The effect of direct interactions in steady state electrophoresis and thermophoresis of colloids

Applying a stochastic scheme we show how to obtain the density profile of a suspension of weakly interacting charged colloids in a steady state situation. The density profile corresponds to the set of macroions and depends of the electrophoretic velocity and the self-diffusion, as observed in experiments on dilute solutions of charged colloids. Our approach permits us to observe the deviation of the density profile from an ideal case when the pair interactions between the macroions are important and permits a better interpretation of such experiments. For the case of colloids with tuning interactions under a temperature gradient we obtain the behaviour of the collective diffusion and the thermal diffusion of the particles in terms of the volume fraction. This result could be important for understanding the boosting of DNA in thermocapillary traps.