  We consider a sheared colloidal suspension under the influence of an external
potential that varies slowly in space in the plane perpendicular to the flow
and acts on one selected (tagged) particle of the suspension. Using a
Chapman-Enskog type expansion we derive a steady state equation for the tagged
particle density distribution. We show that for potentials varying along one
direction only, the tagged particle distribution is the same as the equilibrium
distribution with the temperature equal to the effective temperature obtained
from the violation of the Einstein relation between the self-diffusion and
tagged particle mobility coefficients. We thus prove the usefulness of this
effective temperature for the description of the tagged particle behavior
beyond the realm of linear response. We illustrate our theoretical predictions
with Brownian dynamics computer simulations.
