title: Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification with two-sided diffusion.
abstract: We present the variational formulation of a quantitative phase-field model for isothermal low-speed solidification in a binary dilute alloy with diffusion in the solid. In the present formulation, cross-coupling terms between the phase field and composition field, including the so-called antitrapping current, naturally arise in the time evolution equations. One of the essential ingredients in the present formulation is the utilization of tensor diffusivity instead of scalar diffusivity. In an asymptotic analysis, it is shown that the correct mapping between the present variational model and a free-boundary problem for alloy solidification with an arbitrary value of solid diffusivity is successfully achieved in the thin-interface limit due to the cross-coupling terms and tensor diffusivity. Furthermore, we investigate the numerical performance of the variational model and also its nonvariational versions by carrying out two-dimensional simulations of free dendritic growth. The nonvariational model with tensor diffusivity shows excellent convergence of results with respect to the interface thickness.
authors: Division of Materials Science and Engineering, Faculty of Engineering, Hokkaido University, Kita 13 Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan.
authors: Munekazu
authors: M
authors: Ohno
authors: Faculty of Mechanical Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan.
authors: Tomohiro
authors: T
authors: Takaki
authors: Department of Materials Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
authors: Yasushi
authors: Y
authors: Shibuta