The averaged momentum equation for flow through a columnar dendritic porous structure presenting evolving heterogeneities and the associated local closure problem leading to the determination of the permeability are presented. Dueto the continuous spatial variations of the porosity (liquid fraction), this analysis explicitly involves the porosity gradients both inthe macroscopic equation and in the closure problem and these terms have to be considered under particular conditions, depending on the rate of geometry variations. In this case, the local closure problem becomes very complex and the full solution is still out of reach. However, for "moderate" values of the rate of geometry variations, the classical closure problem can be used to physically represent the permeability of the columnar dendritic layer.
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