A new phase-field model for a water-oil-surfactant system

We propose a new phase-field model to investigate the hydrodynamics of a water-oil-surfactant system. The phase-field method based on the time-dependent Ginzbug-Landau model is developed for the water-oil-surfactant system using two order parameters. We derive the new model in which the water-oil interfacial profile is independent of the surfactant concentration. The proposed model is coupled with the Navier-Stokes equation to have hydrodynamics and it provides an accurate surface tension from the numerical point of view. Various numerical results are presented such as the pressure difference test, calculation of the Dirac-delta function, and the interfacial profile effect to demonstrate the good performance of our model. A droplet deformation under shear flows with Marangoni force is also numerically investigated.