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arXiv · 2011.10792

Travelling wave solutions for gravity fingering in porous media flows

K. Mitra·A. Rätz·B. Schweizer
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Abstract

We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper, we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.

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K. Mitra, A. Rätz, B. Schweizer. 2020-11-21. Travelling wave solutions for gravity fingering in porous media flows. https://doi.org/10.13140/rg.2.2.23096.78083

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