Numerical analysis of surfactant dynamics at air-water interface using the Henry isotherm

This paper focuses on the surfactant behavior at air-water interface, taking into account the diffusion-controlled model together with the Henry isotherm to model the relation between the surface and the subsurface concentrations. The existence and uniqueness of a weak solution is stated. Fully discrete approximations are obtained by using a finite element method and the backward Euler scheme. Error estimates are then proved from which, under adequate additional regularity conditions, the linear convergence of the algorithm is derived. Finally, some numerical simulations are presented in order to demonstrate the accuracy of the algorithm and the behavior of the solution.