Viscosity of bimodal and polydisperse colloidal suspensions

We present a theoretical framework for the viscosity of bimodal and polydisperse colloidal suspensions. For colloidal dispersions both interparticle forces between pairs of particles and many-particle effects such as depletion forces can have a significant effect on rheology. As hydrodynamic interactions are also important for colloidal systems, a theoretical description that includes hydrodynamic and thermodynamic interactions is required. An integral equation theory for multicomponent systems accounts for the contribution of thermodynamic interactions to the viscosity of dispersions. Introduction of small particles into a system of larger particles causes depletion forces between the large particles that increase the viscosity, while replacing large particles with an equal volume fraction of small particles increases the free volume in the system and decreases the viscosity. The integral equations model both of these effects in concentrated suspensions and provide a microscopic interpretation of free volume changes as changes in radial distribution functions. For a bimodal mixture they predict a dependence of the viscosity on size ratio, composition, and total volume fraction. Polydispersity is modeled by a small number of components whose sizes and weights are chosen to match the moments of the size distribution. This theory predicts a reduction in viscosity due to polydispersity and explains conflicting experimental measurement of the viscosity of hard-sphere colloids. Existing theoretical approaches that neglect the multiparticle correlations, included through the integral equations, yield qualitatively incorrect results for the change in the viscosity relative to monodisperse systems.