Thin Film Equations with Soluble Surfactant and Gravity: Modeling and Stability of Steady States

TL;DR

This paper derives and analyzes a mathematical model for a thin liquid film with soluble surfactant under gravity, demonstrating the asymptotic stability of its steady states.

Contribution

It introduces a new model incorporating gravity and soluble surfactant effects, and proves the stability of steady states within this framework.

Findings

Steady states are asymptotically stable.

Derived degenerate parabolic equations for film height and surfactant concentrations.

Model accounts for gravity and solubility effects.

Abstract

A thin film on a horizontal solid substrate and coated with a soluble surfactant is considered. The governing degenerate parabolic equations for the film height and the surfactant concentrations on the surface and in the bulk are derived using a lubrication approximation when gravity is taken into account. It is shown that the steady states are asymptotically stable.