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Dynamics of gas bubbles in time-variant temperature fields

Published online by Cambridge University Press:  17 September 2010

I. R. WEBB ,
M. ARORA ,
R. A. ROY ,
S. J. PAYNE  and
C.-C. COUSSIOS
I. R. WEBB
Affiliation:
Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
M. ARORA
Affiliation:
Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
R. A. ROY
Affiliation:
Department of Aerospace and Mechanical Engineering, Boston University, Boston, MA 02215, USA
S. J. PAYNE
Affiliation:
Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
C.-C. COUSSIOS*
Affiliation:
Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
*
†Email address for correspondence: constantin.coussios@eng.ox.ac.uk
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Abstract

The effect of time-variant temperature on the dynamics of a single gas bubble in a liquid is investigated. With changes in temperature, several physical parameters controlling bubble behaviour change including surface tension, diffusivity, vapour pressure and gas solubility. A single-bubble model is formulated and a numerical simulation implemented to model the radius–time profile of a bubble, across a range of initial bubble sizes and rates of heating, taking into account the aforementioned parameter temperature dependences. The model is validated experimentally in a xanthan gum gel phantom, tracking the evolution of the bubbles using digital photography and an image analysis sizing algorithm. It is shown that the natural tendency for a bubble to dissolve can be reversed by an increase in temperature, but only above a certain radius-dependent threshold rate of heating.

JFM classification

Drops and Bubbles: Bubble dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 209 - 232
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Arefmanesh, A., Advani, S. G. & Michaelides, E. E. 1992 An accurate numerical solution for mass diffusion-induced bubble growth in viscous liquids containing limited dissolved gas. Intl J. Heat Mass Transfer 35, 1711–1722.CrossRefGoogle Scholar
Barlow, E. J. & Langlois, W. E. 1962 Diffusion of gas from a liquid into an expanding bubble. IBM J. 6, 329–337.CrossRefGoogle Scholar
Cable, M. & Frade, J. R. 1987 Diffusion-controlled growth of multi-component gas bubbles. J. Mater. Sci. 22, 919–924.CrossRefGoogle Scholar
Church, C. C. 2005 Frequency, pulse length, and the mechanical index. Acoust. Res. Lett. Online 6, 162–168.CrossRefGoogle Scholar
Coussios, C. C. & Roy, R. A. 2008 Applications of acoustics and cavitation to noninvasive therapy and drug delivery. Annu. Rev. Fluid Mech. 40, 395–420.CrossRefGoogle Scholar
Divinis, N., Kostoglou, M., Karapantsios, T. D. & Bontozoglou, V. 2005 Self-similar growth of a gas bubble induced by localized heating: the effect of temperature-dependent transport properties. Chem. Engng Sci. 60, 1673–1683.CrossRefGoogle Scholar
Epstein, P. S. & Plesset, M. S. 1950 On the stability of gas bubbles in liquid–gas solutions. J. Chem. Phys. 18, 1505–1509.CrossRefGoogle Scholar
Fan, J., Mitchell, J. R. & Blanshard, J. M. V. 1999 A model for the oven rise of dough during baking. J. Food Engng 41, 69–77.CrossRefGoogle Scholar
Filimonov, V. E. 1991 Equations for the computer calculation of the partial water vapor pressure and of the dew point of humid air. Chem. Pet. Engng 27, 254–256.CrossRefGoogle Scholar
Fyrillas, M. M. & Szeri, A. J. 1994 Dissolution or growth of soluble spherical oscillating bubbles. J. Fluid Mech. 277, 381–407.CrossRefGoogle Scholar
Han, P. & Bartels, D. M. 1996 Temperature dependence of oxygen diffusion in H2O and D2O. J. Phys. Chem. 100, 5597–5602.CrossRefGoogle Scholar
IAPWS 1994 IAPWS Release on Surface Tension of Ordinary Water Substance. Available at http://www.iapws.org/Google Scholar
Miyatake, O., Tanaka, I. & Lior, N. 1994 Bubble growth in superheated solutions with a non-volatile solute. Chem. Engng Sci. 49, 1301–1312.CrossRefGoogle Scholar
Rabkin, B. A., Zderic, V. & Vaezy, S. 2005 Hyperecho in ultrasound images of HIFU therapy: involvement of cavitation. Ultrasound Med. Biol. 31, 947–956.CrossRefGoogle ScholarPubMed
Rayleigh, L. 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 94–98.CrossRefGoogle Scholar
Rettich, T. R., Battino, R. & Wilhelm, E. 2000 Solubility of gases in liquids. 22. High-precision determination of Henry's law constants of oxygen in liquid water from T = 274 K to T = 328 K. J. Chem. Thermodyn. 32, 1145–1156.CrossRefGoogle Scholar
Riemer, B., Haines, J., Wendel, M., Bauer, G., Futakawa, M., Hasegawa, S. & Kogawa, H. 2005 Cavitation damage experiments for mercury spallation targets at the LANSCE-WNR in 2005. J. Nucl. Mater. 377, 162–173.CrossRefGoogle Scholar
Robinson, A. J. & Judd, R. L. 2001 Bubble growth in a uniform and spatially distributed temperature field. Intl J. Heat Mass Transfer 44, 2699–2710.CrossRefGoogle Scholar
Schafer, R., Merten, C. & Eigenberger, G. 2002 Bubble size distributions in a bubble column reactor under industrial conditions. Exp. Therm. Fluid Sci. 26, 595–604.CrossRefGoogle Scholar
Scriven, L. E. 1959 On the dynamics of phase growth. Chem. Engng Sci. 10, 1–13.CrossRefGoogle Scholar
Teresaka, K. & Shibata, H. 2003 Oxygen transfer in viscous non-Newtonian liquids having yield stress in bubble columns. Chem. Engng Sci 58, 5331–5337.CrossRefGoogle Scholar
Zahringer, K., Martin, J.-P. & Petit, J.-P. 2001 Numerical simulation of bubble growth in expanding perlite. J. Mater. Sci. 36, 2691–2705.CrossRefGoogle Scholar