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A non-singular boundary element method for modelling bubble dynamics in viscoelastic fluids

Walters, M. J. and Phillips, T. N. 2016. A non-singular boundary element method for modelling bubble dynamics in viscoelastic fluids. Journal of Non-Newtonian Fluid Mechanics 235 , pp. 109-124. 10.1016/j.jnnfm.2016.07.012

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When a cavity forms near a solid boundary a liquid jet can form directed towards the boundary, causing the generation of high pressures at the wall (potentially causing damage) and the formation of a toroidal bubble. In this paper several recent developments in the boundary element modelling of the dynamics of cavitation bubbles in viscoelastic fluids are presented. The standard formulation of the boundary element method (BEM) is in terms of a boundary integral equation with a singular kernel. A reformulation of the BEM in terms of a non-singular kernel is shown to provide enhanced stability. In situations when a liquid jet forms and impacts the far side of the bubble there is a transition to a toroidal form. This topological singularity in bubble geometry is modelled by placing a vortex ring inside the bubble to account for the circulation in the fluid and the discontinuity in potential following jet impact. The bubble dynamics are dependent on the initial stand-off distance from the boundary as well as the viscous and elastic properties of the fluid. It is shown that, while the viscosity of the fluid inhibits jet formation, the dynamics are particularly dependent on the relative strength of viscous, elastic and inertial forces. In particular, if the Deborah number is large enough elastic effects effectively negate fluid viscosity and behaviour similar to the inviscid case is recovered in terms of liquid jet formation.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: Pdf uploaded in accordance with publisher's policy at (accessed 04/08/2016)
Publisher: Elsevier
ISSN: 0377-0257
Funders: EPSRC
Date of First Compliant Deposit: 4 August 2016
Date of Acceptance: 30 July 2016
Last Modified: 20 Jan 2021 06:31

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