A mixture theory for a phase-changing snowpack

The continuum theory of mixtures is used as the mathematical framework for a four-constituent model of a natural snowpack. The general conservation equations in point form are derived from appropriate integral balances and constitutive requirements are identified. In particular, constitutive postulates are made for the interaction terms due to phase change in the momentum and energy equations. The conservation equations are written in terms of partial variables whereas material constitutive laws are given in terms of intrinsic variables. Generalising Morland's theory* enables these two types of variable to be related when mass transfer due to phase change is included. A reduced model is proposed which assumes linear hypo-thermoelastic response for the ice and linearly viscous fluid response for the water, water-vapour and air.