Microstructure of strongly sheared suspensions

The eects of Brownian motion alone and in combination with an interparticle force of hard-sphere type upon the particle conguration in a strongly sheared suspension are analysed. In the limit Pe! 1 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-diusivity. Here, Pe = _γa2=2D is the Peclet number with _γ the shear rate, a the particle radius, and D the diusivity of an isolated particle. Brownian diusion at large Pe gives rise to an O(aPe−1) thin boundary layer at contact in which the eects of Brownian diusion and advection balance, and the pair-distribution function is asymmetric within the boundary layer with a contact value of O(Pe0:78) in pure-straining motion; non-Newtonian eects, which scale as the product of the contact value and the O(a3Pe−1) layer volume, vanish as Pe−0:22 as Pe!1. If, however, particles are maintained at a minimum separation of 2b, with b> a, by a hard-sphere force there is also a boundary layer of thickness of O(aPe−1), but the asymmetry of the pair-distribution function for this situation is O(Pe), with a