Ageing of a gas/liquid interface elongated by standing waves

This paper aims at modelling the interfacial ageing induced by the sudden arising of standing capillary waves at a contaminated air/water interface. Here is thus considered a brimful cylindrical reactor filled with a water bath in which surfactants are solubilized. The cylindrical capillary waves at the air/water free surface are responsible for further production of interfacial area. The surface diffusion being supposed instantaneous, Marangoni effect does not play any damping role. The thermodynamical equilibrium achieved when the interface is at rest, is considered as initial condition. The time-dependence of the surface concentration in surfactants, Γ(t), and of the bulk concentration in surfactants at the vicinity of the interface, Cs(t), is analytically modelled taking into account the serial coupling between bulk diffusion and sorption phenomena. As recommended by Yariv and Frankel [E. Yariv, I. Frankel, Phys. Rev. Lett. 89 (2002) 26], none assumption on the source of the ageing is formulated in the transient regime under consideration.