Variational formulation of non-equilibrium void fraction

A general variational formulation of the dissipative two-phase flows based on the extremization of the entropy production is developed. The entropy generation rate is written outside phase equilibrium by introducing interfacial contributions due to surface tension as well as heat and mass transfer between the two phases. Prigogine's theorem of minimum entropy production is used to estimate the steady state void fraction of the two-phase flow. The corresponding flow representation is investigated out of phase equilibrium for an annular flow, experiencing friction, surface tension effects, and interphase heat and mass transfer, within a diabatic channel. It is demonstrated that the present formulation generalises previous theories by capturing the effect of mass and heat fluxes variations, and that the widely accepted expression from Zivi represents a particular case obtained under certain simplifying assumptions. Finally, a first validation of the developed formulation of two-phase void fraction is presented for different flow conditions, heat flux from the external environment, and thermophysical properties of the refrigerant with reference to data obtained from a dedicated experimental apparatus adopting a capacitance sensor and from previous literature.