Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 61
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    King, Jack 2016. Viscosity in air-gun bubble modeling. GEOPHYSICS, Vol. 81, Issue. 1, p. T1.


    Kondo, Tomoki and Ando, Keita 2016. One-way-coupling simulation of cavitation accompanied by high-speed droplet impact. Physics of Fluids, Vol. 28, Issue. 3, p. 033303.


    Liu, Liu Yan, Hongjie Zhao, Guojian and Zhuang, Jiacai 2016. Experimental studies on the terminal velocity of air bubbles in water and glycerol aqueous solution. Experimental Thermal and Fluid Science, Vol. 78, p. 254.


    van Wijngaarden, Leen 2016. Mechanics of collapsing cavitation bubbles. Ultrasonics Sonochemistry, Vol. 29, p. 524.


    Xiao, W. Zhang, A.M. and Wang, S.P. 2016. Investigation of bubble dynamics of underwater explosion based on improved compressible numerical model. Applied Ocean Research, Vol. 59, p. 472.


    King, J.R.C. Ziolkowski, A.M. and Ruffert, M. 2015. Boundary conditions for simulations of oscillating bubbles using the non-linear acoustic approximation. Journal of Computational Physics, Vol. 284, p. 273.


    King, Jack R. C. 2015. Air-gun bubble-ghost interactions. GEOPHYSICS, Vol. 80, Issue. 6, p. T223.


    Liu, Liu Yan, Hongjie and Zhao, Guojian 2015. Experimental studies on the shape and motion of air bubbles in viscous liquids. Experimental Thermal and Fluid Science, Vol. 62, p. 109.


    Wang, Qianxi Liu, Wenke Zhang, A. M. and Sui, Yi 2015. Bubble dynamics in a compressible liquid in contact with a rigid boundary. Interface Focus, Vol. 5, Issue. 5, p. 20150048.


    WANG, Qian-xi YANG, Yuan-xiang TAN, Danielle Sweimann SU, Jian and TAN, Soon Keat 2015. Non-spherical multi-oscillations of a bubble in a compressible liquid. Journal of Hydrodynamics, Ser. B, Vol. 26, Issue. 6, p. 848.


    Ye, X. Yao, X.-L. Sun, L.-Q. and Wang, B. 2015. Cavitation Bubble in Compressible Fluid Near the Rigid Wall Subjected to the Acoustic Wave with Arbitrary Incidence Angle in Three-Dimensional. Journal of Mechanics, Vol. 31, Issue. 03, p. 307.


    Zhang, Yuning and Du, Xiaoze 2015. Influences of non-uniform pressure field outside bubbles on the propagation of acoustic waves in dilute bubbly liquids. Ultrasonics Sonochemistry, Vol. 26, p. 119.


    Zhang, Y N Zhang, Y N Du, X Z and Xian, H Z 2015. Enhancement of heat and mass transfer by cavitation. IOP Conference Series: Materials Science and Engineering, Vol. 72, Issue. 1, p. 012002.


    Geers, Thomas L. 2014. Optimization of an augmented Prosperetti-Lezzi bubble modela). The Journal of the Acoustical Society of America, Vol. 136, Issue. 1, p. 30.


    Liu, Gang Jayathilake, Pahala Gedara and Khoo, Boo Cheong 2014. Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid. Ultrasonics, Vol. 54, Issue. 2, p. 576.


    Paul, Shirshendu Nahire, Rahul Mallik, Sanku and Sarkar, Kausik 2014. Encapsulated microbubbles and echogenic liposomes for contrast ultrasound imaging and targeted drug delivery. Computational Mechanics, Vol. 53, Issue. 3, p. 413.


    Wang, Qianxi 2014. Multi-oscillations of a bubble in a compressible liquid near a rigid boundary. Journal of Fluid Mechanics, Vol. 745, p. 509.


    Hua, Chengyun and Johnsen, Eric 2013. Nonlinear oscillations following the Rayleigh collapse of a gas bubble in a linear viscoelastic (tissue-like) medium. Physics of Fluids, Vol. 25, Issue. 8, p. 083101.


    Wang, Q. X. 2013. Non-spherical bubble dynamics of underwater explosions in a compressible fluid. Physics of Fluids, Vol. 25, Issue. 7, p. 072104.


    Zhang, A.M. Wang, S.P. and Wu, G.X. 2013. Simulation of bubble motion in a compressible liquid based on the three dimensional wave equation. Engineering Analysis with Boundary Elements, Vol. 37, Issue. 9, p. 1179.


    ×
  • Journal of Fluid Mechanics, Volume 185
  • December 1987, pp. 289-321

Bubble dynamics in a compressible liquid. Part 2. Second-order theory

  • A. Lezzi (a1) and A. Prosperetti (a1) (a2)
  • DOI: http://dx.doi.org/10.1017/S0022112087003185
  • Published online: 01 April 2006
Abstract

The radial dynamics of a spherical bubble in a compressible liquid is studied by means of a rigorous singular-perturbation method to second order in the bubble-wall Mach number. The results of Part 1 (Prosperetti & Lezzi, 1986) are recovered at orders zero and one. At second order the ordinary inner and outer structure of the solution proves inadequate to correctly describe the fields and it is necessary to introduce an intermediate region the characteristic length of which is the geometric mean of the inner and outer lengthscales. The degree of indeterminacy for the radial equation of motion found at first order is significantly increased by going to second order. As in Part 1 we examine several of the possible forms of this equation by comparison with results obtained from the numerical integration of the complete partial-differential-equation formulation. Expressions and results for the pressure and velocity fields in the liquid are also reported.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax