Dynamics of rigid dumbbells in confined geometries Part II. Time-dependent shear flow

This paper describes analytical solutions to the response of a rigid dumbbell to a time-dependent simple shear flow in a channel of arbitrary size. The results were applied for specific flows, such as the sudden inception and cessation of simple shear and oscillatory shear flow. The introduction of confining walls leads to several qualitative differences compared with an unbounded flow such as initial negative jumps in the contribution of the dumbbell to the viscosity and the first normal stress coefficient. In addition, wall effects lead to a breakdown of well-known relationships between the complex viscosity and the complex normal stress coefficient during oscillatory flow.