Surface phase-field surfactant fluid model and its practical closest point type finite difference computation

Abstract

To investigate the fluid surfactant material on three-dimensional objects, we herein develop a simple and practical model based on phase-field method and design its efficient algorithm. The binary fluids and surfactant are represented by two order parameters. The fluid evolution is governed by the incompressible Navier–Stokes equations. To achieve high-performance computation, a linear semi-implicit scheme with stabilizers is proposed for the phase-field type equations in time. The projection method with pressure correction is used to decouple the velocity and the pressure. Based on the closest-point type embedded narrow domain method and a simple pseudo-Neumann boundary treatment, the calculation on curved surface is extended into a narrow band region including the surface. The surface spatial operators are approximately replaced by the standard spatial operators. In the three-dimensional narrow band, the finite difference method is used to discretize the equations on staggered grids. The mass compensation and vector projection techniques are designed to obtain physically meaningful solutions. In each time iteration, the proposed algorithm is efficient to implement. Numerical results indicate that the proposed method is capable to simulate surfactant-laden phase separation, fluid instabilities, and coarsening dynamics with variable mobility on various surfaces.