A numerical method to simulate interfacial surfactant mechanics within a volume of fluid method has been developed. Two important features of this new method are that it conserves surfactant mass exactly and the form of the equation of state is not restricted, i.e. the relation between surfactant concentration and surface tension can be linear or nonlinear. To conserve surfactant, the surfactant mass and the interfacial surface area are tracked as the interface evolves, and then the surfactant concentration is reconstructed. The algorithm is coupled to an incompressible Navier-Stokes solver that uses a continuum method to incorporate both the normal and tangential components of the surface tension force into the momentum equation.
Numerical simulations demonstrate the effect of surfactant on the dynamics of several problems by comparison to surfactant-free simulations. First, the buoyant rise of a bubble is examined. Next, the evolution of a drop in an extensional flow is studied. Finally, the motion of a drop through a constriction is investigated. In each of these problems surfactant accumulation allows high interface curvature and the formation of small secondary drops or bubbles.