The Mathematical Institute, University of Oxford, Eprints Archive

Spin coating of an evaporating polymer solution

Münch, A. and Please, C. P. and Wagner, B. (2010) Spin coating of an evaporating polymer solution. Physics of Fluids . (Submitted)



We consider a mathematical model of spin coating of a single polymer blended in a solvent. The model describes the one-dimensional development of the thin layer of the mixture as the layer thins due to flow created by a balance of viscous forces and centrifugal forces and due to 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 volume 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. The critical parameters controlling this behaviour are found to be $\epsilon$ the ratio of the diffusion to advection time scales, $\delta$ the ratio of the evaporation to advection time scales and $\exp(\gamma)$, the ratio of the diffusivity of the initial mixture and the pure polymer. In particular, our analysis shows that for very small evaporation with $\delta << \exp(-3/(4\gamma)) \epsilon^{3/4}$ skin formation can be prevented.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1036
Deposited By:Peter Hudston
Deposited On:07 Jan 2011 08:43
Last Modified:09 Feb 2012 15:49

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