# American Institute of Mathematical Sciences

June  2012, 17(4): 1289-1307. doi: 10.3934/dcdsb.2012.17.1289

## Simulating binary fluid-surfactant dynamics by a phase field model

 1 Department of Applied Mathematics, Center of Mathematical Modeling and Scientiﬁc Computing, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30010, Taiwan, Taiwan 2 Department of Mathematics, National Center for Theoretical Sciences (Taipei offce), National Taiwan University, Taipei 10617, Taiwan

Received  February 2011 Revised  September 2011 Published  February 2012

In this paper, the dynamics of a binary fluid-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 fluid 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.
Citation: Chun-Hao Teng, I-Liang Chern, Ming-Chih Lai. Simulating binary fluid-surfactant dynamics by a phase field model. Discrete & Continuous Dynamical Systems - B, 2012, 17 (4) : 1289-1307. doi: 10.3934/dcdsb.2012.17.1289
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