Spin coating of an evaporating polymer solution

Andreas Münch, Colin P. Please, Barbara Wagner

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


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
Original languageEnglish (US)
Pages (from-to)102101
JournalPhysics of Fluids
Issue number10
StatePublished - Oct 5 2011
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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