Porous Media with Hydrophile Granules
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A diaper is a porous medium with water-absorbing grains. The flow of a liquid in the presence of such absorption is studied taking Darcy’s law as the basic equation for the liquid motion. The swelling of the granules, which obeys a given kinetic law, produces a progressive reduction of porosity. The mass balance leads to a nonlinear partial differential equation (parabolic in the unsaturated region and elliptic in the saturated region) with history-dependent coefficients. Here we present a careful analysis of the boundary conditions, which can be selected in various ways, according to the specific physical situations, on both the injection surface and the penetration front. We illustrate in some detail the one-dimensional case for unsaturated and saturated flows, and we point out the main open problems.
KeywordsPorous Medium Free Boundary Complex Flow Free Boundary Problem Saturated Flow
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- 4.Fasano, A., Some two-scale processes involving parabolic equations, Proc. Int. Conf. on Free Boundary Problems (Creta, 1997), edited by I. Athanasopoulos, G. Makzakis and J.F. Rodriguez, CRC Press.Google Scholar
- 5.Fasano, A., and Solonnikov, V., An existence and uniqueness theorem for a flow problem through absorbing porous media, to appear.Google Scholar
- 6.Gianni, R., and Mannucci, P., The propagation of a wetting front through an absorbing porous material with saturation dependent permeability, to appear.Google Scholar