title: On the predictions and limitations of the Becker-Döring model for reaction kinetics in micellar surfactant solutions.
abstract: We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker-Döring system of equations, using realistic expressions for the reaction constants fit to results from Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated timescales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker-Döring theory for re-equilibration of surfactant solutions.
authors.affiliation: Mathematical Institute, University of Oxford, OX1 3LB, UK. ian.griffiths@maths.ox.ac.uk
authors.forename: I M
authors.initials: IM
authors.lastname: Griffiths
authors.forename: C D
authors.initials: CD
authors.lastname: Bain
authors.forename: C J W
authors.initials: CJ
authors.lastname: Breward
authors.forename: D M
authors.initials: DM
authors.lastname: Colegate
authors.forename: P D
authors.initials: PD
authors.lastname: Howell
authors.forename: S L
authors.initials: SL
authors.lastname: Waters