Travelling wave solutions for gravity fingering in porous media flows

TL;DR

This paper models gravity-driven fingering in porous media flows using a free boundary problem, demonstrating the existence of traveling wave solutions and analyzing their behavior numerically.

Contribution

It introduces a novel free boundary framework for describing single finger propagation in porous media with gravity effects.

Findings

Existence of traveling wave solutions for the finger problem.

Numerical investigation of the shape and speed of the propagating finger.

Model captures key features of gravity-induced fingering phenomena.

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.