Abstract
In this article we introduce a new two-phase model for compressible viscous flows of saturated mixtures consisting of a carrier fluid and a granular material. 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 introduced as additional degrees of freedom. Then, by applying the classical theory of irreversible processes we derive algebraic expressions for the viscous stresses and heat flux vectors, the momentum and energy exchanges between the two phases, as well as a parabolic partial differential equation for the volume fraction. In our model, thermal non-equilibrium between the two phases emerges as a source term of the evolution equation for the volume fraction, in contrast with earlier models.
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