Simulations of a heavy ball falling through a sheared suspension

In recent experiments, Blanc et al. (J Fluid Mech 746:R4, 2014) dropped a heavy sphere through a concentrated suspension of smaller, neutrally buoyant particles. They found that the application of a lateral oscillatory shear flow caused the heavy ball to fall faster on average, and that for highly concentrated suspensions, at certain moments of the cycle of shear oscillation, the heavy ball moved upwards. We use Stokesian Dynamics to model these experiments and other related scenarios. We show how the motion of the heavy particle and the microstructure of the suspension depend on two key dimensionless parameters: the frequency of the oscillations (relative to a typical settling time) and the strength of repulsive interparticle forces, relative to the buoyancy-adjusted weight of the heavy ball. We offer a mechanism which describes some of the observed behaviours: the formation and breakup of vertical repulsion chains.