Confined steady simple shear flow of polymeric liquids

Abstract

In a confined simple shear flow, the macromolecules of a polymeric liquid reorient near the walls so that the measured viscosity decreases. For instance, in a small-amplitude oscillatory shear flow, the real part of the complex viscosity decreases with confinement, and macromolecular orientation explains this. These effects in oscillation have been explained analytically for a rigid dumbbell suspension and, for a confined small-amplitude oscillatory shear flow, the summation coefficients have been determined. By contrast, for the confined steady shear flow, the summation coefficients are undetermined. In this paper, we determine these coefficients and use them to evaluate the steady shear (i) viscosity and (ii) normal stress coefficients for a rigid dumbbell suspension. We find that the zero-shear viscosity and the zero-shear first normal stress coefficients decrease with confinement. We further find that the dimensionless (i) steady shear viscosity curve increases with confinement and (ii) first normal stress coefficient first decreases with light confinement and then increases with greater confinement. We confirm our theory, at low confinement, by comparing with our new measurements of the confined zero-shear viscosity of a polystyrene solution.