The shear-induced migration of particles in concentrated suspensions

In the course of viscometric measurements of concentrated suspensions of spheres in Newtonian fluids using a Couette device, Gadala-Maria & Acrivos (1980) observed a decrease in the suspension viscosity after long periods of shearing even though the viscosity of the pure suspending fluid remained constant under identical conditions. In the present work we demonstrate that this phenomenon is due to the shear-induced migration of particles out of the sheared Couette gap and into the fluid reservoir, which reduces the particle concentration in the gap and thereby the observed viscosity. We show further that this rate of viscosity decrease is consistent with a gap-limited shear-induced diffusion process normal to the plane of shear, with the relevant diffusion coefficient being proportional to $a^2\dot{\gamma}$ , where a is the particle radius and $\dot{\gamma}$ is the applied shear rate. Additional experiments also uncovered a new phenomenon - a short-term increase in the viscosity upon initial shearing of a suspension in a Couette device - which was attributed to the diffusive migration of particles across the width of the Couette gap and thus was used to infer values of the corresponding diffusion coefficient within the plane of shear parallel to gradients in fluid velocity. In the theoretical part we demonstrate that the particle migrations that led to these observed phenomena may be explained in terms of the irreversible interparticle interactions that occur in these suspensions. From simple arguments, these interactions are shown to lead to effective diffusivities both normal to the plane of shear and normal to the direction of fluid motion within the plane of shear whose estimated magnitudes are comparable with those that were inferred from the experimental measurements. Furthermore, these interactions should induce, within a shear flow, particle drifts from regions of high to low shear stress, which are estimated to be of sufficient intensity to account for the observed initial viscosity increase mentioned above.