Development of shear bands for a model of a thixotropic yield stress fluid

Abstract

The PEC (partially extending strand convection) model of Larson is able to describe thixotropic yield stress behavior in the limit where the relaxation time is large relative to the retardation time. In this paper, we discuss the development of shear bands in a Poiseuille flow which is started up from rest with an imposed pressure gradient. We analyze the asymptotic limit of large relaxation time; the small parameter ϵ measures the ratio of retardation time to relaxation time. We determine the position and width of shear bands as a function of time. We identify an initial phase of “fast yielding” during which the width of the transition between high and low shear rate regions behaves like t−3. This continues until t (measured on the scale of the retardation time) is on the order of ϵ−1/3. Then there is a phase of “delayed yielding” during which the width of the transition is of order ϵ. Eventually, the width sharpens as 1/(ϵ2t3). We also show how these results are modified by introducing Korteweg stresses which prevent the transition from becoming infinitely sharp and also change the location where the transition takes place.This paper is dedicated to Roger Tanner on the occasion of his eighty-second birthday.