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

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 influen...

Full description

Saved in:

Bibliographic Details
Main Authors:	Euan Barlow, Aoibhinn M. Bradley, Anthony J. Mulholland, Carmen Torres
Format:	Default Article
Published:	2017
Subjects:	Mechanical engineering not elsewhere classified Bubble growth Polymeric foam Oldroyd-B fluid Analytic solution Inertia Mechanical Engineering not elsewhere classified
Online Access:	https://hdl.handle.net/2134/24767
Tags:	Add Tag No Tags, Be the first to tag this record!

id	rr-article-9576854
record_format	Figshare
spelling	rr-article-95768542017-01-01T00:00:00Z A weak-inertia mathematical model of bubble growth in a polymer foam Euan Barlow (7215641) Aoibhinn M. Bradley (7215644) Anthony J. Mulholland (7215647) Carmen Torres (1259328) Mechanical engineering not elsewhere classified Bubble growth Polymeric foam Oldroyd-B fluid Analytic solution Inertia Mechanical Engineering not elsewhere classified 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. 2017-01-01T00:00:00Z Text Journal contribution 2134/24767 https://figshare.com/articles/journal_contribution/A_weak-inertia_mathematical_model_of_bubble_growth_in_a_polymer_foam/9576854 CC BY 4.0
institution	Loughborough University
collection	Figshare
topic	Mechanical engineering not elsewhere classified Bubble growth Polymeric foam Oldroyd-B fluid Analytic solution Inertia Mechanical Engineering not elsewhere classified
spellingShingle	Mechanical engineering not elsewhere classified Bubble growth Polymeric foam Oldroyd-B fluid Analytic solution Inertia Mechanical Engineering not elsewhere classified Euan Barlow Aoibhinn M. Bradley Anthony J. Mulholland Carmen Torres A weak-inertia mathematical model of bubble growth in a polymer foam
description	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.
format	Default Article
author	Euan Barlow Aoibhinn M. Bradley Anthony J. Mulholland Carmen Torres
author_facet	Euan Barlow Aoibhinn M. Bradley Anthony J. Mulholland Carmen Torres
author_sort	Euan Barlow (7215641)
title	A weak-inertia mathematical model of bubble growth in a polymer foam
title_short	A weak-inertia mathematical model of bubble growth in a polymer foam
title_full	A weak-inertia mathematical model of bubble growth in a polymer foam
title_fullStr	A weak-inertia mathematical model of bubble growth in a polymer foam
title_full_unstemmed	A weak-inertia mathematical model of bubble growth in a polymer foam
title_sort	weak-inertia mathematical model of bubble growth in a polymer foam
publishDate	2017
url	https://hdl.handle.net/2134/24767
_version_	1797282731887951872

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

Similar Items