Translational and rotational dynamics of colloidal particles in suspension: effect of shear

We report a generalization of a nonequilibrium thermodynamic theory for the mesoscopic dynamics of radially symmetric interacting particles to anisotropic pairwise interactions and attain the one- and two-particle Fokker-Planck kinetics equations at a low-density limit that provides the translational-rotational coupling of their motion due to hydrodynamic interactions, from which we derived the balance equations of linear, angular momentum, and energy dissipation due to particle interactions and energy interchange with heat bath. In this low-density approximation, an already-known virial expression for the long-time translational collective diffusion coefficient of an orientational isotropic suspension in terms of the fluid equilibrium microstructure is recovered. An external shear flow induces, in the diffusive regime, vorticity effects into the rotational diffusion property of the colloidal particles. They manifest in the appearance of the particle's rotational viscosity due to vortex flow. The Smoluchowski equation that governs the dynamical relaxation of colloid microstructure due to particle's Brownian motion under stationary flow is provided.