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

dc.contributor.authorHennessy, M. G.
dc.contributor.authorMunch, A.
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
dc.date.accessioned2016-02-25T13:11:27Z
dc.date.available2016-02-25T13:11:27Z
dc.date.issued2014-06-17
dc.date.published-online2014-06-17
dc.date.published-print2014-08-01
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.
dc.description.sponsorshipThis work was supported by the King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04].
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.
dc.identifier.doi10.1093/imamat/hxu024
dc.identifier.issn0272-4960
dc.identifier.issn1464-3634
dc.identifier.journalIMA Journal of Applied Mathematics
dc.identifier.urihttp://hdl.handle.net/10754/598037
dc.publisherOxford University Press (OUP)
dc.subjectevaporating films
dc.subjectmultiple scales
dc.subjectoscillatory Marangoni instability
dc.subjectWKB approximation
dc.titleDynamics of a slowly evaporating solvent-polymer mixture with a deformable upper surface
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Hennessy, M. G.,equals">Hennessy, M. G.</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Munch, A.,equals">Munch, A.</a><br><br><h5>KAUST Grant Number</h5>KUK-C1-013-04<br><br><h5>Online Publication Date</h5>2014-06-17<br><br><h5>Print Publication Date</h5>2014-08-01<br><br><h5>Date</h5>2014-06-17</span>
display.details.right<span><h5>Abstract</h5>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.<br><br><h5>Citation</h5>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.<br><br><h5>Acknowledgements</h5>This work was supported by the King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04].<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Oxford University Press (OUP),equals">Oxford University Press (OUP)</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=IMA Journal of Applied Mathematics,equals">IMA Journal of Applied Mathematics</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1093/imamat/hxu024">10.1093/imamat/hxu024</a></span>
kaust.grant.numberKUK-C1-013-04
orcid.authorHennessy, M. G.
orcid.authorMunch, A.
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