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, the width of which increases as t at times t≫τ. In systems that exhibit disparate fast and slow bulk relaxation times τ and τ in response to small perturbations, τ is usually comparable to or greater than τ but much less than τ. Such systems exhibit a wide intermediate time regime τ更多