Shear-induced particle migration in viscous suspensions with continuous size distribution: the cases of parallel plates and cone and plate

Abstract When the effective viscosity of a viscous suspension is measured in rotating devices as parallel plates or cone and plate, the detected measurement changes continuously in time. This dynamic phenomenon is caused by shear induced particle migration. Stationary measurements are obtained only after the migration ceases in the entire volume of the sheared domain. In this work, we examine the stationary situation in cases when the suspension contains particles that have a continuous size distribution. The problem is formulated in terms of moments of the particle size distribution. We examine a particular case for which the stationary properties, such as local concentration and average particle size, are determined, and the effects on physical variables are obtained. The work provides a comparison between the results obtained for the two mentioned devices.