On the growth rates for a three-layer flow in porous media

TL;DR

This paper analyzes the stability of a three-layer flow of immiscible fluids in porous media, revealing that the linear stability problem generally has no solution, indicating potential instability in such flows.

Contribution

It provides a theoretical analysis of the linear stability of three-layer immiscible fluid displacement in porous media, highlighting the inherent instability of the process.

Findings

The linear stability problem often has no solution.

The middle-layer fluid's bounded region influences stability.

Instability is a common feature in three-layer flows.

Abstract

We study the displacement of three immiscible Stokes fluids with constant viscosities in a porous medium. The middle-layer fluid is contained in a bounded region. We give an analysis of the linear stability of this process. This stability problem has no solution (in general).