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We consider a sheared colloidal suspension under the influence of an externalpotential that varies slowly in space in the plane perpendicular to the flowand acts on one selected (tagged) particle of the suspension. Using aChapman-Enskog type expansion we derive a steady state equation for the taggedparticle density distribution. We show that for potentials varying along onedirection only, the tagged particle distribution is the same as the equilibriumdistribution with the temperature equal to the effective temperature obtainedfrom the violation of the Einstein relation between the self-diffusion andtagged particle mobility coefficients. We thus prove the usefulness of thiseffective temperature for the description of the tagged particle behaviorbeyond the realm of linear response. We illustrate our theoretical predictionswith Brownian dynamics computer simulations.

europhysics letters

Tagged particle in a sheared suspension: effective temperature  determines density distribution in a slowly varying external potential beyond  linear response