TY - JOUR
T1 - On the predictions and limitations of the Becker–Döring model for reaction kinetics in micellar surfactant solutions
AU - Griffiths, I.M.
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.
PY - 2011/8
Y1 - 2011/8
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/599065
UR - https://linkinghub.elsevier.com/retrieve/pii/S0021979711005108
UR - http://www.scopus.com/inward/record.url?scp=79958781882&partnerID=8YFLogxK
U2 - 10.1016/j.jcis.2011.04.074
DO - 10.1016/j.jcis.2011.04.074
M3 - Article
C2 - 21571292
SN - 0021-9797
VL - 360
SP - 662
EP - 671
JO - Journal of Colloid and Interface Science
JF - Journal of Colloid and Interface Science
IS - 2
ER -