Instability of Inelastic Shear-Thinning Liquids in a Couette Flow Between Concentric Cylinders

Abstract

Circular Couette flow of inelastic shear-thinning materials in annuli is examined. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, well known as Taylor vortices. The presence of these vortices changes the hydrodynamic and heat transfer characteristics of the processes at which this type of flow occurs. Therefore, it is quite important to be able to predict the onset of instability. Most of the available theoretical and experimental analyses are for Newtonian and viscoelastic (dilute polymeric solutions) liquids. In this work, the effect of the shear-thinning behavior of high concentration suspensions on the onset of the Taylor vortices is determined theoretically by solving the conservation equations, constructing the solution path as the inner cylinder speed rises and searching for the critical conditions. This procedure avoids the need for a stability analysis of the flow and the solution of an eigenproblem. The differential equations were solved by the Galerkin/finite-element method and the resulting set of nonlinear algebraic equations, by Newton’s method.