Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5102979 | Physica A: Statistical Mechanics and its Applications | 2017 | 12 Pages |
Abstract
Relaxation of micellar systems can be described with the help of the Becker-Döring kinetic difference equations for aggregate concentrations. Passing in these equations to continual description, when the aggregation number is considered as continuous variable and the concentration difference is replaced by the concentration differential, allows one to find analytically the eigenvalues (to whom the inverse times of micellar relaxation are related) and eigenfunctions (or the modes of fast relaxation) of the linearized differential operator of the kinetic equation corresponding to the Fokker-Planck approximation. At this the spectrum of eigenvalues appears to be degenerated at some surfactant concentrations. However, as has been recently found by us, there is no such a degeneracy at numerical determination of the eigenvalues of the matrix of coefficients for the linearized difference Becker-Döring equations. It is shown in this work in the frameworks of the perturbation theory, that taking into account the corrections to the kinetic equation produced by second derivatives at transition from differences to differentials and by deviation of the aggregation work from a parabolic form in the vicinity of the work minimum, lifts the degeneracy of eigenvalues and improves markedly the agreement of concentration-dependent fast relaxation time with the results of the numerical solution of the linearized Becker-Döring difference equations.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
I.A. Babintsev, L.Ts. Adzhemyan, A.K. Shchekin,