epl draft Mobility and Diffusion of a Tagged Particle in a Driven Colloidal Suspension

Abstract.- We study numerically the influence of density and strain rate on the diffusion and mobility of a single tagged particle in a sheared colloidal suspension. We determine independently the time-dependent velocity autocorrelation functions and, through a novel method, the response functions with respect to a small force. While both the diffusion coefficient and the mobility depend on the strain rate the latter exhibits a rather weak dependency. Somewhat surprisingly, we find that the initial decay of response and correlation functions coincide, allowing for an interpretation in terms of an ’effective temperature’. Such a phenomenological effective temperature recovers the Einstein relation in nonequilibrium. We show that our data is well described by two expansions to lowest order in the strain rate. Introduction. – The mobility of a single spherical particle immersed in a solvent determines the velocity of the particle in response to an applied external force. For small Reynolds numbers Stokes ’ law yields the famous ex-pression µ−10 = 3piηa in terms of the sphere diameter a an