On the predictions and limitations of the Becker-Doring model for reaction kinetics in micellar surfactant solutions.
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 simul...
| Main Authors: | , , , , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2011
|
| _version_ | 1797082705627709440 |
|---|---|
| author | Griffiths, I Bain, C Breward, C Colegate, D Howell, P Waters, S |
| author_facet | Griffiths, I Bain, C Breward, C Colegate, D Howell, P Waters, S |
| author_sort | Griffiths, I |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T01:31:35Z |
| format | Journal article |
| id | oxford-uuid:93c9f431-beeb-4f30-ad21-14bf1f86a6c2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:31:35Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:93c9f431-beeb-4f30-ad21-14bf1f86a6c22022-03-26T23:34:41ZOn the predictions and limitations of the Becker-Doring model for reaction kinetics in micellar surfactant solutions.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:93c9f431-beeb-4f30-ad21-14bf1f86a6c2EnglishSymplectic Elements at Oxford2011Griffiths, IBain, CBreward, CColegate, DHowell, PWaters, SWe 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. |
| spellingShingle | Griffiths, I Bain, C Breward, C Colegate, D Howell, P Waters, S On the predictions and limitations of the Becker-Doring model for reaction kinetics in micellar surfactant solutions. |
| title | On the predictions and limitations of the Becker-Doring model for reaction kinetics in micellar surfactant solutions. |
| title_full | On the predictions and limitations of the Becker-Doring model for reaction kinetics in micellar surfactant solutions. |
| title_fullStr | On the predictions and limitations of the Becker-Doring model for reaction kinetics in micellar surfactant solutions. |
| title_full_unstemmed | On the predictions and limitations of the Becker-Doring model for reaction kinetics in micellar surfactant solutions. |
| title_short | On the predictions and limitations of the Becker-Doring model for reaction kinetics in micellar surfactant solutions. |
| title_sort | on the predictions and limitations of the becker doring model for reaction kinetics in micellar surfactant solutions |
| work_keys_str_mv | AT griffithsi onthepredictionsandlimitationsofthebeckerdoringmodelforreactionkineticsinmicellarsurfactantsolutions AT bainc onthepredictionsandlimitationsofthebeckerdoringmodelforreactionkineticsinmicellarsurfactantsolutions AT brewardc onthepredictionsandlimitationsofthebeckerdoringmodelforreactionkineticsinmicellarsurfactantsolutions AT colegated onthepredictionsandlimitationsofthebeckerdoringmodelforreactionkineticsinmicellarsurfactantsolutions AT howellp onthepredictionsandlimitationsofthebeckerdoringmodelforreactionkineticsinmicellarsurfactantsolutions AT waterss onthepredictionsandlimitationsofthebeckerdoringmodelforreactionkineticsinmicellarsurfactantsolutions |