Inertia and dissipation mechanism in jammed soft-particle suspensions

Suspensions of soft particles exhibit a remarkable bifurcation at the random close packing volume fraction, fc. There is a yield stress above fc but not below, and the flow curves at various f have been shown to collapse onto a universal scaling function near this point. Particle-level models take contact deformation into account to model elastic forces and treat the drag forces in the very dense regime where long-range hydrodynamic interactions are thought to be negligible - with varying levels of sophistication: from ``pair-drag'' formulations that apply a lubrication calculation to the film at contact to simple ``mean drag'' approaches where the mobility matrix is diagonal. We show that, in simple shear, these two model give consistent results for the shear modulus, yield stress, and single-particle diffusivity as functions of f but only in the quasi-static regime. They show dramatically different behavior in the rate-dependent regime. In particular, the diffusion constant scales as the shearing rate to a non-trivial power with the power depending on the damping mechanism. Furthermore, we explore a ``granular'' regime where the inertia of the particles is no longer negligible and the finite rate behavior shows a complex interplay between inertial and dissipative timescales.