Modelling of solidification of binary fluids with non-linear viscosity models

This paper deals with the numerical modelling of multiphase flows with phase transition during solidification of binary alloys. First, verification of the effective viscosity assumption in the regime of moving solid (equiaxed crystals) and liquid (melt) for large solid mass fractions is presented. In order to extend the effective viscosity model to the region of stationary solid (columnar crystals); non-linear dependence of the viscosity on the solid mass fraction and the shear velocity is introduced based on the experimental evidence. The proposed formulation is used in a numerical study of the metal alloy solidification in a rectangular cavity.