A Phase - Field Model of Solidi cationwith
نویسنده
چکیده
We develop a phase-eld model for the solidiication of a pure material that includes convection in the liquid phase. The model permits the interface to have an anisotropic surface energy, and allows a quasi-incompressible thermodynamic description in which the densities in the solid and liquid phases may each be uniform. The solid phase is modeled as an extremely viscous liquid, and the formalism of irreversible thermodynamics is employed to derive the governing equations. We investigate the behavior of our model in two important simple situations corresponding to the solidiication of a planar interface at constant velocity: density change ow and a shear ow. In the former case we obtain a non-equilibrium form of the Clausius-Clapeyron equation and investigate its behavior by both a direct numerical integration of the governing equations, and an asymptotic analysis corresponding to a small density diierence between the two phases. In the case of a parallel shear ow we are able to obtain an exact solution which allows us to investigate its behavior in the sharp interface limit, and for large values of the viscosity ratio.
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