Abstract
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.
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© 2000 Springer Science+Business Media New York
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Fasano, A. (2000). Porous Media with Hydrophile Granules. In: Fasano, A. (eds) Complex Flows in Industrial Processes. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1348-2_10
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DOI: https://doi.org/10.1007/978-1-4612-1348-2_10
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7106-2
Online ISBN: 978-1-4612-1348-2
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