Kinetics of Mass Transfer in Micellar Systems: Surfactant Adsorption, Solubilization Kinetics, and Ripening

We consider the problem of the surfactant adsorption from a micellar solution in the spirit of the theory of Johner and Joanny ( Macromolecules 1990, 23, 5299). The problem is solved for two geometries: the adsorption through a stagnant layer and the adsorption onto a spherical particle. We analyze the case when the critical micelle concentration (cmc) is many orders of magnitude less than the total surfactant concentration. At low volume fraction of micelles in the bulk φ, the steady state mass flux into the interface J is the same as in the absence of micelles, J = D mon C̃ mon /δ, where δ is the diffusion path of the problem (i.e., the thickness of the stagnant layer or the radius of the spherical particle), D mon is the monomer diffusion coefficient, and C̃ mon is the cmc. Increasing the concentration of micelles leads to the crossover to a smaller diffusion path 1/κ ∼ λ/(3φ) 1/2, where λ is the micellar radius. The driving force of the mass transfer is still equal to the molecular solubility gradient (i.e., cmc) and is not affected by the concentration of micelles. We show that the problems of solubilization kinetics and the effects of micelles on the Ostwald ripening and “composition ripening” processes can be treated similarly.