Effect of a crystal-melt interface on Taylor-Vortex flow with buoyancy

During crystal growth from the liquid, a fundamental problem is to understand the interaction of the crystal-melt interface with fluid flow in the liquid. This problem combines the complexities of the Navier-Stokes equations for fluid flow in the liquid with the nonlinear behavior of the free boundary representing the crystal-melt interface. Some progress has been made by studying explicit flows that allow a base state corresponding to a one-dimensional crystal-melt interface with solute and/or temperature fields that depend only on the distance from the interface. This allows the strength of the interaction between the flow and the interface to be assessed by a linear stability analysis of the simple base state. The case of a Taylor-Couette flow interacting with a cylindrical crystalline interface is currently being investigated both experimentally and theoretically. The authors consider the changes in the linear stability of this system produced by density-driven convection generated by the interaction of the density gradients with the gravitational and centripetal acceleration.