Mathematical Modelling of Surfactant Self-assembly at Interfaces

Handle URI:
http://hdl.handle.net/10754/598773
Title:
Mathematical Modelling of Surfactant Self-assembly at Interfaces
Authors:
Morgan, C. E.; Breward, C. J. W.; Griffiths, I. M.; Howell, P. D.
Abstract:
© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary differential equations that couple the rearrangement of surfactant within the multilayer to the surface adsorption kinetics is first derived. This model is then extended to the macroscopic scale by taking the continuum limit that exploits the typically large number of surfactant layers, which results in a novel third-order partial differential equation. The model is generalized to allow for the presence of two adsorbing boundaries, which results in an implicit free-boundary problem. The system predicts physically observed features in multilayer systems such as the initial formation of smaller lamellar structures and the typical number of layers that form in equilibrium.
Citation:
Morgan CE, Breward CJW, Griffiths IM, Howell PD (2015) Mathematical Modelling of Surfactant Self-assembly at Interfaces. SIAM Journal on Applied Mathematics 75: 836–860. Available: http://dx.doi.org/10.1137/140983641.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Mathematics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2015
DOI:
10.1137/140983641
Type:
Article
ISSN:
0036-1399; 1095-712X
Sponsors:
This work was partially supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).The first author's work was supported by EPSRC via a CASE award.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMorgan, C. E.en
dc.contributor.authorBreward, C. J. W.en
dc.contributor.authorGriffiths, I. M.en
dc.contributor.authorHowell, P. D.en
dc.date.accessioned2016-02-25T13:40:56Zen
dc.date.available2016-02-25T13:40:56Zen
dc.date.issued2015-01en
dc.identifier.citationMorgan CE, Breward CJW, Griffiths IM, Howell PD (2015) Mathematical Modelling of Surfactant Self-assembly at Interfaces. SIAM Journal on Applied Mathematics 75: 836–860. Available: http://dx.doi.org/10.1137/140983641.en
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/140983641en
dc.identifier.urihttp://hdl.handle.net/10754/598773en
dc.description.abstract© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary differential equations that couple the rearrangement of surfactant within the multilayer to the surface adsorption kinetics is first derived. This model is then extended to the macroscopic scale by taking the continuum limit that exploits the typically large number of surfactant layers, which results in a novel third-order partial differential equation. The model is generalized to allow for the presence of two adsorbing boundaries, which results in an implicit free-boundary problem. The system predicts physically observed features in multilayer systems such as the initial formation of smaller lamellar structures and the typical number of layers that form in equilibrium.en
dc.description.sponsorshipThis work was partially supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).The first author's work was supported by EPSRC via a CASE award.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAdsorption kineticsen
dc.subjectFree-boundary problemsen
dc.subjectPartial differential equationsen
dc.titleMathematical Modelling of Surfactant Self-assembly at Interfacesen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.