Transient aging of a liquid-gas interface stretched by standing waves: on the interplay of chemical kinetics

This article discusses the aging of a liquid surface enriched with surface active species and suddenly perturbed by standing capillary waves. Special attention is paid to deriving an accurate initial condition of the surface elevation. Due to the arising of the waves, the sub-phase and surface concentrations, C and Gamma, which were initially uniform and controlled by thermodynamic equilibrium, are modified by a transient oscillatory regime. A complete analytical description of the time-dependent carrier wave and oscillating chemical modulations associated with these concentrations is proposed for: (1) a small surface elevation, (2) a weak coupling with momentum transport, (3) but a strong coupling between all chemical transport phenomena which might be involved during transient regime: surface adsorption/desorption, 3-D diffusion within the sub-phase as well as near the liquid surface, and 2-D chemical diffusion along the surface. Analytical expressions resulting from regular perturbation series are compared to the limit aging regimes most commonly invoked in the literature, namely, diffusion- or sorption-limited surface aging. Finally, the (surface) compositional elasticity due to the arising of surface tension gradients is derived.