A mixed kinetic-diffusion surfactant model for the Henry isotherm

This paper focuses on the mathematical modeling and the variational and numerical analyses of surfactants behavior at the air–water interface, taking into account the mixed kinetic-diffusion model evolving to the Henry isotherm. The existence and uniqueness of a weak solution is proved applying classical results for linear parabolic equations and fixed-point techniques. 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 for a commercially available surfactant.