Statistical description of the shear-induced diffusion of a suspension of non-Brownian particles

Abstract

Using mesoscopic nonequilibrium thermodynamics, we calculate the entropy production of a dilute suspension of non-Brownian particles subject to an oscillatory shear flow. We find that an Onsager coupling leads to a breakdown of the fluctuation-dissipation theorem and to the shear induced diffusion effect observed in experiments. By contracting the description, we derive a Smoluchowski equation from which the scaling of the mean square displacement on the shear rate and particle diameter reported in experiments is obtained. We also perform lattice Boltzmann simulations to show the shear induced diffusion effects, and how the transition to irreversibility can be characterized through the power spectra of particle trajectories.