Controlled Topological Transitions in Thin-Film Phase Separation

Handle URI:
http://hdl.handle.net/10754/597864
Title:
Controlled Topological Transitions in Thin-Film Phase Separation
Authors:
Hennessy, Matthew G.; Burlakov, Victor M.; Goriely, Alain; Wagner, Barbara; Münch, Andreas
Abstract:
© 2015 Society for Industrial and Applied Mathematics. In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls toward each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model. Using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that this newly created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving their area. A quantitative analysis of this mechanism is carried out via a thin-film model for the free interfaces, which is derived asymptotically from the sharp-interface model.
Citation:
Hennessy MG, Burlakov VM, Goriely A, Wagner B, Münch A (2015) Controlled Topological Transitions in Thin-Film Phase Separation. SIAM Journal on Applied Mathematics 75: 38–60. Available: http://dx.doi.org/10.1137/130950227.
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:
10.1137/130950227
Type:
Article
ISSN:
0036-1399; 1095-712X
Sponsors:
The work of these authors was supported by KAUST (award KUK-C1-013-04). The second and third authors were also supported by the James Martin School. The third author is a Wolfson/Royal Society Merit Award Holder and acknowledges support from a reintegration grant under EC Framework VII.This author's work was supported by the Federal Ministry of Education (BMBF) and the state government of Berlin (SENBWF) in the framework of the program "Spitzenforschung und Innovation in den Neuen Landern" (grant 03IS2151).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorHennessy, Matthew G.en
dc.contributor.authorBurlakov, Victor M.en
dc.contributor.authorGoriely, Alainen
dc.contributor.authorWagner, Barbaraen
dc.contributor.authorMünch, Andreasen
dc.date.accessioned2016-02-25T12:58:01Zen
dc.date.available2016-02-25T12:58:01Zen
dc.date.issued2015-01en
dc.identifier.citationHennessy MG, Burlakov VM, Goriely A, Wagner B, Münch A (2015) Controlled Topological Transitions in Thin-Film Phase Separation. SIAM Journal on Applied Mathematics 75: 38–60. Available: http://dx.doi.org/10.1137/130950227.en
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/130950227en
dc.identifier.urihttp://hdl.handle.net/10754/597864en
dc.description.abstract© 2015 Society for Industrial and Applied Mathematics. In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls toward each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model. Using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that this newly created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving their area. A quantitative analysis of this mechanism is carried out via a thin-film model for the free interfaces, which is derived asymptotically from the sharp-interface model.en
dc.description.sponsorshipThe work of these authors was supported by KAUST (award KUK-C1-013-04). The second and third authors were also supported by the James Martin School. The third author is a Wolfson/Royal Society Merit Award Holder and acknowledges support from a reintegration grant under EC Framework VII.This author's work was supported by the Federal Ministry of Education (BMBF) and the state government of Berlin (SENBWF) in the framework of the program "Spitzenforschung und Innovation in den Neuen Landern" (grant 03IS2151).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectPhase separation in confined geometryen
dc.subjectSharp-interface asymptoticsen
dc.subjectThin-film equationsen
dc.subjectTopological transformationsen
dc.titleControlled Topological Transitions in Thin-Film Phase Separationen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionTechnische Universitat Berlin, Berlin, Germanyen
dc.contributor.institutionWeierstrass Institute for Applied Analysis and Stochastics, Berlin, Germanyen
kaust.grant.numberKUK-C1-013-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.