The influence of an external field on a binary colloidal mixture performing Brownian dynamics in a solvent is investigated by nonequilibrium computer simulations and simple theory. In our model, one half of the particles are pushed into the field direction while the other half of them are pulled into the opposite direction. For increasing field strength, we show that the system undergoes a nonequilibrium phase transition from a disordered state to a state characterized by lane formation parallel to the field direction. The lanes are formed by the same kind of particles moving collectively with the field. Lane formation accelerates particle transport parallel to the field direction but suppresses massively transport perpendicular to the field. We further show that lane formation also occurs in a time-dependent oscillatory field. If the frequency of the external field exceeds a critical value, however, the system exhibits a transition back to the disordered state. Our results can be experimentally verified in binary colloidal suspensions exposed to external fields under nonequilibrium conditions.

The influence of a time-dependent oscillatory external field on the melting transition of a polydisperse colloidal crystal is examined by theory and computer simulation. In a monodisperse crystal the field just induces an overall dynamical mode which does not affect the melting line. For a polydisperse sample, on the other hand, the field shifts the melting line towards smaller temperatures. Combining a solid cell approach and a Lindemann criterion in nonequilibrium, a simple theory is presented showing that the temperature shift scales with the square of the relative polydispersity. The theory is in reasonable agreement with nonequilibrium Brownian dynamics computer simulations.

Using non-equilibrium computer simulations, it is shown that various phenomenological criteria for melting and freezing hold not only in equilibrium but in steady-state non-equilibrium as well. In particular, we study the steady state of charge-polydisperse Brownian particles shaken by a time-dependent oscillatory electric field. Among these criteria are the Lindemann melting rule, the Hansen-Verlet freezing rule and the dynamical freezing criterion proposed for colloidal fluids by Löwen, Palberg and Simon.

Abstract. The melting transition of a charge-polydisperse dusty plasma crystal under the influence of a time-dependent oscillating field is studied within a simple model. The stochastic dynamics of the dust particles is modelled by a Fokker-Planck description. Using non-equilibrium computer simulations we detect a non-monotonic behaviour of the melting line as a function of the frequency of the external field. This is attributed to a cage resonance effect which is controlled by the intrinsic polydispersity of the sample. The results are qualitatively explained within a cage theory of the polydisperse solid combined with a generalized Lindemann rule of melting.