DENDRITIC SOLIDIFICATION .1. ANALYSIS OF CURRENT THEORIES AND MODELS

Recent advances in the theory of dendritic growth are reviewed. These theories have attempted to obtain mathematically rigorous solutions to dendritic growth under steady state conditions, incorporating in them, with various degrees of success, essentially all the physical principles governing dendritic growth. Traditionally, these theories have relied on an ad hoc hypothesis requiring that the dendrite grow at the maximum possible growth rate. More recently, this hypothesis has been abandoned in favor of criteria which determine the conditions under which a dendrite tip will advance in a stable fashion into the liquid ahead of it. However, all models relying on the simpler approach and theoretically inconsistent and do not satisfactorily predict the limiting undercoolings at a dendrite tip for both very small and very large growth rates. The essential elements of satisfactory model have been summarized and a new model proposed.