viscoelastic Fluids With Fading Memory

Instabilities in Shear Flow of Viscoelastic Fluids with Fading Memory

For certain models of viscoelastic fluids with fading memory, classical steady channel flow does not exist beyond a maximal wall shear stress. This occurs when the shear stress for steady flow decreases with strain. For generalized Newtonian models of viscoelastic flow, such a decrease implies that the flow is unstable. Because of this example, a constitutive relation that exhibits a maximal wall shear stress in regarded as defective. The author reports on work showing that, contrary to this intuition, such models correctly describe the experimentally observed spurt phenomenon: exceeding this critical stress results in large increase in volumetric flow rate. The transition to spurt flow is analogous to a dynamically generated phase transition. To analyze this phenomenon, we derive a system of conservation laws that govern the flow; these equations take the form of gas dynamics with relaxation terms. We solve the Riemann problem for this non-strictly-hyperbolic system, and incorporate this solution into the random choice method. Numerical simulation of channel flow, with the maximal wall shear stress exceeded, shows that a discontinuity forms at the wall, allowing the fluid to slip; no steady state exists. However, when a small Newtonian viscosity is included in the model, a slip layer forms and the flow approaches a discontinuous steady state. (KR).

The Breadth and Depth of Continuum Mechanics

This volume collects papers dedicated to Jerry Ericksen on his sixtieth birthday, December 20, 1984. They first appeared in Volumes 82-90 (1983-1985) of the Archive for Rational Mechanics and Analysis. At the request of the Editors the list of authors to be invited was drawn up by C. M. Dafermos, D. D. Joseph, and F. M. Leslie. The breadth and depth of the works here reprinted reflect the corresponding qualities in Jerry Ericksen's research, teaching, scholarship, and inspiration. His interests and expertness center upon the mechanics of materials and extend to everything that may contribute to it: pure analysis, algebra, geometry, through all aspects of theoretical mechanics to fundamental experiment, all of these illumi nated by an intimate and deep familiarity with the sources, even very old ones. He is independent of school and contemptuous of party spirit; his generosity in giving away his ideas is renowned, but not everyone is capable of accepting what is offered. His writings are totally free of broad claims and attributions beyond his own study. Some are decisive, some are prophetic, and all are forthright. His work has served as a beacon of insight and simple honesty in an age of ever more trivial and corrupt science. The authors of the memoirs in this volume are his students, colleagues, admirers, and (above all) his friends.

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