Viscosities of concentrated dispersions

A theory is presented to describe the effects of particle shape, orientation, and volume fraction on the anisotopic viscosities of concentrated colloidal dispersions. We start with Stokesian dynamics; a particle-shape tensor is derived from the analysis, which is then included in a fluid lattice model for the determination of the anisotopic viscosities. The theory considers not only the interaction between the particles but also the local interaction within the equilibrium microstructure. For spherical particles, our theory compares well with experimental data from dilute, semidilute, or concentrated dispersions. For nonspherical particles at high concentrations, our calculation reveals that the system undergoes a transition which is identified as the percolation threshold. At this critical concentration (${\mathrm{\phi }}_{\mathit{c}}$), the fluidity of concentrated dispersions slows down drastically. Our calculation reveals that this threshold is a strong function of particle shape and orientation.