The viscosity of bimodal and polydisperse suspensions of hard spheres in the dilute limit

Abstract

An exact result is calculated numerically for the dilute limiting, zero shear viscosity of bimodal suspensions of hard spheres. The required hydrodynamic functions are calculated from recent results for the resistivities of unequal spheres. Both the hydrodynamic and Brownian contributions to the Huggins coefficient exhibit a minimum that is symmetric in mixing volume fraction. The resultant minimum deepens with increasing size ratio. The results are discussed in the light of published measurements of the viscosity for bimodal suspensions and previous phenomenological theories. The reduction of viscosity upon mixing is seen to be a result of near-field hydrodynamic shielding of asymmetric particle pairs. It is also shown that the use of far-field hydrodynamic interactions yields qualitatively incorrect results for the viscosity of binary mixtures. A parametrization of the bimodal results allows an estimation of the effects of suspension polydispersity on the Huggins coefficient. For polydispersities of ten percent or less, the Huggins coefficient is essentially unchanged from the value calculated for an equivalent, monodisperse suspension at equal volume fraction. A parametrization of these results is provided for relating the reduction in Huggins coefficient to the polydispersity index.