Computation of rheological properties of suspensions of rigid rods: Stress growth after inception of steady shear flow

The orientation distribution and stress growth for a suspension of rigid rods (or dumbbells) in a Newtonian solvent are calculated for inception of steady shear flow. Galerkin's method, with spherical harmonics as trial functions, is used in the spatial coordinates to obtain a system of ordinary differential equations in time which is solved by the spectral method. The method is applicable over a wide range of dimensionless shear rates (Peclet numbers) and has been coded with standard system-solvent and eigensystem packages. For sufficiently large Peclet numbers, the results give the well known rigid-dumbbell prediction of an overshoot in the shear viscosity and normal stress differences. This overshoot is then followed by an undershoot. An explicit analytical approximation for the fluid stresses is presented which is reasonably accurate for Peclet numbers less than unity.