Microstructure of strongly sheared suspensions and its impact on rheology and diffusion

The effects of Brownian motion alone and in combination with an interparticle force of hard-sphere type upon the particle configuration in a strongly sheared suspension are analysed. In the limit Pe →∞ under the influence of hydrodynamic interactions alone, the pair-distribution function of a dilute suspension of spheres has symmetry properties that yield a Newtonian constitutive behaviour and a zero self-diffusivity. Here, Pe =γ˛ a 2 /2 D is the Péclet number with γ˛ the shear rate, a the particle radius, and D the diffusivity of an isolated particle. Brownian diffusion at large Pe gives rise to an O ( aPe −1 ) thin boundary layer at contact in which the effects of Brownian diffusion and advection balance, and the pair-distribution function is asymmetric within the boundary layer with a contact value of O ( Pe 0.78 ) in pure-straining motion; non-Newtonian effects, which scale as the product of the contact value and the O ( a 3 Pe −1 ) layer volume, vanish as Pe −0.22 as Pe →∞.