A Multiple-Scale Analysis of Evaporation Induced Marangoni Convection

Handle URI:
http://hdl.handle.net/10754/597323
Title:
A Multiple-Scale Analysis of Evaporation Induced Marangoni Convection
Authors:
Hennessy, Matthew G.; Münch, Andreas
Abstract:
This paper considers the stability of thin liquid layers of binary mixtures of a volatile (solvent) species and a nonvolatile (polymer) species. Evaporation leads to a depletion of the solvent near the liquid surface. If surface tension increases for lower solvent concentrations, sufficiently strong compositional gradients can lead to Bénard-Marangoni-type convection that is similar to the kind which is observed in films that are heated from below. The onset of the instability is investigated by a linear stability analysis. Due to evaporation, the base state is time dependent, thus leading to a nonautonomous linearized system which impedes the use of normal modes. However, the time scale for the solvent loss due to evaporation is typically long compared to the diffusive time scale, so a systematic multiple scales expansion can be sought for a finite-dimensional approximation of the linearized problem. This is determined to leading and to next order. The corrections indicate that the validity of the expansion does not depend on the magnitude of the individual eigenvalues of the linear operator, but it requires these eigenvalues to be well separated. The approximations are applied to analyze experiments by Bassou and Rharbi with polystyrene/toluene mixtures [Langmuir, 25 (2009), pp. 624-632]. © 2013 Society for Industrial and Applied Mathematics.
Citation:
Hennessy MG, Münch A (2013) A Multiple-Scale Analysis of Evaporation Induced Marangoni Convection. SIAM Journal on Applied Mathematics 73: 974–1001. Available: http://dx.doi.org/10.1137/110849006.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Mathematics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
23-Apr-2013
DOI:
10.1137/110849006
Type:
Article
ISSN:
0036-1399; 1095-712X
Sponsors:
This work was supported by King Abdullah University of Science and Technology (KAUST) through award KUK-C1-013-04.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorHennessy, Matthew G.en
dc.contributor.authorMünch, Andreasen
dc.date.accessioned2016-02-25T12:30:41Zen
dc.date.available2016-02-25T12:30:41Zen
dc.date.issued2013-04-23en
dc.identifier.citationHennessy MG, Münch A (2013) A Multiple-Scale Analysis of Evaporation Induced Marangoni Convection. SIAM Journal on Applied Mathematics 73: 974–1001. Available: http://dx.doi.org/10.1137/110849006.en
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/110849006en
dc.identifier.urihttp://hdl.handle.net/10754/597323en
dc.description.abstractThis paper considers the stability of thin liquid layers of binary mixtures of a volatile (solvent) species and a nonvolatile (polymer) species. Evaporation leads to a depletion of the solvent near the liquid surface. If surface tension increases for lower solvent concentrations, sufficiently strong compositional gradients can lead to Bénard-Marangoni-type convection that is similar to the kind which is observed in films that are heated from below. The onset of the instability is investigated by a linear stability analysis. Due to evaporation, the base state is time dependent, thus leading to a nonautonomous linearized system which impedes the use of normal modes. However, the time scale for the solvent loss due to evaporation is typically long compared to the diffusive time scale, so a systematic multiple scales expansion can be sought for a finite-dimensional approximation of the linearized problem. This is determined to leading and to next order. The corrections indicate that the validity of the expansion does not depend on the magnitude of the individual eigenvalues of the linear operator, but it requires these eigenvalues to be well separated. The approximations are applied to analyze experiments by Bassou and Rharbi with polystyrene/toluene mixtures [Langmuir, 25 (2009), pp. 624-632]. © 2013 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis work was supported by King Abdullah University of Science and Technology (KAUST) through award KUK-C1-013-04.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectMarangoni convectionen
dc.subjectMultiple scalesen
dc.subjectSlow evaporationen
dc.titleA Multiple-Scale Analysis of Evaporation Induced Marangoni Convectionen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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