  The rheology of dense Brownian suspensions of hard spheres is investigated
numerically beyond the low shear rate Newtonian regime. We analyze an athermal
analogue of these suspensions, with an effective logarithmic repulsive
potential representing the vibrational entropic forces. We show that both
systems present the same rheology without adjustable parameters. Moreover, all
rheological responses display similar Herschel-Bulkley relations once the shear
stress and the shear rate are respectively rescaled by a characteristic stress
scale and by a microscopic reorganization time-scale, both related to the
normal confining pressure. This pressure-controlled approach, originally
developed for granular flows, reveals a striking physical analogy between the
colloidal glass transition and granular jamming.
