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Flow in a double-film-fed fluid bead between contra-rotating rolls, Part 1: equilibrium flow structure

Wilson, M.C.T., Gaskell, P.H. and Savage, M.D. (2001) Flow in a double-film-fed fluid bead between contra-rotating rolls, Part 1: equilibrium flow structure. European Journal of Applied Mathematics, 12 (3). pp. 395-411. ISSN 0956-7925

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Abstract

In multiple-roll coaters thin liquid films are transferred from roll to roll by means of liquid ‘beads’ which occupy the small gaps between adjacent rolls. Double-Film-Fed (DFF) beads are those which feature two ingoing films instead of the usual one, and arise in the intermediate stages of certain types of roll coater. One of the ingoing films, h1, is supplied from the previous inter-roll gap while the other, h2, ‘returns’ from the subsequent gap. Such a flow is investigated here under the conditions of low flow rate, small capillary number and negligible gravity and inertia, using lubrication theory and finite element analysis.

The thickness of film h1 is fixed independently, while that of h2 is specified as a fraction, [zeta], of the film output on the same roll. This simple approach allows a degree of feedback between the output and input of the bead, and enables one to simulate different conditions in the subsequent gap. Predictions of outgoing film thicknesses made using the two models agree extremely well and show that, for each value of [zeta] < 1, one outgoing film thickness decreases monotonically with speed ratio, S, while the other features a maximum. Good agreement is also seen in the pressure profiles, which are entirely sub-ambient in keeping with the small capillary number conditions. The finite element solutions reveal that in the ‘zero-flux’ case (when [zeta] = 1) the flow structures are very similar to those seen in an idealized cavity problem. In the more general ([zeta] < 1) situation, as in single-film-fed meniscus roll coating, several liquid transfer-jets occur by which liquid is conveyed through the bead from one roll to the other. The lubrication model is used to calculate several critical flow rates at which the flow is transformed, and it is shown that when the total dimensionless flow rate through the bead exceeds 1/3, the downstream flow structure is independent of the relative sizes of the ingoing films.

Item Type: Article
Copyright, Publisher and Additional Information: © Cambridge University Press, 2001
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 Assistant
Date Deposited: 09 Jun 2006
Last Modified: 06 Jun 2014 21:24
Published Version: http://dx.doi.org/10.1017/S0956792501004399
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
Identification Number: 10.1017/S0956792501004399
URI: http://eprints.whiterose.ac.uk/id/eprint/1268

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