Entropy of averaging for compressible two-pressure two-phase flow models

We propose here a new closure for compressible two-pressure two-phase flow models, which satisfies conservation requirements, boundary conditions at the edges of the mixing zone, hyperbolic stability (real eigenvalues for the characteristic version of the equations of motion) and an entropy inequality. Except for the latter, these properties are direct consequences of the proposed closures. The entropy, which is the main focus of this Letter, inequality (as opposed to entropy conservation for microphysically adiabatic processes) implies positivity for the entropy of averaging.