An arbitrary Lagrangian -Eulerian method for interfacial flows with insoluble surfactants

An arbitrary Lagrangian-Eulerian (ALE) method for interfacial flows with insoluble surfactants is presented. The interface is captured using a coupled level set and volume of fluid method, which takes advantage of the strengths of both the level set method and the volume of fluid method. By directly tracking the surfactant mass, the method conserves surfactant mass, and prevents surfactant from diffusing off the interface. Interfacial area is also tracked. To accurately approximate the interfacial area, the fluid interface is reconstructed using piecewise parabolas. The surfactant concentration, which determines the local surface tension through an equation of state, is then computed as surfactant mass per interfacial area. The evolution of the level set function, volume fraction, interfacial area, and surfactant mass is performed using an ALE method. The fluid flow is governed by the Stokes equations, which are solved using a finite element method. The surface tension force is included in the momentum equation using a continuum surface stress formulation. To efficiently resolve the complex interfacial dynamics, the grid is adapted at every time step so that the grid near the moving interface is always refined. The method is extendible to 3D, and can be generalized to other types of grids as well. Communicated by John Lowengrub (GuestEditor) and Mark Sussman. keyword: Interfacial flow, Surfactant, Volume of fluid (VOF), Level set, Arbitrary Lagrangian-Eulerian (ALE), Unstructured grid.

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