Simulating binary fluid-surfactant dynamics by a phase field model

In this paper, the dynamics of a binary uid-surfactant system described by a phenomenological phase field model is investigated through analytical and numerical computations. We first consider the case of one-dimensional planar interface and prove the existence of the equilibrium solution. Then we derive the analytical equilibrium solution for the order parameter and the surfactant concentration in a particular case. The results show that the present phase field formulation qualitatively mimics the surfactant adsorption on the binary uid interfaces. We further study the time-dependent solutions of the system by numerical computations based on the pseudospectral Fourier computational framework. The present numerical results are in a good agreement with the previous theoretical study in the way that the surfactant favors the creation of interfaces and also stabilizes the formation of phase regions.