Thermodynamics of two-phase granular fluids

Starting from basic thermodynamic principles, we derive equations for a two-phase fluid. The first phase is the micropolar fluid and the second phase is the viscous Newtonian fluid. The phases differ in velocities, densities and viscosities. The first granular phase is described with the use of notion of the Cosserat continuum. To illustrate the model, we consider steady pressure driven flows between two parallel planes. Particularly, we address the "tubular pinch effect" of Ségre and Silberberg.