EFFECT OF MICROSTRUCTURE ON THE VISCOSITY OF HARD-SPHERE DISPERSIONS AND MODULUS OF COMPOSITES

Results from theory and experiment in the literature for the viscosity of dispersions of monodisperse hard spheres are contrasted to highlig ht the effects of particle microstructure, such as ordered spatial dis tributions versus random or partially aggregated dispersions. Hard sph eres, comprising a simple ideal limit with no interparticle forces oth er than infinite repulsion at contact, are achieved experimentally by either minimizing van der Waals attractions or negating them with shor t range repulsions. For dispersions, the balance between viscous force s and Brownian motion, as gauged by the Peclet number Pe, determines t he microstructure and, hence, the viscosity. This results in a progres sion from isotropic equilibrium at Pe = 0, a small perturbation orient ed in the principle direction of strain for Pe much less than 1, two-d imensional anisotropy for Pe much greater than 1, and a return to isot ropy, albeit hydrodynamically dominated, at Pe = infinity. The viscosi ties for hard spheres vary in the order eta(hyd)(Pe - infinity) greate r-than-or-equal-to eta0(Pe much less than 1) greater-than-or-equal-to eta(infinity)(Pe much greater than 1) greater-than-or-equal-to eta(inf inity)'(Pe = 0). The first three represent steady shear viscosities, w hile the last results from high frequency, small amplitude oscillation s. At low Peclet numbers, both aggregation owing to short range attrac tions and long range repulsions increase the steady shear viscosity. W ith permanent aggregates the effect persists to Pe = infinity, with th e data available for n(hyd) indicating a monotonic increase with degre e of aggregation. Hence, these results for hard spheres generally repr esent limiting cases. A fundamental connection also exists between com posites of hard particles in an incompressible, elastic continuous pha se and dispersions of spheres with a corresponding microstructure. The analogy between Hookean elasticity and Stokes flow means that the sta tic shear modulus of the former, normalized by the modulus of the cont inuous phase, equals the high frequency limiting relative viscosity of the latter. A combination of data and rigorous theory demonstrates th at the modulus of a composite decreases in the order: simple cubic > r andom > body centered cubic > face centered cubic, that is, in order o f increasing distance between nearest neighbors at the same volume fra ction.