Stability of an unsupported multi-layer surfactant laden liquid curtain under gravity

Handle URI:
http://hdl.handle.net/10754/622252
Title:
Stability of an unsupported multi-layer surfactant laden liquid curtain under gravity
Authors:
Henry, D.; Uddin, J.; Marston, J. O.; Thoroddsen, Sigurdur T. ( 0000-0001-6997-4311 )
Abstract:
The industrial process of curtain coating has long been an important method in coating applications, by which a thin liquid curtain is formed to impinge upon a moving substrate, due to its highly lucrative advantage of being able to coat multiple layers simultaneously. We investigate the linear stability of an unsupported two-layer liquid curtain, which has insoluble surfactants in both liquids, which are widely used in industry to increase the stability of the curtain. We formulate the governing equations, simplified by making a thin film approximation, from which we obtain equations describing the steady-state profiles. We then examine the response of the curtain to small perturbations about this steady state to identify conditions under which the curtain is unstable, finding the addition of surfactants stabilizes the curtain. Our results are then compared to experimental data, showing a favourable trend and thereby extending the works of Brown (J Fluid Mech 10:297–305, 1960) and Dyson et al. (J Eng Math 64:237–250, 2009).
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Henry D, Uddin J, Marston JO, Thoroddsen ST (2015) Stability of an unsupported multi-layer surfactant laden liquid curtain under gravity. Journal of Engineering Mathematics 99: 119–136. Available: http://dx.doi.org/10.1007/s10665-015-9824-8.
Publisher:
Springer Nature
Journal:
Journal of Engineering Mathematics
Issue Date:
7-Nov-2015
DOI:
10.1007/s10665-015-9824-8
Type:
Article
ISSN:
0022-0833; 1573-2703
Sponsors:
D.H. would like to thank the EPSRC for their financial support, and KAUST for funding the experimental work conducted whilst D.H. was on a research visit. The authors would also like to thank the anonymous reviewers who have contributed in improving this paper.
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorHenry, D.en
dc.contributor.authorUddin, J.en
dc.contributor.authorMarston, J. O.en
dc.contributor.authorThoroddsen, Sigurdur T.en
dc.date.accessioned2017-01-02T08:42:40Z-
dc.date.available2017-01-02T08:42:40Z-
dc.date.issued2015-11-07en
dc.identifier.citationHenry D, Uddin J, Marston JO, Thoroddsen ST (2015) Stability of an unsupported multi-layer surfactant laden liquid curtain under gravity. Journal of Engineering Mathematics 99: 119–136. Available: http://dx.doi.org/10.1007/s10665-015-9824-8.en
dc.identifier.issn0022-0833en
dc.identifier.issn1573-2703en
dc.identifier.doi10.1007/s10665-015-9824-8en
dc.identifier.urihttp://hdl.handle.net/10754/622252-
dc.description.abstractThe industrial process of curtain coating has long been an important method in coating applications, by which a thin liquid curtain is formed to impinge upon a moving substrate, due to its highly lucrative advantage of being able to coat multiple layers simultaneously. We investigate the linear stability of an unsupported two-layer liquid curtain, which has insoluble surfactants in both liquids, which are widely used in industry to increase the stability of the curtain. We formulate the governing equations, simplified by making a thin film approximation, from which we obtain equations describing the steady-state profiles. We then examine the response of the curtain to small perturbations about this steady state to identify conditions under which the curtain is unstable, finding the addition of surfactants stabilizes the curtain. Our results are then compared to experimental data, showing a favourable trend and thereby extending the works of Brown (J Fluid Mech 10:297–305, 1960) and Dyson et al. (J Eng Math 64:237–250, 2009).en
dc.description.sponsorshipD.H. would like to thank the EPSRC for their financial support, and KAUST for funding the experimental work conducted whilst D.H. was on a research visit. The authors would also like to thank the anonymous reviewers who have contributed in improving this paper.en
dc.publisherSpringer Natureen
dc.subjectCurtain coatingen
dc.subjectMulti-layeren
dc.subjectStabilityen
dc.subjectSurfactantsen
dc.titleStability of an unsupported multi-layer surfactant laden liquid curtain under gravityen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalJournal of Engineering Mathematicsen
dc.contributor.institutionSchool of Mathematics, University of Birmingham, Birmingham, B15 2TT, United Kingdomen
dc.contributor.institutionDepartment of Chemical Engineering, Texas Tech University, Lubbock, TX, 79409-3121, United Statesen
kaust.authorThoroddsen, Sigurdur T.en
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