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 scaling laws are used to transfer the results to the prototype. More general scaling laws that relax these restrictions are presented. For permeants that are immiscible with an accompanying gas phase, model-prototype (i.e., centrifuge model experiment–target system) scaling is demonstrated. Scaling is shown to be feasible for Miller-similar (or geometrically similar) media. Scalings are presented for a more general class, Lisle-similar media, based on the equivalence mapping of Richards' equation onto itself. Whereas model-prototype scaling of Miller-similar media can be realized easily for arbitrary boundary conditions, Lisle-similarity in a finite length medium generally, but not always, involves a mapping to a moving boundary problem. An exception occurs for redistribution in Lisle- similar porous media, which is shown to map to spatially fixed boundary conditions. Complete model-prototype scalings for this example are derived.
Keywords: Diffusion-advection equation ; Constant rate rainfall infiltration ; Versatile nonlinear model ; Solute transport ; Geotechnical centrifuge ; Unstable infiltration ; Richards' equation ; Water content ; Porous media ; Soil
Record created on 2005-12-09, modified on 2016-08-08