Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-23T09:59:39.749Z Has data issue: false hasContentIssue false
  • English
  • Français

Interaction of lithotripter shockwaves with single inertial cavitation bubbles

Published online by Cambridge University Press:  23 November 2007

EVERT KLASEBOER ,
SIEW WAN FONG ,
CARY K. TURANGAN ,
BOO CHEONG KHOO ,
ANDREW J. SZERI ,
MICHAEL L. CALVISI ,
GEORGY N. SANKIN  and
PEI ZHONG
EVERT KLASEBOER
Affiliation:
Institute of High Performance Computing, 1 Science Park Road, #01-01 The Capricorn, Singapore Science Park II, Singapore117528
SIEW WAN FONG
Affiliation:
Institute of High Performance Computing, 1 Science Park Road, #01-01 The Capricorn, Singapore Science Park II, Singapore117528
CARY K. TURANGAN
Affiliation:
Institute of High Performance Computing, 1 Science Park Road, #01-01 The Capricorn, Singapore Science Park II, Singapore117528
BOO CHEONG KHOO*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore119260 Singapore-MIT Alliance, 4 Engineering Drive 3, Singapore117576
ANDREW J. SZERI
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA
MICHAEL L. CALVISI
Affiliation:
School of Mathematics, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
GEORGY N. SANKIN
Affiliation:
Department of Mechanical Engineering and Materials Science, Duke University, Box 90300 Durham, NC 27708, USA
PEI ZHONG
Affiliation:
Department of Mechanical Engineering and Materials Science, Duke University, Box 90300 Durham, NC 27708, USA
*
†Author to whom correspondence should be addressed.
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamic interaction of a shockwave (modelled as a pressure pulse) with an initially spherically oscillating bubble is investigated. Upon the shockwave impact, the bubble deforms non-spherically and the flow field surrounding the bubble is determined with potential flow theory using the boundary-element method (BEM). The primary advantage of this method is its computational efficiency. The simulation process is repeated until the two opposite sides of the bubble surface collide with each other (i.e. the formation of a jet along the shockwave propagation direction). The collapse time of the bubble, its shape and the velocity of the jet are calculated. Moreover, the impact pressure is estimated based on water-hammer pressure theory. The Kelvin impulse, kinetic energy and bubble displacement (all at the moment of jet impact) are also determined. Overall, the simulated results compare favourably with experimental observations of lithotripter shockwave interaction with single bubbles (using laser-induced bubbles at various oscillation stages). The simulations confirm the experimental observation that the most intense collapse, with the highest jet velocity and impact pressure, occurs for bubbles with intermediate size during the contraction phase when the collapse time of the bubble is approximately equal to the compressive pulse duration of the shock wave. Under this condition, the maximum amount of energy of the incident shockwave is transferred to the collapsing bubble. Further, the effect of the bubble contents (ideal gas with different initial pressures) and the initial conditions of the bubble (initially oscillating vs. non-oscillating) on the dynamics of the shockwave-bubble interaction are discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 593 , 25 December 2007 , pp. 33 - 56
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ball, G. J., Howell, B. P., Leighton, T. G. & Schofield, M. J. 2000 Shock-induced collapse of a cylindrical air cavity in water: a free-Lagrange simulation. Shock Waves 10, 265–276.CrossRefGoogle Scholar
Blake, J. R., Taib, B. B. & Doherty, G. 1986 Transient cavities near boundaries. Part 1. Rigid boundary. J. Fluid Mech. 170, 479–497.CrossRefGoogle Scholar
Blake, J. R., Keen, G. S., Tong, R. P. & Wilson, M. 1999 Acoustic cavitation: the fluid dynamics of non-spherical bubbles. Phil. Trans. R. Soc. Lond. A 357, 251–267.CrossRefGoogle Scholar
Bourne, N. K. & Field, J. E. 1992 Shock-induced collapse of single cavities in liquids. J. Fluid Mech. 244, 225–240.CrossRefGoogle Scholar
Bourne, N. K. & Field, J. E. 1999 Shock-induced collapse and luminescence by cavities. Phil. Trans. R. Soc. Lond. A 357, 295–311.CrossRefGoogle Scholar
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.CrossRefGoogle Scholar
Brunton, J. H. 1966 High speed liquid impact. Phil. Trans. R. Soc. Lond. A 260, 79–85.Google Scholar
Calvisi, M. L., Szeri, A. J., Sankin, G. N., Zhong, P. & Blake, J. R. 2005 Shock interaction with a growing or collapsing bubble. 58th Annual Meeting of the American Physical Society, Division of Fluid Dynamics, Chicago, Illinois.Google Scholar
Chaussy, C., Brendel, W. & Schmiedt, E. 1980 Extracorporeally induced destruction of kidney stones by shock waves. Lancet 2, 1265–1268.CrossRefGoogle ScholarPubMed
Cleveland, R. O. & Sapozhnikov, O. A. 2005 Modeling elastic wave propagation in kidney stones with application to shock wave lithotripsy. J. Acoust. Soc. Am. 118. 2667–2676.CrossRefGoogle ScholarPubMed
Cole, R. H. 1948 Underwater Explosions. Princeton University Press.CrossRefGoogle Scholar
Coleman, A. J., Saunders, J. E., Crum, L. A. & Dyson, M. 1987 Acoustic cavitation generated by an extracorporeal shockwave lithotripter. Ultrasound Med. Biol. 13, 69–76.CrossRefGoogle ScholarPubMed
Crum, L. A. 1988 Cavitation microjets as a contributory mechanism for renal calculi disintegration in ESWL. J. Urol. 140, 1587–1596.CrossRefGoogle ScholarPubMed
Delius, M. 2000 History of shock wave lithotripsy. Proc. 15th Intl Symp. on Nonlinear Acoustics at the Turn of the Millennium. ISNA 15, 524, pp. 23–32.Google Scholar
Delius, M. & Brendel, W. 1988 A mechanism of gallstone destruction by extracorporeal shock waves. Naturwissenschaften 75, 200–201.CrossRefGoogle ScholarPubMed
Ding, Z. & Gracewski, S. M. 1996 The behaviour of a gas cavity impacted by a weak or strong shock wave. J. Fluid Mech. 309, 183–209.CrossRefGoogle Scholar
Eisenmenger, W. 2001 The mechanisms of stone fragmentation in ESWL. Ultrasound Med. Biol. 27, 683–693.CrossRefGoogle ScholarPubMed
Gracewski, S. M., Dahake, G., Ding, Z., Burns, S. J. & Everbach, E. C. 1993 Internal stress wave measurements in solids subjected to lithotripter pulses. J. Acoust. Soc. Am. 94, 652–661.CrossRefGoogle ScholarPubMed
Inoue, Y. & Kobayashi, T. 1993 Nonlinear oscillation of a gas-filled spherical cavity in an incompressible fluid. Fluid Dyn. Res. 11, 84–97.CrossRefGoogle Scholar
Jamaluddin, A. R. 2006 Free-Lagrange simulations of shock–bubble interaction in ESWL. PhD thesis, School of Engineering Sciences, University of Southampton, UK.Google Scholar
Khoo, B. C., Klaseboer, E. & Hung, K. C. 2005 A collapsing bubble-induced micro-pump using the jetting effect. Sensors Actuat. A 118, 152–161.CrossRefGoogle Scholar
Klaseboer, E. & Khoo, B. C. 2006 Modified Rayleigh–Plesset model for a non-spherically symmetric oscillating bubble with applications to boundary integral methods. Engng Anal. Boundary Elements 30, 59–71.CrossRefGoogle Scholar
Klaseboer, E., Hung, K. C., Wang, C., Wang, C. W., Khoo, B. C., Boyce, P., Debono, S. & Charlier, H. 2005 a Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure. J. Fluid Mech. 537, 387–413.CrossRefGoogle Scholar
Klaseboer, E., Khoo, B. C. & Hung, K. C. 2005 b Dynamics of an oscillating bubble near a floating structure. J. Fluids Struct. 21, 395–412.CrossRefGoogle Scholar
Klaseboer, E., Fong, S. W., Turangan, C. & Khoo, B. C. 2006 a Shockwave non-equilibrium bubble interaction: BEM simulations with experimental comparison. Proc. Sixth Intl Symp. on Cavitation CAV2006, Wageningen, The Netherlands.Google Scholar
Klaseboer, E., Turangan, C. K., Fong, S. W., Liu, T. G., Hung, K. C. & Khoo, B. C. 2006 b Simulations of pressure pulse–bubble interaction using boundary element method. Comput. Meth. Appl. Mech. Engng 195, 4287–4302.CrossRefGoogle Scholar
Kodama, T. & Takayama, K. 1998 Dynamics behavior of bubbles during extracorporeal shock-wave lithotripsy. Ultrasound Med. Biol. 24, 723–738.CrossRefGoogle ScholarPubMed
Kornfeld, M. & Suvorov, L. 1944 On the destructive action of cavitation. J. Appl. Phys. 15, 495–506.CrossRefGoogle Scholar
Lew, K. S. F., Klaseboer, E. & Khoo, B. C. 2007 A collapsing bubble-induced micropump: an experimental study. Sensors Actuat. A 133, 161–172.CrossRefGoogle Scholar
Lokhandwalla, M. & Sturtevant, B. 2000 Fracture mechanics model of stone comminution in ESWL and implications for tissue damage. Phys. Med. Biol. 45, 1923–1940.CrossRefGoogle ScholarPubMed
Ohl, C. D. & Ikink, R. 2003 Shock-wave-induced jetting of micron sized bubbles. Phys. Rev. Lett. 90, 214502.CrossRefGoogle Scholar
Pearson, A., Blake, J. R. & Otto, S. R. 2004 Jets in bubbles. J. Engng Maths 48, 391–412.CrossRefGoogle Scholar
Philipp, A. & Lauterborn, W. 1998 Cavitation erosion by single laser-produced bubbles. J. Fluid Mech. 361, 75–116.CrossRefGoogle Scholar
Philipp, A., Delius, M., Scheffczyk, C., Vogel, A. & Lauterborn, W. 1993 Interaction of lithotripter-generated shock waves with air bubbles. J Acoust. Soc. Am. 93, 2496–2509.CrossRefGoogle Scholar
Rayleigh, Lord 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 94–98.CrossRefGoogle Scholar
Sankin, G. N. & Zhong, P. 2006 Interaction between shock wave and single inertial bubbles near an elastic boundary. Phys. Rev. E 74, 046304.Google ScholarPubMed
Sankin, G. N., Simmons, W. N., Zhu, S. L. & Zhong, P. 2005 Shockwave interaction with laser-generated single bubbles. Phys. Rev. Lett. 95, 034501.CrossRefGoogle Scholar
Szeri, A. J., Storey, B. D., Pearson, A. & Blake, J. R. 2003 Heat and mass transfer during the violent collapse of nonspherical bubbles. Phys. Fluids 15, 2576–2586.CrossRefGoogle Scholar
Tomita, Y., Robinson, P. B., Tong, R. P. & Blake, J. R. 2002 Growth and collapse of cavitation bubbles near a curved rigid boundary. J. Fluid Mech. 466, 259–283.CrossRefGoogle Scholar
Turangan, C. K., Jamaluddin, A. R., Ball, G. J. & Leighton, T. G. 2008 Free-Lagrange simulations of the expansion and jetting collapse of air bubbles in water. J. Fluid Mech. (in press).CrossRefGoogle Scholar
Wang, Q. X., Yeo, K. S., Khoo, B. C. & Lam, K. Y. 1996 Strong interaction between a buoyancy bubble and a free surface. Theor. Comput. Fluid Dyn. 8, 73–88.CrossRefGoogle Scholar
Xi, X. F. & Zhong, P. 2000 Improvement of stone fragmentation during shock wave lithotripsy using a combined EH/PEAA shock wave generator – In vitro experiments. Ultrasound Med. Biol. 26, 457–467.CrossRefGoogle ScholarPubMed
Xi, X. F. & Zhong, P. 2001 Dynamic photoelastic study of the transient stress field in solids during SWL. J. Acoust. Soc. Am. 109, 1226–1239.CrossRefGoogle Scholar
Young, F. R. 1989 Cavitation. McGraw-Hill.Google Scholar
Zhong, P. & Chuong, C. J. 1993 Propagation of shock waves in elastic solids caused by cavitation microjet impact. I: Theoretical formulation J. Acoust. Soc. Am. 94, 19–28.CrossRefGoogle ScholarPubMed
Zhong, P. & Zhou, Y. F. 2001 Suppression of large intraluminal bubble expansion in shock wave lithotripsy without compromising stone comminution: methodology and in vitro experiments. J. Acoust. Soc. Am. 110, 3283–3291.CrossRefGoogle ScholarPubMed
Zhong, P., Chuong, C. J. & Preminger, G. M. 1993 Propagation of shock waves in elastic solids caused by cavitation microjet impact. II: Application in extracorporeal shock wave lithotripsy. J. Acoust. Soc. Am. 94, 29–36.CrossRefGoogle ScholarPubMed
Zhong, P., Zhou, Y. F. & Zhu, S. L. 2001 Dynamics of bubble oscillation in constrained media and mechanisms of vessel rupture in SWL. Ultrasound Med. Biol. 27, 119–134.CrossRefGoogle ScholarPubMed
Zhu, S. L., Cocks, F. H., Preminger, G. M. & Zhong, P. 2002 The role of stress waves and cavitation in stone comminution in shock wave lithotripsy. Ultrasound Med. Biol. 28, 661–671.CrossRefGoogle ScholarPubMed
Zhou, Y. F., Cocks, F. H., Preminger, G. M. & Zhong, P. 2004 Innovations in shock wave lithotripsy technology: updates in experimental studies. J. Urology 172, 1892–1898.CrossRefGoogle ScholarPubMed