Convective diffusion, zone refining

Convective Diffusion in Zone Refining of Low Prandtl Number Liquid Metals and Semiconductors... 

Several elementary aspects of mass diffusion, heat transfer and fluid flow are considered in the context of the separation and control of mixtures of liquid metals and semiconductors by crystallization and float-zone refining. First, the effect of convection on mass transfer in several configurations is considered from the viewpoint of film theory. Then a nonlinear, simplified, model of a low Prandtl number floating zone in microgravity is discussed. It is shown that the nonlinear inertia terms of the momentum equations play an important role in determining surface deflection in thermocapillary flow, and that the deflection is small in the case considered, but it is intimately related to the pressure distribution which may exist in the zone. However, thermocapillary flows may be vigorous and can affect temperature and solute distributions profoundly in zone refining, and thus they affect the quality of the crystals produced. 

A solute distribution exists in the melt because the solidification is carried out at a finite rate. For example, if k0 < 1, then solute is rejected and accumulates at the surface which is solidifying, and this creates solute gradients in the melt which tend to be relaxed by molecular diffusion and any convection which may exist. The interfacial distribution coefficient, k, refers to the solid to liquid solute concentration ratio at the interface. It is k which is used in transport calculations when one is trying to understand the dynamic behavior of zone refining systems. It usually is found that equilibrium exists locally at the solid-liquid interface, in which case k ko. 

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