<title>Flow and crystallization in two-layer liquid systems with and without a magnetic field</title>

Abstract

Flow and heat and mass transfer in a two-layer liquid system is investigated when the layers are subjected to a constant magnetic field. The physical system consists of two immiscible liquids in a layer configuration with a free surface and a boundary between layers simulating two crystal growth methods, namely, floating zone and horizontal zone melting. Mass transfer effects due to crystallization of one of the layers is also considered. The diversity of flows is reduced to three types depending on (1) the dominance of the free surface effects of the top layer, (2) a balance between the thermocapillary effect on the free surface and the interface effect between the two layers, or (3) the dominance of interfacial effects, in determining the system thermo-fluid characteristics. The use of an additional liquid layer atop the basic crystallizing layer leads to a reduction of the radial dopant inhomogeneity in comparison to the one-layer case. The effect an externally imposed magnetic field on dopant distribution in this two-layer configuration is ambiguous and depends on its direction and intensity resulting in the necessity of optimizing the applied magnetic field for a specific situation.