Diffusion of surfactant from a micellar solution to a bare interface. 1. Absorbing boundary

We analyze dynamic adsorption of surfactant from a micellar solution to a rapidly created surface that acts as an absorbing boundary for surfactant monomers (single molecules), along which the monomer concentration vanishes, with no direct micelle adsorption. This somewhat idealized situation is analyzed as a prototype for situations in which strong suppression of monomer concentration accelerates micelle dissociation, and will be used as a starting point for analysis of more realistic boundary conditions in subsequent work. We present scaling arguments and approximate models for particular time and parameter regimes and compare the resulting predictions to numerical simulations of the reaction-diffusion equations for a polydisperse system containing surfactant monomers and clusters of arbitrary aggregation number. The model considered here exhibits an initial period of rapid shrinkage and ultimate dissociation of micelles within a narrow region near the interface. This opens a micelle-free region near the interface after some time τ_e, the width of which increases as t^1/2 at times t≫τ_e. In systems that exhibit disparate fast and slow bulk relaxation times τ₁ and τ₂ in response to small perturbations, τ_e is usually comparable to or greater than τ₁ but much less than τ₂. Such systems exhibit a wide intermediate time regime τ_e2 in which the remaining micellar region reaches a state of partial local equilibrium, followed by a final stage t≫τ₂ in which full local equilibrium is established.