Everitt, SL, Harlen, OG orcid.org/0000-0002-4593-3547 and Wilson, HJ (2006) Bubble growth in a two-dimensional viscoelastic foam. Journal of Non-Newtonian Fluid Mechanics, 137 (1-3). pp. 46-59. ISSN 0377-0257
Abstract
The effects of viscoelasticity on the expansion of gas bubbles arranged in a hexagonal array in a polymeric fluid are investigated. The expansion is driven by the diffusion of a soluble gas from the liquid phase, and the rate of expansion is controlled by a combination of gas diffusion, fluid rheology and surface tension.
In the diffusion limited case, the initial growth rate is slow due to small surface area, whereas at high diffusivity initial growth is rapid and resisted only by background solvent viscosity. In this high Deborah number limit, we see a two stage expansion in which there is an initial rapid expansion up to the size at which the elastic stresses balance the pressure difference. Beyond this time the bubble expansion is controlled by the relaxation of the polymer. We also illustrate how viscoelasticity affects the shape of the bubble.
In addition to a full finite element calculation of the two-dimensional flow, two one-dimensional approximations valid in the limits of small and large gas area fractions are presented. We show that these approximations give accurate predictions of the evolution of the bubble area, but give less accurate predictions of the bubble shape.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Copyright © 2006 Elsevier B.V. All rights reserved. This is an author produced version of a paper published in Journal of Non-Newtonian Fluid Mechanics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Bubble growth; Polymer foams; Oldroyd B; Finite elements |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Aug 2019 13:58 |
Last Modified: | 23 Aug 2019 13:58 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jnnfm.2006.03.004 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:135827 |