Modelling surfactant systems out of thermodynamic equlibrium

We develop and explore a simple mathematical model describing the behavior of surfactants in situations where molecules adsorbed at an air-liquid interface are not in thermodynamic equilibrium with those just below the surface. Our model incorporates a gradient flow which links the flux of molecules to/from the surface with the change in energy that occurs through this process. We use our model to examine three key situations: adsorption onto a clean surface, desorption into a clean bulk liquid, and desorption from a saturated surface. In each case, we solve the system numerically and compare our results with asymptotic predictions in the limit of fast adsorption and desorption. We show that the dynamic surface energy during the process can differ significantly from that predicted by previous theories which either assume thermodynamic equilibrium or use an adhoc combination of non-equilibrium adsorption with an equilibrium relationship for the surface energy.