Zone melting, convective-diffusive

A detailed review of zone melting and its applications has been given recently by Shaw (2). In the present paper we shall confine our attention primarily to the convective-diffusive characteristics of such systems, and we shall strive primarily to obtain a sound qualitative understanding of their behavior. 

In another example, Richard et al. (2002) simulated the transport of water in a two-dimensional mantle convection model. They found that mantle flow, not diffusion, was the primary control on water distribution, which led to a homogeneous distribution of water in the mantle. If this is the case, the transition zone may contain less water than could be dissolved into the nominally anhydrous phases present there. Because of the low solubility of water in lower-mantle nominally anhydrous phases (Bolfan-Casanova et al., 2000), Richard et al. proposed that there might be a water-rich fluid phase in the lower mantle. They did not, however, consider the possibility of water-induced partial melting, leading to a melt rather than a fluid. 

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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