Surfactants in a Non-local Model for Phase Transitions

TL;DR

This paper models how surfactants affect interface stability in non-local phase transition systems, deriving an effective surface tension that decreases with surfactant segregation, using Gamma-convergence analysis.

Contribution

It introduces a novel non-local energy model incorporating surfactant effects and derives the effective surface tension behavior as the interface thickness approaches zero.

Findings

Surfactants lower the effective surface tension at interfaces.

The model predicts surfactant segregation to interfaces.

Gamma-convergence yields the limiting surface tension model.

Abstract

We investigate the influence of surfactants on stabilizing the formation of interfaces in non-local anisotropic two-phase fluid at equilibrium. The analysis focuses on singularly perturbed non-local van der Waals-Cahn-Hillard-type energies, supplemented with a term that accounts for the interaction between the surfactant and the fluid. We derive by Gamma-convergence the effective surface tension model as the thickness of the transition layer vanishes and show that it decreases when the surfactant segregates to the interface.