The flow of dilute polymer solution in a narrow channel. I. The slip effect in simple shear flow

Abstract

Existing experimental data have suggested that the flow of a dilute polymer solution near a wall exhibits a slip effect. In the case of a plane shear flow, the suspension of macromolecules contributes a nonuniform stress field profile across the channel which causes the velocity field to deviate from its otherwise linear profile. The apparent slip velocity can be calculated from such deviation. In this paper, we consider the flow problem of a suspension of bead-spring molecules in the presence of solid reflective boundary. Analytical and simulation solutions to the problem are obtained which do not require any small shear rate assumption. The added stresses contributed by the molecules are used to derive the slip velocity and the effective viscosity. Extension to nonlinear Warner spring model is also attempted by the simulation and the results give rise to some qualitative features which cannot be accounted for by the linear model.