Scaling relationships between viscosity and diffusivity in shear-thickening suspensions.

Abstract

Dense suspensions often exhibit a dramatic response to large external deformation. The recent body of work has related this behavior to transition from an unconstrained lubricated state to a constrained frictional state. Here, we use numerical simulations to study the flow behavior and shear-induced diffusion of frictional non-Brownian spheres in two dimensions under simple shear flow. We first show that both viscosity <i>η</i> and diffusivity <i>D</i>/<i></i> of the particles increase under characteristic shear stress, which is associated with lubrication to frictional transition. Subsequently, we propose a one-to-one relationship between viscosity and diffusivity using the length scale <i>ξ</i> associated with the size of collective motions (rigid clusters) of the particles. We demonstrate that <i>η</i> and <i>D</i>/<i></i> are controlled by <i>ξ</i> in two distinct flow regimes, <i>i.e.</i> in the frictionless and frictional states, where the one-to-one relationship is described as a crossover from <i>D</i>/<i></i> ∼ <i>η</i> (frictionless) to <i>η</i>^1/3 (frictional). We also confirm that the proposed power laws are insensitive to the interparticle friction and system size.