Free-energy-based lattice Boltzmann model for emulsions with soluble surfactant

Abstract

We propose a diffuse interface model to simulate a system of two immiscible liquids with surfactant. This model is based on a modified Ginzburg-Landau free energy functional to account for non-ionic soluble surfactants and couples the Navier-Stokes equations with two Cahn-Hilliard transport equations to represent immiscible fluids and surfactant concentration. The governing equations are solved using a lattice Boltzmann framework. The proposed model is validated for Langmuir and Frumkin adsorption isotherms when applied to simulate a planar interface and a spherical drop equilibration. The model ensures numerical stability and accurate results for low and high surfactant concentrations, and the diffuse interface thickness remains constant even for high surfactant loads. The model also allows achieving a surface tension reduction of 45-50% compared to the clean system, even at low surfactant concentrations. The appropriate surfactant mobility and solubility values are recommended for different values of the strength of nonlinear surfactant coupling.