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This paper is concerned with the dynamics of a binary mixture of rod--like,repulsive colloidal particles driven out of equilibrium by means of a steadyshear flow (Couette geometry). To this end we first derive, starting from amicroscopic density functional in Parsons--Lee approximation, a mesoscopic freeenergy functional whose main variables are the orientational order parametertensors. Based on this mesoscopic functional we then explore the stability ofisotropic and nematic equilibrium phases in terms of composition and rodlengths. Second, by combining the equilibrium theory with the Doi--Hessapproach for the order parameter dynamics under shear, we investigate theorientational dynamics of binary mixtures for a range of shear rates andcoupling parameters. We find a variety of dynamical states, includingsynchronized oscillatory states of the two components, but also symmetrybreaking behavior where the components display different in--plane oscillatorystates.

Binary mixtures of rod-like colloids under shear: microscopically-based equilibrium theory and order--parameter dynamics