Isotropic Viscosity of Solid Spherical Suspensions in crystalline States

A geometric description of particle stresses in a mixture determines isentropic viscosity of solid spherical suspensions at arbitrary concentrations based on the suspensions’ microstructural crystallinity. For an equal-sized spherical suspension system, the resulting geometric expression predicts well the classical experimental and numerical viscosity data at different particle concentrations, when the crystalline states are considered as simple cubic, random distribution, face-centered cubic or body-centered cubic. It is concluded that some observed non-Newtonian behaviors of a suspension system can be construed as micro-structural transitions. This geometric model agrees remarkably well with light-scattering experimental observations on structural transitioning in colloidal and non-colloidal mixtures. Effects of particle inertia and particle Brownian fluctuations on the viscosity are taken to be dependent on solutions’ crystalline states. For colloidal suspensions, flow-induced particle pressure and collective self-diffusion of particles mitigate a mixture to transitioning to a less dissipative, higher-order jamming symmetry at higher volume fractions or higher shear rates.