The interpretation of observed pressure gradients in laminar flow of non-newtonian liquids through tubes

Abstract

It is possible to detect anomalous flow of a non-Newtonian liquid near a rigid boundary, by plotting the apparent fluidity (as given by Poiseuille's formula) against the reciprocal of the shear stress at the wall in laminar flow through tubes of various diameters. This method of plotting has some advantages over others. If the properties of the liquid in shear are everywhere specified by a unique stress/rate-of-strain relationship, all the plotted points should lie on a single curve, and a wall effect is indicated if distinct curves arise from different diameters of tube. It is shown that a wall effect can be measured by an effective slip coefficient, which is a function of the stress at the wall. The mathematical argument is based on the assumptions (i) that the flow is rectilinear, (ii) that there is no actual slip at the wall, and (iii) that the functional relationship between stress and rate-of-strain is dependent on the normal distance from a solid boundary, in a thin layer of liquid near the boundary only.