A two-phase model for compressible flows of granular mixtures based on non-equilibrium thermodynamics

In this talk we present a new two-phase model for compressible, viscous flows of mixtures consisting of a carrier fluid and a granular material. According to standard mixture-theory approaches, the mixture is treated as a multicomponent fluid, with a set of thermodynamic variables assigned to each of its constituents. The volume fraction occupied by the granular phase and its spatial gradient are included as thermodynamic variables. By applying directly the classical theory of non-equilibrium thermodynamics we derive constitutive relations for the viscous stresses, heat flux vectors, the momentum and energy exchanges between the two phases, and a parabolic partial differential equation for the volume fraction. In the proposed model, thermal non-equilibrium between the two phases emerges as a source term in this equation, in contrast with earlier models