Modeling Of Dendritic Solidification Systems - Reassessment Of The Continuum Momentum Equation

In recent years there has been renewed interest in modeling transport phenomena associated with the dendritic solidification of binary mixtures. Solidification occurs in a two-phase (mushy) region characterized by complex, solid-liquid interfacial geometries, and development of a model which is amenable to solution dictates the use of continuum (mixture theory) assumptions and/or volume-averaging procedures. A review of the recent literature would suggest that solidification models developed from mixture theory assumptions are less valid and less general than similar models based on volume-averaging, particularly with regard to the respective momentum equations which describe interdendritic fluid flow. In this paper, these different approaches are shown to yield identical macroscopic conservation equations, and the continuum momentum equation is reconsidered in an effort to reconcile matters which have lead to confusion about the validity of the continuum model. Consistency between recently presented momentum equations is demonstrated.