Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration

TL;DR

This paper develops thermodynamically consistent models for the hydrodynamics of liquid films with high concentrations of insoluble surfactants, extending classical models to include nonlinear effects, phase transitions, and substrate interactions.

Contribution

It introduces a gradient dynamics formulation based on free energy, allowing for systematic extensions to classical models for insoluble surfactant-covered films.

Findings

Reformulation of classical models within a thermodynamic framework

Inclusion of nonlinear equations of state and phase transitions

Discussion of differences from existing literature models

Abstract

In this paper we propose several models that describe the dynamics of liquid films which are covered by a high concentration layer of insoluble surfactant. First, we briefly review the 'classical' hydrodynamic form of the coupled evolution equations for the film height and surfactant concentration that are well established for small concentrations. Then we re-formulate the basic model as a gradient dynamics based on an underlying free energy functional that accounts for wettability and capillarity. Based on this re-formulation in the framework of nonequilibrium thermodynamics, we propose extensions of the basic hydrodynamic model that account for (i) nonlinear equations of state, (ii) surfactant-dependent wettability, (iii) surfactant phase transitions, and (iv) substrate-mediated condensation. In passing, we discuss important differences to most of the models found in the literature.