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 , 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 skin formation can be prevented.
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October 2011
Research Article|
October 04 2011
Spin coating of an evaporating polymer solution
Andreas Münch;
Andreas Münch
a)
1Mathematical Institute,
University of Oxford
, 24-29 St. Giles’, Oxford OX1 3LB, United Kingdom
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Colin P. Please;
Colin P. Please
b)
2School of Mathematics,
University of Southampton
, University Road, Southampton SO17 1BJ, United Kingdom
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Barbara Wagner
Barbara Wagner
c)
3
Department of Mathematics
, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
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a)
Electronic mail: muench@maths.ox.ac.uk.
b)
Electronic mail: c.p.please@soton.ac.uk.
c)
Electronic mail: bwagner@math.tu-berlin.de.
Physics of Fluids 23, 102101 (2011)
Article history
Received:
October 04 2010
Accepted:
September 07 2011
Citation
Andreas Münch, Colin P. Please, Barbara Wagner; Spin coating of an evaporating polymer solution. Physics of Fluids 1 October 2011; 23 (10): 102101. https://doi.org/10.1063/1.3643692
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