Numerical Solution of Generalized Smoluchowski Equations for Cylindrical Micelles

Abstract

The relaxation kinetics of polydisperse cylindrical micelles has been numerically studied under different initial conditions corresponding to fast concentration and dilution of a surfactant solution. The kinetic description has been based on a set of difference Smoluchowski equations, which takes into account the capture and release of surfactant monomers by micelles, as well as the fusion and fission of micelles. The dependences of fusion coefficients of cylindrical aggregates on aggregation numbers have been plotted on the basis of the Burgers−Oseen equations for translational motion of spherocylindrical particles in a viscous liquid. The solution of the generalized Smoluchowski kinetic equations obtained for a nonequilibrium distribution of cylindrical micelles over aggregation numbers has been compared with the numerical solution of the Becker−Döring kinetic equations for cylindrical micelles under the same initial conditions given the mechanism of molecular aggregation via the attachment and detachment of surfactant monomers.