Analysis of instability at solid-liquid interface from molar flux balance in diffuse interface layer

By assuming a balance in molar flux at a diffuse interface layer between a solid and liquid with thickness delta, we explain the interfacial instability in the directional solidification of alloys. The state of constitutional undercooling is equivalent to the directional change in the molar flux at the interface, j(i). We compared the interfacial instability criterion from the present model with that from Mullins-Sekerka's theory. From the flux balance between A and the interfacial diffusion (j(d)), we deduced the thickness of the interface, which shows good agreement with experimental results. Since an empirical relation of interfacial energy per mole, gamma (m) = RT(f)delta, was analytically explained, the flux balance can provide new models for capillary-effected phenomena, where R is the gas constant and T-i is the temperature at the solid and liquid interface.