Mixture Theory of Mass Transfer Based upon Microstructure

Abstract

A mixture theory has been developed to model equitemperature metamorphism of snow. This formulation is a volume fraction theory which models the inter change of mass between the constitueats making up the mixture. The formulation has been developed so that the microstructure of the materialis included to correctly describe the mechanical and thermal processes. The second law of thermo dynamics is used to impose restrictions upon the various constitutive relations. These constitutive relationsare then described in terms of microstructure of the material. The micsostructure of each constituentis represented by constituent size (mean grain size, intergranular bond size), intergranular neckgeometry, 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 thedistribution of grain size, neck size and dispersed densities of each of the constituents. The resultsobtained show that the formulation can describe how the material changes under equitemperatureconditions. 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.