Self-similar Focusing in Porous Media: An Explicit Calculation

TL;DR

This paper analyzes the final stage of gas flow in porous media with a hole, providing an explicit calculation for a self-similar solution that describes the hole-filling process.

Contribution

It offers the first explicit calculation of the self-similar constant in a symmetric porous media flow, previously determined only numerically.

Findings

Explicit self-similar solution for a symmetric flow

Analytical expression for the self-similar constant

Enhanced understanding of the hole-filling process in porous media

Abstract

We consider a porous mediaum flow in which the gas is initially distributed in the exterior of an empty region (a hole) and study the final stage of the hole-filling process. Hole-filling is asymptotically described by a self-similar solution which depends on a constant determined by the initial configuration. In general, this constant must be found numerically.. Here we give an example of a one-dimensional symmetric flow where the constant is obtained explicitly.