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A model for deformable roll coating with negative gaps and incompressible compliant layers

Gostling, M.J., Savage, M.D., Young, A.E. and Gaskell, P.H. (2003) A model for deformable roll coating with negative gaps and incompressible compliant layers. Journal of Fluid Mechanics, 489. pp. 155-184. ISSN 1469-7645

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Abstract

A soft elastohydrodynamic lubrication model is formulated for deformable roll coating involving two contra-rotating rolls, one rigid and the other covered with a compliant layer. Included is a finite-strip model (FSM) for the deformation of the layer and a lubrication model with suitable boundary conditions for the motion of the fluid. The scope of the analysis is restricted to Newtonian fluids, linear elasticity/viscoelasticity and equal roll speeds, with application to the industrially relevant highly loaded or 'negative gap' regime. Predictions are presented for coated film thickness, interroll thickness, meniscus location, pressure and layer deformation as the control parameters - load (gap), elasticity, layer thickness and capillary number, Ca - are varied. There are four main results:

(i) Hookean spring models are shown to be unable to model effectively the deformation of a compliant layer when Poisson's ratio nu --> 0.5. In particular, they fall to predict the swelling of the layer at the edge of the contact region which increases as v - 0.5; they also fail to locate accurately the position of the meniscus, X-M, and to identify the presence, close to the meniscus, of a 'nib' (constriction in gap thickness) and associated magnification of the sub-ambient pressure loop.

(ii) Scaling arguments suggest that layer thickness and elasticity may have similar effects on the field variables. It is shown that for positive gaps this is true, whereas for negative gaps they have similar effects on the pressure profile and flow rate yet quite different effects on layer swelling (deformation at the edge of the contact region) and different effects on X-M.

(iii) For negative gaps and Ca similar to O(1), the effect of varying either viscosity or speed and hence Ca is to significantly alter both the coating thickness and X-M. This is contrary to the case of fixed-gap rigid roll coating.

(iv) Comparison between theoretical predictions and experimental data shows quantitive agreement in the case of X-M and qualitive agreement for flow rate. It is shown that this difference in the latter case may be due to viscoelastic effects in the compliant layer.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2003 Cambridge University Press.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds)
The University of Leeds > Faculty of Engineering (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds)
Depositing User: Repository Officer
Date Deposited: 15 May 2006
Last Modified: 05 Jun 2014 08:16
Published Version: http://dx.doi.org/10.1017/S0022112003005068
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
Identification Number: 10.1017/S0022112003005068
URI: http://eprints.whiterose.ac.uk/id/eprint/1202

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