A Phase Field Method for surfactant-laden multiphase flows with different solubilities

In this work we present a new phase field model for multiphase flows with soluble surfactants that accounts for unmatched solubility. The advection-diffusion of the phase field and of the surfactant is described using two Cahn-Hilliard equations together with a two-order-parameter Ginzburg-Landau free energy functional. Here, an asymmetric term is introduced to penalize the presence of surfactant in one of the phases. This modification allows to circumvent existing limitations on phase field method applications to liquid-gas systems. The model has been tested on planar configurations characterized by two phases with different solubility using a pseudo-spectral code. The results demonstrate the ability to accurately reproduce the expected surfactant distribution. The simulation of a single droplet and of a droplet-droplet interaction in shear flow is then examined in order to understand how the difference in surfactant bulk concentration between the phases affects the overall interfacial behavior.