Permeability of interdendritic channels

During solidification of metallic alloys that freeze over a range of temperatures a variation of solute concentration ahead of the solid/liquid interface is observed leading to a dendritic growth of the solid phase. The shrinkage of the alloy during solidification must be compensated by a flow of liquid metal in the fine mesh of interdendritic channels formed, in order to avoid pore formation. For typical dendrite arm spacing this flow can be treated as a flow through a finely porous media and the Darcy's law can be applied if the permeability of the interdendritic channels is known. In this paper, a heuristic method to estimate variation of permeability of interdendritic channels during solidification of metallic alloys as function of primary and secondary dendrite arms spacings and liquid fraction, applied to liquid flow parallel and normal to primary dendrite arm, is proposed and compared with experimental results obtained by different authors.