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Molecular gas dynamics analysis on condensation coefficient of vapour during gas–vapour bubble collapse

Published online by Cambridge University Press:  12 October 2018

Kazumichi Kobayashi Open the ORCID record for Kazumichi Kobayashi [Opens in a new window] ,
Takahiro Nagayama ,
Masao Watanabe Open the ORCID record for Masao Watanabe [Opens in a new window] ,
Hiroyuki Fujii  and
Misaki Kon
Kazumichi Kobayashi*
Affiliation:
Division of Mechanical and Space Engineering, Faculty of Engineering, Hokkaido University, Kita-ku, Kita 13 Nishi 8, Sapporo, Hokkaido 060-8628, Japan
Takahiro Nagayama
Affiliation:
Division of Mechanical and Space Engineering, Faculty of Engineering, Hokkaido University, Kita-ku, Kita 13 Nishi 8, Sapporo, Hokkaido 060-8628, Japan
Masao Watanabe
Affiliation:
Division of Mechanical and Space Engineering, Faculty of Engineering, Hokkaido University, Kita-ku, Kita 13 Nishi 8, Sapporo, Hokkaido 060-8628, Japan
Hiroyuki Fujii
Affiliation:
Division of Mechanical and Space Engineering, Faculty of Engineering, Hokkaido University, Kita-ku, Kita 13 Nishi 8, Sapporo, Hokkaido 060-8628, Japan
Misaki Kon
Affiliation:
Division of Mechanical and Space Engineering, Faculty of Engineering, Hokkaido University, Kita-ku, Kita 13 Nishi 8, Sapporo, Hokkaido 060-8628, Japan
*
†Email address for correspondence: kobakazu@eng.hokudai.ac.jp
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Abstract

This study investigates the influence of the condensation coefficient of vapour on the collapse of a bubble composed of condensable gas (vapour) and non-condensable gas (NC gas). We simulated vapour and NC gas flow inside a bubble based on the molecular gas dynamics analysis in order to replicate the phase change (viz., evaporation and condensation) precisely, by changing the initial number density ratio of the NC gas and vapour, the initial bubble radius and the value of the condensation coefficient. The results show that the motion of the bubble is unaffected by the value of the condensation coefficient when that value is larger than approximately 0.4. We also discuss NC gas drift at the bubble wall during the final stage of the bubble collapse and its influence on the condensation coefficient. We conclude that vapour molecules can behave as NC gas molecules when the bubble collapses, owing to the large concentration of NC gas molecules at the gas–liquid interface. That is, the condensation coefficient reaches almost zero when the bubble collapses violently.

JFM classification

Drops and Bubbles: Bubble dynamics Phase change: Condensation/evaporation Rarefied Gas Flow: Kinetic theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 856 , 10 December 2018 , pp. 1045 - 1063
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Copyright
© 2018 Cambridge University Press 

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References

Akhatov, I., Lindau, O., Topolnikov, A., Mettin, R., Vakhitova, N. & Lauterborn, W. 2001 Collapse and rebound of a laser-induced cavitation bubble. Phys. Fluids 13 (10), 2805–2819.Google Scholar
Andries, P., Aoki, K. & Perthame, B. 2002 A consistent bgk-type model for gas mixtures. J. Stat. Phys. 106 (5), 993–1018.Google Scholar
Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press.Google Scholar
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Cambridge University Press.Google Scholar
Cercignani, C. 2000 Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations, vol. 21. Cambridge University Press.Google Scholar
Chahine, G. L., Kapahi, A. & Hsiao, C.-T. 2016 Coupling bubble and material dynamics to model cavitation peening and pitting. J. Fluid Sci. Technol. 11 (4), JFST0023.Google Scholar
Frezzotti, A. 2011 Boundary conditions at the vapor-liquid interface. Phys. Fluids 23 (3), 030609.Google Scholar
Frezzotti, A. & Barbante, P. 2017 Kinetic theory aspects of non-equilibrium liquid-vapor flows. Mech. Engng Rev. 4 (2), 16-00540.Google Scholar
Fujikawa, S. & Akamatsu, T. 1980 Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid. J. Fluid Mech. 97 (03), 481–512.Google Scholar
Fujikawa, S., Yano, T. & Watanabe, M. 2011 Vapor-Liquid Interfaces, Bubbles and Droplets: Fundamentals and Applications. Springer Science & Business Media.Google Scholar
Fuster, D., Hauke, G. & Dopazo, C. 2010 Influence of the accommodation coefficient on nonlinear bubble oscillations. J. Acoust. Soc. Am. 128 (1), 5–10.Google Scholar
Gumerov, N. A 2000 Dynamics of vapor bubbles with nonequilibrium phase transitions in isotropic acoustic fields. Phys. Fluids 12 (1), 71–88.Google Scholar
Hao, Y., Zhang, Y. & Prosperetti, A. 2017 Mechanics of gas-vapor bubbles. Phys. Rev. Fluids 2, 034303.Google Scholar
Hilgenfeldt, S., Lohse, D. & Moss, W. C. 1998 Water temperature dependence of single bubble sonoluminescence. Phys. Rev. Lett. 80, 1332–1335.Google Scholar
Kawashima, H. & Kameda, M. 2008 Dynamics of a spherical vapor/gas bubble in varying pressure fields. J. Fluid Sci. Technol. 3 (8), 943–955.Google Scholar
Kobayashi, K., Hori, K., Kon, M., Sasaki, K. & Watanabe, M. 2016 Molecular dynamics study on evaporation and reflection of monatomic molecules to construct kinetic boundary condition in vapor–liquid equilibria. Heat Mass Transfer 52 (9), 1851–1859.Google Scholar
Kobayashi, K., Sasaki, K., Kon, M., Fujii, H. & Watanabe, M. 2017 Kinetic boundary conditions for vapor–gas binary mixture. Microfluid Nanofluid 21 (3), 53, 1–13.Google Scholar
Kon, M., Kobayashi, K. & Watanabe, M. 2014 Method of determining kinetic boundary conditions in net evaporation/condensation. Phys. Fluids 26 (7), 072003.Google Scholar
Kon, M., Kobayashi, K. & Watanabe, M. 2016 Liquid temperature dependence of kinetic boundary condition at vapor–liquid interface. Intl J. Heat Mass Transfer 99, 317–326.Google Scholar
Kon, M., Kobayashi, K. & Watanabe, M. 2017 Kinetic boundary condition in vapor-iquid two-phase system during unsteady net evaporation/condensation. Eur. J. Mech. (B/Fluids) 64, 81–92; special Issue on Non-equilibrium Gas Flows.Google Scholar
Kreider, W., Crum, L. A., Bailey, M. R. & Sapozhnikov, O. A. 2011 A reduced-order, single-bubble cavitation model with applications to therapeutic ultrasound. J. Acoust. Soc. Am. 130 (5), 3511–3530.Google Scholar
Kryukov, A. P. & Levashov, V. Y. 2016 Boundary conditions on the vapor liquid interface at strong condensation. Heat Mass Transfer 52 (7), 1393–1401.Google Scholar
Lauer, E., Hu, X. Y., Hickel, S. & Andreas, N. A. 2012 Numerical modelling and investigation of symmetric and asymmetric cavitation bubble dynamics. Comput. Fluids 69, 1–19.Google Scholar
Magaletti, F., Marino, L. & Casciola, C. M. 2015 Shock wave formation in the collapse of a vapor nanobubble. Phys. Rev. Lett. 114 (6), 064501.Google Scholar
Matsumoto, Y. & Takemura, F. 1994 Influence of internal phenomena on gas bubble motion: effects of thermal diffusion, phase change on the gas-liquid interface and mass diffusion between vapor and noncondensable gas in the collapsing phase. JSME Intl J. B 37 (2), 288–296.Google Scholar
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9 (1), 145–185.Google Scholar
Prosperetti, A. 2017 Vapor bubbles. Annu. Rev. Fluid Mech. 49 (1), 221–248.Google Scholar
Rayleigh, L. 1917 VIII. On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34 (200), 94–98.Google Scholar
Sone, Y. 2007 Molecular Gas Dynamics: Theory, Techniques, and Applications. Springer Science & Business Media.Google Scholar
Taguchi, S., Aoki, K. & Takata, S. 2004 Vapor flows condensing at incidence onto a plane condensed phase in the presence of a noncondensable gas. II. Supersonic condensation. Phys. Fluids 16 (1), 79–92.Google Scholar
Yasui, K. 2001 Effect of liquid temperature on sonoluminescence. Phys. Rev. E 64, 016310.Google Scholar