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

Euan Barlow, Aoibhinn M. Bradley, Anthony J. Mulholland, Carmen Torres-Sanchez

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.
LanguageEnglish
Pages1-14
Number of pages14
JournalJournal of Non-Newtonian Fluid Mechanics
Volume244
Early online date5 Apr 2017
DOIs
Publication statusPublished - 30 Jun 2017

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Foam
foams
inertia
Inertia
Bubble
Foams
mathematical models
Polymers
bubbles
Acoustics
Mathematical Model
Mathematical models
polymers
acoustics
Scaffolds
Scaffold
Fluids
Porosity
Fluid
Irradiation

Keywords

  • bubble growth
  • polymeric foam
  • oldroyd-B fluid
  • analytic solution
  • inertia

Cite this

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title = "A weak-inertia mathematical model of bubble growth in a polymer foam",
abstract = "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.",
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A weak-inertia mathematical model of bubble growth in a polymer foam. / Barlow, Euan; Bradley, Aoibhinn M.; Mulholland, Anthony J.; Torres-Sanchez, Carmen.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 244, 30.06.2017, p. 1-14.

Research output: Contribution to journalArticle

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