The kinetics of flowing dispersions. VI. Transient orientation and rheological phenomena of rods and discs in shear flow

Abstract

The nonequilibrium state of the probability distribution of orientations of nonspherical axisymmetric rigid particles is derived for a dilute suspension subjected to a simple shear flow assuming no particle interactions and negligible Brownian motion. If the particles in the suspension are initially oriented randomly, the orientation distribution function undergoes undamped oscillations of frequency twice that of a particle rotation about the vorticity axis. Thus the instantaneous rheological properties of the suspension, such as the intrinsic normal stress differences and the intrinsic viscosity which are obtained as averages with respect to orientation, should also oscillate with time. Experiments on sheared suspensions of rigid rods and discs have shown that the orientation distribution does oscillate but is damped, dying away to an equilibrium distribution which may then proceed to change slowly with time. Two possible causes for this damping are considered, the first being the slight variation in shape between particles and the second, the changes in orientations resulting from 2-body interactions. In both cases, the rotating particles experience changes in rotational phase which lead eventually to the equilibrium distribution of orientation and of the associated rheological properties. It is predicted that the systems are non-Newtonian in the nonequilibrium state except when the equivalent axis ratio is unity (corresponding to spheres), but Newtonian in the equilibrium state. Each mechanism has its own relaxation time for which approximate equations are derived.