Travelling waves in phase field models of solidification

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Abstract
The existence and selection of steady-state travelling planar fronts in a set of typical phase field equations for solidification are investigated by a combination of numerical and analytical methods. Such solutions are conjectured to exist only for a unique velocity of propagation and to be unique except for translation. This behaviour is in marked contrast to the situation in conventional Stefan models in which travelling fronts exist for all velocities. The value of the steady-state velocity depends upon the various material parameters which enter the phase field equations. Numerical and, in certain tractable limits, analytical results for the velocity are presented for a number of physical situations.

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