Linear stability of a binary fluid layer with freezing

Abstract

The linear convective instabilities of a fluid layer of binary alloy, cooled from above and consequently frozen at the bottom, are considered. Due to the density jump across the freezing interface, some light material is then released and diffused by pressure and composition gradients. As a result of a low cooling rate, the effect of thermal buoyancy is insignificant and the freezing interface advances upward at a slow speed by accumulating the solidified binary alloy. As Schmidt number P_L approaches infinity, instabilities set in stationarily at the marginal state. Cellular convective modes are possible, provided a destabilizing compositional profile occurs in the fluid layer, while morphological modes, associated with non‐cellular convection, require a constitutional supercooling near the freezing interface. In the absence of a constitutional supercooling, morphological modes are not important and cellular convective modes become dominant.

Key Words:

• stability
• binary fluid
• freezing