We develop a thermodynamically consistent phase-field model for soluble surfactants in two-phase flows, incorporating both interfacial and solid surface adsorption. The model is derived via variational principles consistent with the second law of thermodynamics, resulting in modified free energies and boundary conditions that capture surfactant transport, adsorption and wetting dynamics. A key contribution of this work is the inclusion of surfactant adsorption on solid walls, which leads to qualitative agreement with experimental observations: unlike prior numerical studies that predicted hydrophilic surfaces becoming more hydrophilic and hydrophobic surfaces more hydrophobic, our model shows a shift towards increased hydrophilicity across all contact angles – consistent with experimental trends. Our results establish that solid adsorption provides the missing mechanism required for predictive modelling of surfactant-laden contact line dynamics.
Kannan et al. (Thu,) studied this question.