A Front-Tracking Method for Motion by Mean Curvature with Surfactant (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we present a finite difference method to track a network ofcurves whose motion is determined by mean curvature. To study the effect of inhomogeneoussurface tension on the evolution of the network of curves, we includesurfactant which can diffuse along the curves. The governing equations consist ofone parabolic equation for the curve motion coupled with a convection-diffusionequation for the surfactant concentration along each curve. Our numerical methodis based on a direct discretization of the governing equations which conserves thetotal surfactant mass in the curve network. Numerical experiments are carried outto examine the effects of inhomogeneous surface tension on the motion of the network,including the von Neumann law for cell growth in two space dimensions.