Diffusive Contact between Randomly Driven Colloidal Suspensions

We study the relaxation process of two driven colloidal suspensions in contact, to a joint steady state, similar to the process of thermalization. First, we study a single suspension, subjecting it to random driving forces via holographic optical tweezers, which agitate it to a higher effective temperature. Interestingly, the effective temperature of the suspension, defined by the Einstein relation, exhibits a nonmonotonic dependence on the driving frequency. Next, we follow the flux of particles between two such suspensions in diffusive contact, starting from a uniform density and relaxing to a state with zero net particle flux. At high driving frequencies, we show that the density distribution at steady state is determined by equating the ratio of the chemical potential to the effective temperature in both systems, reminiscent of the thermal equilibrium behavior.