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Spherical bubble collapse in viscoelastic fluids

Lind, Steven John and Phillips, Timothy Nigel 2010. Spherical bubble collapse in viscoelastic fluids. Journal of non-Newtonian fluid mechanics 165 (1-2) , pp. 56-64. 10.1016/j.jnnfm.2009.09.002

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Abstract

The collapse of a spherical bubble in an infinite expanse of viscoelastic fluid is considered. For a range of viscoelastic models, the problem is formulated in terms of a generalized Bernoulli equation for a velocity potential, under the assumptions of incompressibility and irrotationality. The boundary element method is used to determine the velocity potential and viscoelastic effects are incorporated into the model through the normal stress balance across the surface of the bubble. In the case of the Maxwell constitutive equation, the model predicts phenomena such as the damped oscillation of the bubble radius in time, the almost elastic oscillations in the large Deborah number limit and the rebound limit at large values of the Deborah number. A rebound condition in terms of ReDe is derived theoretically for the Maxwell model by solving the Rayleigh–Plesset equation. A range of other viscoelastic models such as the Jeffreys model, the Rouse model and the Doi-Edwards model are amenable to solution using the same technique. Increasing the solvent viscosity in the Jeffreys model is shown to lead to increasingly damped oscillations of the bubble radius

Item Type: Article
Date Type: Publication
Status: Published
Schools: Advanced Research Computing @ Cardiff (ARCCA)
Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: Spherical bubble ; Viscoelastic fluid ; Boundary element method
Publisher: Elsevier
ISSN: 0377-0257
Last Modified: 04 Jun 2017 02:47
URI: http://orca.cf.ac.uk/id/eprint/12136

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