Transport phenomena in saturated porous media undergoing liquid-solid phase change

Abstract

The macroscopic modelling of transport phenomena occurring during the solidification process in porous media is revisited in this paper. The particular case of binary phase change in metallic alloys is considered. Continuum models for momentum, mass, heat and species transport in metallic saturated porous media undergoing liquid-solid phase change are derived from the description at the pore scale by using an upscaling technique. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour. Different macroscopic descriptions are derived in function of the orders of magnitude of dimensionless numbers that characterize the dominating phenomena and the physical properties of the constituents at the microscopic scale. Among the distinct homogenizable situations, the three richest cases are presented in this paper. The domains of validity of the micro-macrosegregation models, i.e. lever-rule type models and Scheil type models, are shown by means of the order of magnitude of dimensionless numbers. The continuous passage between the different models is investigated.