Simulating binary fluid-surfactant dynamics by a phase field model

In this paper, the dynamics of a binary fluid-surfactant systemdescribed by a phenomenological phase field model is investigatedthrough analytical and numerical computations. We first considerthe case of one-dimensional planar interface and prove theexistence of the equilibrium solution. Then we derive theanalytical equilibrium solution for the order parameter and thesurfactant concentration in a particular case. The results showthat the present phase field formulation qualitatively mimics thesurfactant adsorption on the binary fluid interfaces. We furtherstudy the time-dependent solutions of the system by numericalcomputations based on the pseudospectral Fourier computationalframework. The present numerical results are in a good agreementwith the previous theoretical study in the way that the surfactantfavors the creation of interfaces and also stabilizes theformation of phase regions.