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Modelling and analysis of meniscus roll coating

Published online by Cambridge University Press:  26 April 2006

P. H. Gaskell ,
M. D. Savage ,
J. L. Summers  and
H. M. Thompson
P. H. Gaskell
Affiliation:
Department of Mechanical Engineering, University of Leeds, LEEDS, LS2 9JT, UK
M. D. Savage
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, LEEDS, LS2 9JT, UK
J. L. Summers
Affiliation:
Department of Mechanical Engineering, University of Leeds, LEEDS, LS2 9JT, UK
H. M. Thompson
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, LEEDS, LS2 9JT, UK
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Abstract

Three mathematical models are developed for meniscus roll coating in which there is steady flow of a Newtonian fluid in the narrow gap, or nip, between two contrarotating rolls in the absence of body forces.

The zero flux model predicts a constant pressure gradient within the central core and two eddies, each with an inner structure, in qualitative agreement with observation. The small flux model takes account of a small inlet flux and employs the lubrication approximation to represent fluid velocity as a combination of Couette and Poiseuille flows. Results show that the meniscus coating regime is characterized by small flow rates (λ [Lt ] 1) and a sub-ambient pressure field generated by capillary action at the upstream meniscus. Such flows are found to exist for small modified capillary number, Ca(R/H0)1/2 [lsim ] 0.15, where Ca and R/H0 represent capillary number and the radius to semi-gap ratio, respectively.

A third model incorporates the full effects of curved menisci and nonlinear free surface boundary conditions. The presence of a dynamic contact line, adjacent to the web on the upper roll, requires the imposition of an apparent contact angle and slip length. Numerical solutions for the velocity and pressure fields over the entire domain are obtained using the finite element method. Results are in accord with experimental observations that the flow domain consists of two large eddies and fluid transfer jets or ‘snakes’. Furthermore, the numerical results show that the sub-structure of each large eddy consists of a separatrix with one saddle point, two sub-eddies with centres, and an outer recirculation.

Finally finite element solutions in tandem with lubrication analysis establish the existence of three critical flow rates corresponding to a transformation of the pressure field, the emergence of a ‘secondary snake’ (another fluid transfer jet) and the disappearance of a primary snake.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 298 , 10 September 1995 , pp. 113 - 137
Copyright
© 1995 Cambridge University Press

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