Mullins-Sekerka analysis

In this description the temperature field has been taken to be linear in the coordinate y and to be independent of the shape of the melt/crystal interface. This is a good assumption for systems with equal thermal conductivities in melt and crystal and negligible convective heat transport and latent heat release. Extensions of the model that include determination of the temperature field are discussed in the original analysis of Mullins and Sekerka (17) and in other papers (18,19). 

The problem of morphological instability was solved theoretically by Mullins and Sekerka [20], who proposed a linear theory demonstrating that the morphology of a spherical crystal growing in supercooled melt is destabilized due to thermal diffusion the theory dealt quantitatively with and gave linear analysis of the interface instability in one-directional solidification. 

A more stringent condition was derived by Mullins and Sekerka in their now classical linear stability analysis. It reads... 

Later, Mullins and Sekerka (1964) developed a more rigorous theory based on a stability analysis that included the liquid-solid interfacial energy, which can provide a stabilizing effect on the interface. However, the difference between the two theories is so small that, for the most part, the more conservative CS criteria can be used for experiment design. 

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