Permeability for flow of interdendritic liquid in columnar-dendritic alloys

Permeability data for the flow of interdendritic liquid in partially solid Pb-Sn and borneol-paraffin columnar-alloys are summarized. The data are used in regression analyses and simple flow models to arrive at relationships between permeability and the morphology of the solid dendrites. When flow is parallel to the primary dendrite arms, the important morphological aspects are the volume fraction liquid (g _L) and the primary dendrite arm spacing (d ₁). When flow is normal to the primary dendrite arms, the permeability depends upon the secondary dendrite arm spacing (d ₂) as well as d ₁ and g _L. The parallel permeability is best described by a model based on the Hagen-Poiseuille law for laminar flow through a tube; for the normal permeability an empirical multilinear regression gives the best fit to the data. However, those models are not appropriate for extrapolations beyond the range of the available data (0.19≤g _L≤0.66), particularly as g _L approaches 1. For extrapolations, models based upon the Blake-Kozeny equation for flow through porous media are recommended.