Stability of Equilibria of a two-phase Stokes-Osmosis problem

TL;DR

This paper derives a two-phase moving boundary model for viscous liquids separated by a semipermeable membrane, incorporating osmotic pressure and surface tension, and proves local exponential stability of steady states.

Contribution

It introduces a novel variational model for two-phase Stokes-Osmosis and establishes the local exponential stability of its steady states.

Findings

Steady states are locally exponentially attractive.

The model accounts for osmotic pressure and surface tension effects.

The stability analysis provides insights into membrane dynamics.

Abstract

Within the framework of variational modelling we derive a two-phase moving boundary problem that describes the motion of a semipermeable membrane separating two viscous liquids in a fixed container. The model includes the effects of osmotic pressure and surface tension of the membrane. For this problem we prove that the manifold of steady states is locally exponentially attractive.