The foam drainage equation for unsaturated flow in porous media

Authors

  • Dani Or,

    Corresponding author
    1. Department of Environmental Systems Science (D-USYS), Institute of Terrestrial Ecosystems (ITES), Soil and Terrestrial Environmental Physics (STEP), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland
    • Corresponding author: D. Or, Department of Environmental Systems Science (D-USYS), Institute of Terrestrial Ecosystems (ITES), Soil and Terrestrial Environmental Physics (STEP), Swiss Federal Institute of Technology (ETH), CH-8092 Zurich, Switzerland. (dani.orl@env.ethz.ch)

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  • Shmuel Assouline

    1. Department of Environmental Physics and Irrigation, Institute of Soil, Water and Environmental Sciences, A.R.O.—Volcani Center, Bet Dagan, Israel
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Abstract

[1] A class of capillary flows in unsaturated porous media is characterized by quasi steady viscous flow confined behind curved air-water interfaces and within liquid bodies held by capillary forces along crevices and grain contacts. The geometry of the connected capillary liquid network within the pore space resembles channels that form between adjacent bubbles in foam (Plateau borders) with solid grains representing gas bubbles in foam. For simplified channel geometry, we combine expressions for viscous flow with continuity considerations to describe the evolution of the channels cross-sectional area during gravity drainage. This formulation enables modeling of unsaturated flow without invoking the Richards equation and associated hydraulic functions. We adapt a formalism originally developed for foam “free drainage” (drainage under gravity) or “forced drainage” (infiltration front motion) to a class of unsaturated flows in porous media that require a few input parameters only (mean channel corner angle, air entry value, and porosity) for certain initial and boundary conditions. We demonstrate that the reduction in capillary channel cross section yields a consistent description of self-regulating internal fluxes toward attainment of the so-called “field capacity” in soil and provides an alternative method for interpretation of outflow experiments for prescribed pressure boundary conditions. Additionally, the geometrically explicit formulation provides a more intuitive picture of capillary flows across textural boundaries (changes in channel cross section and number of channels). The foam drainage methodology expands the range of tools available for analyses of unsaturated flow processes and offers more realistic links between liquid configuration and flow dynamics in unsaturated porous media.

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