Effects of hydrodynamic interactions in binary colloidal mixtures driven oppositely by oscillatory external fields.

The collective dynamics in a binary mixture of colloidal particles which are driven in opposite directions by an external oscillatory field is examined by computer simulations in two spatial dimensions. Both Brownian dynamics (BD) computer simulations, which ignore solvent-mediated hydrodynamic interactions between the colloidal particles, and multi-particle collision dynamics (MPCD) simulations, which include hydrodynamic interactions, are employed. We first review recent results obtained by BD. Depending on the driving frequency and amplitude, lane formation parallel to the drive and band formation perpendicular to the drive occur. Band formation is stable only in a finite window of oscillation frequencies and driving strengths and is taken over by lane formation if the driving force is increased or the oscillation frequency is decreased. MPCD simulations, on the other hand, reveal that band formation is blurred by hydrodynamic interactions. During the front collisions of oppositely driven particles there is a strong vortical movement of the solvent which tends to mix particles and broaden the interface of the bands. This can either lead to a novel intermittent dynamical behaviour or to band rupture into local clusters. These effects, which are absent for BD, are characterized by the strengths of the enstrophy and its spectrum. We finally discuss possible experimental realizations of the models employed.