Self-diffusion in sheared suspensions: Violation of the Einstein relation

Starting from the Smoluchowski equation we derive exact microscopic expressions for the self-diffusion and the self-mobility coefficients of a sheared suspension of interacting colloidal particles in a semidiluted regime. We find that the usual Einstein relation between the self-mobility and the self-diffusion matrices is no longer valid for this nonequilibrium situation. The self-mobility and self-diffusion matrices are explicitly calculated in a low-shear-rate regime for a charge-stabilized colloidal suspension.