Similitude applied to centrifugal scaling of unsaturated flow

Centrifuge experiments modeling single-phase flow in prototype porous media typically use the same porous medium and permeant. Then, well-known scalin g laws are used to transfer the results to the prototype. More general scal ing laws that relax these restrictions are presented. For permeants that ar e immiscible with an accompanying gas phase, model-prototype (i.e., centrif uge model experiment-target system) scaling is demonstrated. Scaling is sho wn to be feasible for Miller-similar (or geometrically similar) media. Scal ings are presented for a more, general class, Lisle-similar media, based on the equivalence mapping of Richards' equation onto itself. Whereas model-p rototype scaling of Miller-similar media can be realized easily for arbitra ry boundary conditions, Lisle-similarity in a finite length medium generall y, but not always, involves a mapping to a moving boundary problem. An exce ption occurs for redistribution in Lisle-similar porous media, which is sho wn to map to spatially fixed boundary conditions. Complete model-prototype scalings for this example are derived.