A Fluctuating Hydrodynamics Model for Nanoscale Surfactant-laden Interfaces

TL;DR

This paper develops a fluctuating hydrodynamics model for nanoscale surfactant interfaces, capturing the effects of thermal fluctuations, surfactant concentration, and Marangoni convection on interface stability and dynamics.

Contribution

It introduces a generalized ternary mixture model incorporating stochastic fluxes within a diffuse interface framework for nanoscale surfactant-laden interfaces.

Findings

Surface tension decreases linearly with surfactant concentration.

Thermal fluctuations disrupt surfactant stabilization in fluid pinch-off.

Capillary wave spectrum deviates from classical theory due to Gibbs elasticity.

Abstract

A multispecies diffuse interface model is formulated in a fluctuating hydrodynamics framework for the purpose of simulating surfactant interfaces at the nanoscale. The model generalizes previous work to ternary mixtures, employing a Cahn-Hilliard free energy density combined with incompressible, isothermal fluctuating hydrodynamics where dissipative fluxes include both deterministic and stochastic terms. The intermolecular parameters in the free energy are chosen such that one species acts as a partially miscible surfactant. From Laplace pressure measurements we show that in this model the surface tension decreases linearly with surfactant concentration, leading to Marangoni convection for interfaces with concentration gradients. In the capillary wave spectrum for interfaces with and without surfactant we find that for the former the spectrum deviates significantly from classical capillary wave theory, presumably due to Gibbs elasticity. In non-equilibrium simulations of the Rayleigh-Plateau instability, deterministic simulations showed that the surfactant delays pinching of a fluid cylinder into droplets. However, stochastic simulations indicate that thermal fluctuations disrupt the surfactant's stabilizing effect. Similarly, the spreading of a patch of surfactant, driven by Marangoni convection, was found to be partially suppressed by thermal fluctuations.