Microscopic-macroscopic modelling of transport phenomena during solidification in heterogeneous systems

Microscopic-macroscopic approach to modelling of solidification in heterogeneous systems (the mushy zone of binary alloys, in manufacture of metal-matrix composites and in porous media) is addressed in the paper. Microscopic phenomena accompanying solidification and microscopic equations are presented. Averaging procedures (volume and ensemble averaging techniques) and their limitations are discussed. Macroscopic equations are derived and macroscopic phenomena described. Conditions for existence of local thermal and chemical equilibrium during solidification on the macroscopic scale are shown. Some examples of equilibrium and non-equilibrium solidification based on macroscopic approach are presented.