B. Svendsen et Jmnt. Gray, BALANCE RELATIONS FOR CLASSICAL MIXTURES CONTAINING A MOVING NON-MATERIAL SURFACE WITH APPLICATION TO PHASE-TRANSITIONS, Continuum mechanics and thermodynamics, 8(3), 1996, pp. 171-187
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.