Time-dependent shear flows of a suspension of particles with weak Brownian rotations

Abstract

A dilute suspension of rigid axisymmetric particles in a time-dependent shear flow is considered in circumstances where the shear flow alignment of the particles dominates small but not unimportant Brownian disorientations. Three cases are studied: stress relaxation on the cessation of a steady shear, the sudden application of a steady shear from a state of rest and the sudden change from one steady shear rate to another. The rheology exhibits effects on two basic time scales provided that the particle aspect ratio r is not extreme: oscillatory features with a frequency proportional to the shear rate γ which are due to the rotation of the particles about their Jeffery orbits, and an exponentially fading memory due to Brownian diffusion with a characteristic time praportional to the inverse diffusion rate D⁻¹. When the particle aspect ratio r becomes large, the oscillation frequency is reduced to γ/r while the diffusion rate is enhanced to Dr² for some features and to Dr⁴ for others.