Dynamics of a slowly evaporating solvent-polymer mixture with a deformable upper surface

Handle URI:
http://hdl.handle.net/10754/598037
Title:
Dynamics of a slowly evaporating solvent-polymer mixture with a deformable upper surface
Authors:
Hennessy, M. G.; Munch, A.
Abstract:
This paper examines how surface deformations affect the stability of a slowly evaporating solvent-polymer mixture. The destabilizing effect of surface-tension variations arising from evaporation-induced concentration gradients and the counteracting influence of mean gravity and surface tension are incorporated into the mathematical model. A linear stability analysis that takes advantage of the separation between the characteristic time scales of the slowly evolving base state and the perturbations is carried out in combination with numerical solutions of the linearized system. It is shown that the onset of instability can occur for Marangoni numbers that are much lower than the critical value for a non-deformable surface. Moreover, two types of Marangoni instabilities appear in the system: one is associated with the traditional stationary instability, and the other is an oscillatory instability that is not present for a non-deformable liquid surface. A region of the parameter space where the oscillatory instability dominates is identified and used to formulate appropriate conditions for future experiments. © 2014 The authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Citation:
Hennessy MG, Munch A (2014) Dynamics of a slowly evaporating solvent-polymer mixture with a deformable upper surface. IMA Journal of Applied Mathematics 79: 681–720. Available: http://dx.doi.org/10.1093/imamat/hxu024.
Publisher:
Oxford University Press (OUP)
Journal:
IMA Journal of Applied Mathematics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
17-Jun-2014
DOI:
10.1093/imamat/hxu024
Type:
Article
ISSN:
0272-4960; 1464-3634
Sponsors:
This work was supported by the King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04].
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorHennessy, M. G.en
dc.contributor.authorMunch, A.en
dc.date.accessioned2016-02-25T13:11:27Zen
dc.date.available2016-02-25T13:11:27Zen
dc.date.issued2014-06-17en
dc.identifier.citationHennessy MG, Munch A (2014) Dynamics of a slowly evaporating solvent-polymer mixture with a deformable upper surface. IMA Journal of Applied Mathematics 79: 681–720. Available: http://dx.doi.org/10.1093/imamat/hxu024.en
dc.identifier.issn0272-4960en
dc.identifier.issn1464-3634en
dc.identifier.doi10.1093/imamat/hxu024en
dc.identifier.urihttp://hdl.handle.net/10754/598037en
dc.description.abstractThis paper examines how surface deformations affect the stability of a slowly evaporating solvent-polymer mixture. The destabilizing effect of surface-tension variations arising from evaporation-induced concentration gradients and the counteracting influence of mean gravity and surface tension are incorporated into the mathematical model. A linear stability analysis that takes advantage of the separation between the characteristic time scales of the slowly evolving base state and the perturbations is carried out in combination with numerical solutions of the linearized system. It is shown that the onset of instability can occur for Marangoni numbers that are much lower than the critical value for a non-deformable surface. Moreover, two types of Marangoni instabilities appear in the system: one is associated with the traditional stationary instability, and the other is an oscillatory instability that is not present for a non-deformable liquid surface. A region of the parameter space where the oscillatory instability dominates is identified and used to formulate appropriate conditions for future experiments. © 2014 The authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.en
dc.description.sponsorshipThis work was supported by the King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04].en
dc.publisherOxford University Press (OUP)en
dc.subjectevaporating filmsen
dc.subjectmultiple scalesen
dc.subjectoscillatory Marangoni instabilityen
dc.subjectWKB approximationen
dc.titleDynamics of a slowly evaporating solvent-polymer mixture with a deformable upper surfaceen
dc.typeArticleen
dc.identifier.journalIMA Journal of Applied Mathematicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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