Standard models of the adsorption kinetics of surfactants at the air-water surface assume that micelles break down into monomers in the bulk solution and that only monomers adsorb. We show here that micelles of the nonionic surfactant C14E8 adsorb to the surface of a liquid jet at a diffusion-controlled rate. Micellar adsorption can be switched off by incorporation of a small amount of ionic surfactant into the micelle and switched on again by addition of salt. More sophisticated models of adsorption processes in micellar solutions are required that permit a kinetic flux of micelles to the air-water interface.

We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker-Döring system of equations, using realistic expressions for the reaction constants fit to Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated time-scales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker-Döring theory for re-equilibration and discuss potential resolutions.

Micellar surfactant solutions are generally assumed to undergo restructuring via stepwise monomer loss following a dilution. This process is captured by the Becker-Döring equations, an infinite-dimensional system of ordinary differential equations for the concentration of each aggregate in solution. We reveal certain classes of surfactants, such as the non-ionic family C n E m , for which the predicted re-equilibration times via stepwise monomer loss are far greater than those observed experimentally. We investigate two alternative pathways for re-equilibration, first allowing for micelles to break down into two aggregate fragments rather than stepwise monomer release, and secondly by allowing aggregates to merge together to form large super-micelles that exceed the size of a proper micelle. While the former shows no discernible difference in the predicted time to re-equilibration, the latter provides an alternative pathway to re-equilibration: the formation of unstable super-micelles that break down to proper micelles via a cascade of stepwise monomer release. The new theory is shown to describe the re-equilibration of any surfactant system, with the conventional Becker-Döring theory forming a subset of the model that describes the behaviour of a small range of surfactant systems with high critical micelle concentrations and low aggregation numbers. The pathway proposed provides an essential mechanistic route to equilibrium.

The adsorption of nonionic surfactants in the CnE8 family at the air–water interface has been studied on the millisecond timescale in a free liquid jet. The amount of adsorbed surfactant was measured by ellipsometry. The rates of adsorption are compared with a diffusion-controlled adsorption model. In the case of C10E8, which is below its cmc, the monomer diffusion coefficient provides a good fit to the experimental data. For n = 12, 14, and 16, micelles control the mass transport. The best fit diffusion coefficients are close to, but not identical with, the literature values for the micellar diffusion coefficients. Laser Doppler velocimetry was used to measure the change in surface velocity arising from adsorption of the surfactant, for n = 12, 14, and 16. There was a qualitative correlation between the retardation of the surface velocity and the surface tension gradients.