TRAVELING WAVES IN PHASE FIELD MODELS OF SOLIDIFICATION

The existence and selection of steady-state travelling planar fronts i n a set of typical phase field equations for solidification are invest igated by a combination of numerical and analytical methods. Such solu tions are conjectured to exist only for a unique velocity of propagati on and to be unique except for translation. This behaviour is in marke d contrast to the situation in conventional Stefan models in which tra velling 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, an alytical results for the velocity are presented for a number of physic al situations.