Microstructure in Concentrated Sheared Dispersions

This work describes a theory for predicting microstructure of concentrated colloidal hard spheres as a function of P\'eclet number $Pe = 6\pi \eta \dot{\gamma} a^3/kT$ and particle volume fraction, $\phi$; $\dot{\gamma}$ is the shear rate, $a$ is the particle radius, $\eta$ is fluid viscosity and $kT$ is the thermal energy. We study the pair distribution using the pair Smoluchowski equation. Many-body effects in the conservation equation were then formulated self-consistently through probabilistic third-particle integrals, with emphasis on capturing the interaction of flow and excluded volume effects. The resulting integro-differential equation was solved iteratively. Comparison between theory predictions and simulation results show that the theory is able to predict known near-equilibrium ($Pe\ll1$) and dilute-suspension large-$Pe$ results. The approach accurately predicts the major features of microstructure at concentrated $\phi$ under strong shear, which differentiates it from previous theoretical work. Rheological quantities of shear stress, normal stress differences, and particle pressure are computed from the structure.