Uniform shear flow in a binary mixture with general repulsive interactions

Abstract

A kinetic model for a binary mixture under uniform shear flow is exactly solved. The model incorporates a temperature dependence of the collision frequencies that allows the consideration of general repulsive interactions. The rheological properties of the mixture are obtained as functions of the shear rate, the parameters of the mixture (particle masses, concentrations, and force constants), and a parameter characterizing the interaction considered. In addition, the velocity distribution functions are explicitly obtained. While the transport coefficients are hardly sensitive to the interaction potential, the distribution functions are clearly influenced by the interaction parameter. In the tracer limit, a transition to an alternative state recently found in the context of Boltzmann equation is exactly identified in the case of Maxwell molecules. For non-Maxwell molecules, preliminary results suggest that this transition is also present although the phenomenon is less significant. A comparison with previous results derived from the a Boltzmann equation for Maxwell molecules is also carried out.