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A weak-inertia mathematical model of bubble growth in a polymer foam

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journal contribution
posted on 21.04.2017, 12:26 by Euan Barlow, Aoibhinn M. Bradley, Anthony J. Mulholland, Carmen TorresCarmen Torres
One possible manufacturing method for bone scaffolds used in regenerative medicine involves the acoustic irradiation of a reacting polymer foam to generate a graded porosity. This paper derives a mathematical model of a non-reacting process in order to develop theoretical confirmation of the influence of the acoustic signal on the polymer foam. The model describes single bubble growth in a free rising, non-reacting polymer foam irradiated by an acoustic standing wave and incorporates the effects of inertia. Leading and first order asymptotic inner solutions in the temporal domain (early growth) are presented for the case of instantaneous diffusion when the fluid volume surrounding the bubble is large compared to the bubble volume. The leading order asymptotic outer solution (late growth), for the case of instantaneous diffusion, is described analytically using the Picard iteration method. Initial conditions for this outer solution are identified through matching with the asymptotic inner solution. A numerical solution for the leading order outer equation is also presented. Investigations are carried out to explore the influence of inertia on the bubble volume, fluid pressure and the stress tensors of the foam, and to explore the effect of fluid viscosity and acoustic pressure amplitude on the final bubble volume, and the curing time. A key result is that increasing the applied acoustic pressure is shown to result in a reduced steady state bubble volume, indicating that ultrasonic irradiation has the potential to produce tailored porosity profiles in bioengineering scaffolds.

Funding

This work was supported by the Engineering and Physical Sciences Research Council, grant reference EP/I033424/1.

History

School

  • Mechanical, Electrical and Manufacturing Engineering

Published in

Journal of Non-Newtonian Fluid Mechanics

Citation

BARLOW, E. ... et al, 2017. A weak-inertia mathematical model of bubble growth in a polymer foam. Journal of Non-Newtonian Fluid Mechanics, 244, pp. 1-14.

Publisher

Elsevier © The Authors

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/ by/4.0/

Acceptance date

04/04/2017

Publication date

2017

Notes

This is an Open Access Article. It is published by Elsevier under the Creative Commons Attribution 4.0 International Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

ISSN

0377-0257

Language

en