A phase field model of unsaturated flow
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Juanes_A phase.pdf
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Author(s)
Juanes, Ruben
Cueto-Felgueroso, Luis
Date Issued
October 2009
Journal
Water Resources Research
Publisher
American Geophysical Union
Citation
Cueto-Felgueroso, L., and R. Juanes. “A phase field model of unsaturated flow.” Water Resour. Res. 45.10 (2009): W10409. ©2009 American Geophysical Union.
Version
Final published version
Abstract
We present a phase field model of infiltration that explains the formation of gravity fingers during water infiltration in soil. The model is an extension of the traditional Richards equation, and it introduces a new term, a fourth-order derivative in space, but not a new parameter. We propose a scaling that links the magnitude of the new term to the relative strength of gravity-to-capillary forces already present in Richards' equation. We exploit the thermodynamic framework to design a flow potential that constrains the water saturation to be between 0 and 1, its physically admissible values. The model predicts a saturation overshoot at the wetting front, which is in good agreement with experimental measurements. Two-dimensional numerical simulations predict gravity fingers with the appearance and characteristics observed in visual laboratory experiments. A linear stability analysis of the model shows that there is a direct relation between saturation overshoot and the strength of the front instability. Therefore our theory supports the conjecture that saturation overshoot, a pileup of water at the wetting front, is a prerequisite for gravity fingering.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1029/2009wr007945
