Morphological instability of alloy solidification -- asymptotic analysis and generalization of the mullins-sekerka theory

摘要

As solutions solidify, the interaction of heat and mass transfer processes through the condition of phase equilibrium influenced by surface tension leads to an uneven solidifcation front. This is the phenomenon responsible for the characteristic dendritic structure of metal alloys. The fundamental explanation for the onset of uneven growth has been provided by the classical Mullins-Sekerka theory [1964] of morphological instability. The theory considers plain front solidification as the base condition, and uses normal mode analysis to predict the growth rates of perturbations of different wave numbers as functions of a number of solidification parameters. Because of a number of solidification parameters. Because of the large number of seemingly unrelated parameters present, the results of the theory have always been presented and discussed in material specific forms. Such discussions are difficult to summarize and generalize. In this study, through the nondimensionalization of Mullins and Sekerka's stability results and the asymptotic analysis of the nondimensionalized growth rate equation, the stability results are simplified and generalized. A single expression for the wavelength of maximum instability is derived. The result is a concise presentation of the stability theory and lends itself to convenient applications and clearer physical insight. In addition, this analysis also suggest dimensionless parameters which might prove useful for generalized correlations of dendrite spacing versus solidification speed.