c 10 ร
c 10 (G).
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1. 1]
A theoretical approach to the kinetics of adsorption on the expanding interface of a micellar surfactant solution is proposed. For example, it can be the Langmuir adsorption isotherm
The nonlinear partial differential equations of mass transfer of the micelles and monomers are reduced to ordinary differential equations, which are solved numerically along with the nonlin-
earized adsorption isotherm as a boundary condition. Being more general, this theoretical approach is consistent also with the special case of small deviations from equilibrium widely used in the kinetwhere b and G ฯฑ are constants and t denotes time. Both nonics of micellization. The theory is applied further to fit the experiionic (3-5) and ionic (6) surfactants are found to comply mental data for dynamic surface tension of micellar solutions of with the Langmuir adsorption isotherm. More sophisticated sodium dodecyl sulfate and sodium polyoxyethylene-2 sulfate adsorption isotherms are also used (7). In some particular measured by the maximum bubble pressure (MBP) method. The cases (small adsorption, small deviations from equilibrium, expansion of the bubble surface is accounted for by using the etc.) the adsorption isotherm can be linearized and then stanexperimental dependence of the bubble size on time. The calcudard mathematical methods can be applied to solve the diffulated effective rate constant of micelle decay for sodium dodecyl sion problem, see e.g., Refs. (8-10). However, the general sulfate turns out to be sensitive to the mechanism of the micelle's boundary problem is essentially nonlinear. One way to solve disintegration. This provides a possibility for one to determine the it is to use perturbation series methods (11). Another aprate constants of the fast and slow processes in the relaxation kinetics of micellization by using a relatively simple experimental proach is to solve numerically the respective set of equations, technique for dynamic surface tension measurement like the MBP including the partial differential equation of diffusion (12, method.