The Pathological Behaviour of Sheared Hard Spheres with Hydrodynamic Interactions

We present numerical evidence that the ideal model of sheared concentrated hard spheres with just hydrodynamic interactions does not reach a steady state. The distribution of gaps between particles collapses to ever smaller values as strain is increased from rest until the problem becomes numerically intractable. The case of the Reynolds lubrication interaction is marginal in a more general family of models in which viscous interactions diverge as a power law of the inverse interparticle gap. The non-equilibrium hard-sphere model represents a limiting pathology for real colloids.