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 --> infinity 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 = (gamma) over dot a(2)/2D is the Peclet number with (gamma) over dot 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 --> infinity. 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 an excess of particles along the compressional axes. The product of the asymmetric pair-distribution function and the thin boundary layer volume is now O(1) (with dependence on b/a) as Pe --> infinity, thus yielding non-Newtonian rheology with normal stresses scaling as eta(gamma) over dot, where eta is the fluid viscosity. For a dilute suspension without hydrodynamic interactions in a general linear flow, the bulk stress resulting from pair interactions is proportional to eta(gamma)over dot phi(b)(2)(a/b), where phi(b) = 4/3 pi b(3)n is the thermodynamic volume fraction. Including hydrodynamic interactions, the hydrodynamic normal stress differences are O(eta(gamma)over dot phi(2)). The O(phi(2)) hydrodynamic contribution to the viscosity due to the boundary layer is shear-thickening The broken symmetry and boundary-layer structure also yield a shear-induced self-diffusivity of O((gamma) over dot a(2) phi) as Pe --> infinity. At higher concentrations the boundary-layer structure is the same, with the pair-distribution function outside the boundary layer changed from its dilute value to a concentration-dependent function g(infinity)(r;phi), which must be determined self-consistently; the function g(infinity)(r;phi) is not determined here. The appropriate Peclet number at high concentration is based on the concentration-dependent short-time self-diffusivity (P) over bar e = (gamma)over dot a(2)/2D(0)(s)(phi). The stress contributions from the boundary layer scale as eta(gamma) over dot phi(2)g(infinity)(2;phi)D/D-0(s)(phi), where g(infinity)(2;phi) is the pair-distribution function at contact, and are argued to be dominant at high concentrations. The long-time self-diffusivity arising from the boundary-layer structure is predicted to scale as (gamma) over dot a(2) phi g(infinity)(2;phi).