Extra Nodes Added on the Solid/Liquid Interface to Solve the Mass Transfer Problem in a Directional Solidification Process

Abstract

In a directional solidification process, since the liquid solubility is higher than the solid one, the surplus solute will be released from the solid/liquid interface into the liquid, which is the main source of increasing the liquid solute. The release of solute at the moving interface is like that of latent heat. Except the growth rate, the release of extra solute also depends on the liquid concentration at the interface, which is not fixed. Consequently, the numerical treatment of the solute release is not so easy as that of the latent-heat one. If the effect of solute release is not handled appropriately, the concentration solutions will diverge very easily. In this paper, extra nodes added on the solid/liquid interface in a fixed grid system are proposed to solve the mass transfer problem in the directional solidification process. A one-dimensional problem is firstly used to test the proposed method. The computing results are compared with those of other fixed grid methods and the analytical solutions from the literature. Finally, the feasibility of the proposed method is further testified by applying it to solve the concentration field of the crystal growth of GaAs in a Bridgman furnace.