On the predictions and limitations of the Becker–Döring model for reaction kinetics in micellar surfactant solutions

I.M. Griffiths; C.D. Bain; C.J.W. Breward; D.M. Colegate; P.D. Howell; S.L. Waters

doi:10.1016/j.jcis.2011.04.074

On the predictions and limitations of the Becker–Döring model for reaction kinetics in micellar surfactant solutions

I.M. Griffiths, C.D. Bain, C.J.W. Breward, D.M. Colegate, P.D. Howell, S.L. Waters

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23 Scopus citations

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. © 2011 Elsevier Inc.

Original language	English (US)
Pages (from-to)	662-671
Number of pages	10
Journal	Journal of Colloid and Interface Science
Volume	360
Issue number	2
DOIs	https://doi.org/10.1016/j.jcis.2011.04.074
State	Published - Aug 2011
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) and by EPSRC Grant EP/E019323. IMG gratefully acknowledges helpful discussions with Dr. P. J. Dellar, Professor S.D. Howison and Professor J.R. Ockendon. SLW is grateful to the EPSRC for funding in the form of an Advanced Research Fellowship.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.jcis.2011.04.074

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title = "On the predictions and limitations of the Becker–D{\"o}ring 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-D{\"o}ring 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-D{\"o}ring theory for re-equilibration of surfactant solutions. {\textcopyright} 2011 Elsevier Inc.",

author = "I.M. Griffiths and C.D. Bain and C.J.W. Breward and D.M. Colegate and P.D. Howell and S.L. Waters",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) and by EPSRC Grant EP/E019323. IMG gratefully acknowledges helpful discussions with Dr. P. J. Dellar, Professor S.D. Howison and Professor J.R. Ockendon. SLW is grateful to the EPSRC for funding in the form of an Advanced Research Fellowship. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Bain, C.D.

AU - Breward, C.J.W.

AU - Colegate, D.M.

AU - Howell, P.D.

AU - Waters, S.L.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) and by EPSRC Grant EP/E019323. IMG gratefully acknowledges helpful discussions with Dr. P. J. Dellar, Professor S.D. Howison and Professor J.R. Ockendon. SLW is grateful to the EPSRC for funding in the form of an Advanced Research Fellowship. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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On the predictions and limitations of the Becker–Döring model for reaction kinetics in micellar surfactant solutions

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