Simple methods for obtaining flow reversal conditions in Couette–Poiseuille flows

Abstract

Couette–Poiseuille (C–P) flow, which is driven by drag from a moving wall and a pressure gradient, can exist in different states depending on the relative strengths of the two above-mentioned factors. Of particular interest is the onset of flow reversal, which is characterized kinematically by a zero shear rate on the stationary wall. This study presents two different methods for obtaining the critical conditions for the onset of flow reversal in C–P flows. In the first method, exact values of the critical flow rate and pressure gradient are computed by solving a pair of algebraic equations derived from the Weissenberg–Rabinowitsch relation. Using this method, the difficulty in solving the nonlinear differential equation is avoided. In the second method, estimates of the critical conditions are obtained analytically by locally approximating the given fluid as a power-law fluid. To evaluate the prediction accuracy, the methods are applied to the C–P flows of Carreau–Yasuda and Bingham–Carreau–Yasuda fluids. It is demonstrated that the relative errors remained reasonably low in most system parameter ranges, except in cases where the flow curve in the log–log scale is highly nonlinear.