Handle URI:
http://hdl.handle.net/10754/599693
Title:
Spin coating of an evaporating polymer solution
Authors:
Münch, Andreas; Please, Colin P.; Wagner, Barbara
Abstract:
We consider a mathematical model of spin coating of a single polymer blended in a solvent. The model describes the one-dimensional development of a thin layer of the mixture as the layer thins due to flow created by a balance of viscous forces and centrifugal forces and evaporation of the solvent. In the model both the diffusivity of the solvent in the polymer and the viscosity of the mixture are very rapidly varying functions of the solvent mass fraction. Guided by numerical solutions an asymptotic analysis reveals a number of different possible behaviours of the thinning layer dependent on the nondimensional parameters describing the system. The main practical interest is in controlling the appearance and development of a "skin" on the polymer where the solvent concentration reduces rapidly on the outer surface leaving the bulk of the layer still with high concentrations of solvent. In practice, a fast and uniform drying of the film is required. The critical parameters controlling this behaviour are found to be the ratio of the diffusion to advection time scales ε, the ratio of the evaporation to advection time scales δ and the ratio of the diffusivity of the pure polymer and the initial mixture exp(-1/γ). In particular, our analysis shows that for very small evaporation with δ<exp(-3/(4γ))ε3/4 skin formation can be prevented. © 2011 American Institute of Physics.
Citation:
Münch A, Please CP, Wagner B (2011) Spin coating of an evaporating polymer solution. Phys Fluids 23: 102101. Available: http://dx.doi.org/10.1063/1.3643692.
Publisher:
AIP Publishing
Journal:
Physics of Fluids
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
2011
DOI:
10.1063/1.3643692
Type:
Article
ISSN:
1070-6631
Sponsors:
The authors gratefully acknowledge the generous support of OCCAM (Oxford Centre for Collaborative Applied Mathematics) under support supplied by Award No. KUK-C1-013-04, made by the King Abdullah University of Science and Technology (KAUST). C.P.P. and B.W. are especially grateful for the support and hospitality during their OCCAM Visiting Fellowships. The authors also enjoyed lively and very fruitful discussions with Professor John R. Ockendon and Dr. Chris J.W. Breward.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMünch, Andreasen
dc.contributor.authorPlease, Colin P.en
dc.contributor.authorWagner, Barbaraen
dc.date.accessioned2016-02-28T06:07:41Zen
dc.date.available2016-02-28T06:07:41Zen
dc.date.issued2011en
dc.identifier.citationMünch A, Please CP, Wagner B (2011) Spin coating of an evaporating polymer solution. Phys Fluids 23: 102101. Available: http://dx.doi.org/10.1063/1.3643692.en
dc.identifier.issn1070-6631en
dc.identifier.doi10.1063/1.3643692en
dc.identifier.urihttp://hdl.handle.net/10754/599693en
dc.description.abstractWe consider a mathematical model of spin coating of a single polymer blended in a solvent. The model describes the one-dimensional development of a thin layer of the mixture as the layer thins due to flow created by a balance of viscous forces and centrifugal forces and evaporation of the solvent. In the model both the diffusivity of the solvent in the polymer and the viscosity of the mixture are very rapidly varying functions of the solvent mass fraction. Guided by numerical solutions an asymptotic analysis reveals a number of different possible behaviours of the thinning layer dependent on the nondimensional parameters describing the system. The main practical interest is in controlling the appearance and development of a "skin" on the polymer where the solvent concentration reduces rapidly on the outer surface leaving the bulk of the layer still with high concentrations of solvent. In practice, a fast and uniform drying of the film is required. The critical parameters controlling this behaviour are found to be the ratio of the diffusion to advection time scales ε, the ratio of the evaporation to advection time scales δ and the ratio of the diffusivity of the pure polymer and the initial mixture exp(-1/γ). In particular, our analysis shows that for very small evaporation with δ<exp(-3/(4γ))ε3/4 skin formation can be prevented. © 2011 American Institute of Physics.en
dc.description.sponsorshipThe authors gratefully acknowledge the generous support of OCCAM (Oxford Centre for Collaborative Applied Mathematics) under support supplied by Award No. KUK-C1-013-04, made by the King Abdullah University of Science and Technology (KAUST). C.P.P. and B.W. are especially grateful for the support and hospitality during their OCCAM Visiting Fellowships. The authors also enjoyed lively and very fruitful discussions with Professor John R. Ockendon and Dr. Chris J.W. Breward.en
dc.publisherAIP Publishingen
dc.titleSpin coating of an evaporating polymer solutionen
dc.typeArticleen
dc.identifier.journalPhysics of Fluidsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Southampton, Southampton, United Kingdomen
dc.contributor.institutionTechnische Universitat Berlin, Berlin, Germanyen
kaust.grant.numberKUK-C1-013-04en
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