A phase-field model of solidification with convection
The authors developed a phase-field model for the solidification of pure material. The model includes convection in liquid phase permitting the interface to have an anisotropic surface energy. The thermodynamic description is quasi-incompressible with uniform densities in the solid and liquid phases. Governing equations are derived using irreversible thermodynamics principles with the solid phase assumed to be a very viscous liquid. The model is investigated in two solidification cases of a planar interface at constant velocity: density change flow and shear flow. Non-equilibrium equation is analyzed by numerical and asymptotic methods. An exact solution is obtained for the parallel shear flow. The behavior is investigated in the sharp interface limit and for large values of the viscosity ratio. Although buoyancy forces were not considered in this work, the results contribute to the literature in this field.
scientific article; zbMATH DE number 1394443