Porous Media with Hydrophile Granules

  • Antonio Fasano
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


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.


Porous Medium Free Boundary Complex Flow Free Boundary Problem Saturated Flow 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Antonio Fasano
    • 1
  1. 1.Dipartimento di Matematica “U. Dini”Università di FirenzeFirenzeItaly

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