Numerical simulation of binary fluid-surfactant phase field model coupled with geometric curvature on the curved surface

摘要

In this paper, we consider the numerical simulation of the binary fluid-surfactant phase field model coupled with geometric curvature on the curved surface. By taking account of the effect of the curvature, we firstly modify the free energy of the fluid-surfactant system, which results a new phase field model on the curved surface. Then, based on the scalar auxiliary variable method, we study the numerical schemes, which consist of a surface finite element method for the spatial discretization, and first- and second-order implicit schemes for the temporal discretization. The unconditional energy stability of the first-order one is also strictly proved. Finally, some numerical examples are shown to verify the theoretical prediction. Furthermore, two important features of the system are observed: one is that the curvature can cause one of the two fluids to favor or avoid areas of high curvature on the curved surface; the other one is that the higher the coupling intensity is, the faster the energy reaches stability. (C) 2020 Elsevier B.V. All rights reserved.