A mean-field description of two-phase flows with phase changes

Abstract A new version of the two-fluid model is developed, specially devoted to liquid–vapour two-phase mixtures, but also relevant to liquid-gas and liquid–liquid mixtures. It is well-known that, over a large range of volume fractions, liquid–vapour mixtures behave as dispersions of particles in a carrier fluid. But the “particles” belong to one phase at the beginning of the phase change, and to the second phase at the end. Within the present model, the dispersed phase is not prescribed at the outset but is merely the one with the lower volume fraction. To simplify the issue, surface tension and interfacial properties are neglected. However, the differences of pressure, temperature and velocity between the two phases are taken into account. The exchanges of mass, momentum and energy between phases are split into a “mean-field” part corresponding to the average conditions imposed by the whole mixture on the dispersed phase, and a part specifically due to the disturbances created by the particles. Constraints on constitutive relations are obtained from the overall dissipation rate, and result in a closed set of seven equations for seven state variables including one volume fraction. We insist on the general form of the equations but not on the details of the closure relations. The limits of this simple model are clearly stated, and we discuss possible improvements, including a better account of small-scale kinetic phenomena, as well as an eighth equation for the density of interfaces.