Mixture theory of mass transfer based upon microstructure

A mixture theory has been developed to model equitemperature metamorphism of snow. This formulation is a volume fraction theory which models the interchange of mass between the constituents making up the mixture. The formulation has been developed so that the microstructure of the material is included to correctly describe the mechanical and thermal processes. The second law of thermodynamics is used to impose restrictions upon the various constitutive relations. These constitutive relations are then described in terms of microstructure of the material. The microstructure of each constituent is represented by constituent size (mean grain size, intergranular bond size), intergranular neck geometry, specific free surface area and dispersed density. The resulting formulation is then used to model equitemperature metamorphism of snow by determining the time-dependent changes in the distribution of grain size, neck size and dispersed densities of each of the constituents. The results obtained show that the formulation can describe how the material changes under equitemperature conditions. However, it is noted that since microstructure significantly affects the rate of metamorphism, an accurate determination of the microstructure (including grain and neck size distribution) is necessary for this approach to accurately predict changes in the material due to metamorphism.