Implementing surfactant mass balance in 2D FEM?CALE models

Practical aspects of implementing surfactant mass balance computation in finite elements models, where the model geometry shape change is captured by utilizing the arbitrary Lagrange–Eulerian method are discussed briefly. The discussion and the reported simulations are carried out in two-dimensional Cartesian coordinates. Two alternative approaches to formulating the governing equation of surfactant mass balance for solving it computationally are presented and discussed. One of the approaches is based on computing the boundary curvature and boundary tangential velocity, as well as their differentials on the boundary, directly. The other approach is based on reformulating the governing equation in order to track the proportional rate of change of local surface area. As a conclusion, it is found that though both of the presented approaches can be configured to perform adequately in terms of surfactant mass conservation, surface differentials that are necessary to compute the surface curvature and surface tangential velocity in the first one of the methods evoke numerical oscillations near those points of the boundary where it is not smooth. The text is accompanied by example simulations and figures.