On interface transfer terms in two-fluid models

In this note we consider two-fluid models based on the usual formulations for conservation of mass, total momentum and total energy. We present some potentially useful general relationships between the interface exchange terms and the evolution of the mechanical variables. In particular, we discuss the possibility of obtaining in this framework a model that is both thermodynamically reversible and possesses real eigenvalues. We formally prove that such a model must include terms associated with the virtual mass force.We then address a technical issue regarding the modelling of interface transfer terms in the energy equations. In particular, we demonstrate how the formulation of the non-conservative products in these equations determine whether the interface exchange terms represent heat or energy transfer.

► We derive an explicit condition for a class of two-fluid models to be reversible.
► This implies that such well-posed models must include virtual mass force terms.
► We clarify the relationship between heat and energy transfer terms.