BALANCE RELATIONS FOR CLASSICAL MIXTURES CONTAINING A MOVING NON-MATERIAL SURFACE WITH APPLICATION TO PHASE-TRANSITIONS

This work is concerned with an extension of classical mixture theory t o the case in which the mixture contains an evolving non-material surf ace on which the constituents may interact, as well as be created and/ or annihilated. The formulation of constituent and mixture jump balanc e relations on/across such a non-material surface proceed by analogy w ith the standard ''volume'' or ''bulk'' constituent and mixture balanc e relations. On this basis, we derive various forms of the constituent mass, momentum, energy and entropy balances assuming (1), that the co nstituent in question is present on both sides of the moving, non-mate rial surface, and (2), that it is created or annihilated on this surfa ce, as would be the case in a phase transition. In particular, we appl y the latter model to the transition between cold and temperate ice fo und in polythermal ice masses, obtaining in the process the conditions under which melting or freezing takes place at this boundary. On a mo re general level, one of the most interesting aspects of this formulat ion is that it gives rise to certain combinations of the limits of con stituent and mixture volume fields on the moving mixture interface whi ch can be interpreted as the corresponding surface form of these field s, leading to the, possibility of exploiting the surface entropy inequ ality to obtain restrictions on surface constitutive relations.