Kinetic theory of coupled binary-fluid-surfactant systems

TL;DR

This paper develops a comprehensive hydrodynamic model for coupled binary-fluid-surfactant systems derived from microscopic physics, capturing key surfactant phenomena through a mesoscopic free energy functional.

Contribution

It introduces a novel derivation of continuum equations from microscopic surfactant dynamics using Rayleigh's variational principle, including polarization effects.

Findings

Model accurately predicts surface tension reduction.

Captures droplet stabilization phenomena.

Validated by perturbation theory and simulations.

Abstract

We derive a self-consistent hydrodynamic theory of coupled binary-fluid-surfactant systems from the underlying microscopic physics using Rayleigh's variational principle. At the microscopic level, surfactant molecules are modelled as dumbbells that exert forces and torques on the fluid and interface while undergoing Brownian motion. We obtain the overdamped stochastic dynamics of these particles from a Rayleighian dissipation functional, which we then coarse-grain to derive a set of continuum equations governing the surfactant concentration, orientation, and the fluid density and velocity. This approach introduces a polarization field, representing the average orientation of surfactants, and yields a mesoscopic free energy functional from which all governing equations are consistently derived. The resulting model accurately captures key surfactant phenomena, including surface tension reduction and droplet stabilization, as confirmed by both perturbation theory and numerical simulations.