A model for film-forming with Newtonian and shear-thinning fluids

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Title: A model for film-forming with Newtonian and shear-thinning fluids
Author(s): Hewson, RW
Kapur, N
Gaskell, PH
Item Type: Journal Article
Abstract: The formation of a thin film by (i) the slow penetration of a gas bubble into a liquid filled tube, (ii) the withdrawal of a planar substrate from a liquid filled gap, is investigated theoretically for the cases of both Newtonian and shear-thinning liquids; the latter conforming to either a power-law or Ellis model. Formulated as a boundary value problem underpinned by lubrication theory, the analysis gives rise to a system of ordinary differential equations which are solved numerically subject to appropriate boundary conditions. For Newtonian liquids comparison of the predicted residual film thickness for a wide range of capillary number, Ca ∈ (10-4, 10), is made with others obtained using existing expressions, including the classical one of Bretherton, in the region of parameter space over which they apply. In the case of (i), prediction of the behaviour of the residual fluid fraction and gap-to-film thickness ratio, for a Newtonian liquid and one that is shear-thinning and modelled via a power-law, is found to be in particularly good agreement with experimental data for Ca < 0.2. For (ii), both shear-thinning models are utilized and contour plots of residual film thickness generated as a function of Ca and the defining parameters characteristic of each model. © 2009 Elsevier B.V. All rights reserved.
Publication Date: 1-Oct-2009
URI: http://hdl.handle.net/10044/1/14751
DOI: http://dx.doi.org/10.1016/j.jnnfm.2009.05.004
ISSN: 0377-0257
Start Page: 21
End Page: 28
Journal / Book Title: Journal of Non-Newtonian Fluid Mechanics
Volume: 162
Issue: 1-3
Copyright Statement: Copyright © 2009 Elsevier B.V. All rights reserved. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Non-Newtonian Fluid Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Non-Newtonian Fluid Mechanics, 162(1-3), 2009. DOI:10.1016/j.jnnfm.2009.05.004
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