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Bubble cloud dynamics in an ultrasound field

Published online by Cambridge University Press:  16 January 2019

Kazuki Maeda Open the ORCID record for Kazuki Maeda [Opens in a new window]  and
Tim Colonius
Kazuki Maeda*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Present address: Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA. Email address for correspondence: kazuki.e.maeda@gmail.com
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Abstract

The dynamics of bubble clouds induced by high-intensity focused ultrasound is investigated in a regime where the cloud size is similar to the ultrasound wavelength. High-speed images show that the cloud is asymmetric; the bubbles nearest the source grow to a larger radius than the distal ones. Similar structures of bubble clouds are observed in numerical simulations that mimic the laboratory experiment. To elucidate the structure, a parametric study is conducted for plane ultrasound waves with various amplitudes and diffuse clouds with different initial void fractions. Based on an analysis of the kinetic energy of liquid induced by bubble oscillations, a new scaling parameter is introduced to characterize the dynamics. The new parameter generalizes the cloud interaction parameter originally introduced by d’Agostino & Brennen (J. Fluid Mech., vol. 199, 1989, pp. 155–176). The dynamic interaction parameter controls the energy localization and consequent anisotropy of the cloud. Moreover, the amplitude of the far-field, bubble-scattered acoustics is likewise correlated with the proposed parameter. Findings of the present study not only shed light on the physics of cloud cavitation, but may also be of use for the quantification of the effects of cavitation on outcomes of ultrasound therapies including high-intensity focused ultrasound-based lithotripsy.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Cavitation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 1105 - 1134
Copyright
© 2019 Cambridge University Press 

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References

Ando, K., Colonius, T. & Brennen, C. E. 2011 Numerical simulation of shock propagation in a polydisperse bubbly liquid. Intl J. Multiphase Flow 37 (6), 596–608.Google Scholar
Arora, M., Ohl, C.-D. & Lohse, D. 2007 Effect of nuclei concentration on cavitation cluster dynamics. J. Acoust. Soc. Am. 121 (6), 3432–3436.Google Scholar
Bailey, M. R., McAteer, J. A., Pishchalnikov, Y. A., Hamilton, M. F. & Colonius, T. 2006 Progress in lithotripsy research. Acoust. Today 2 (2), 18–29.Google Scholar
Biesheuvel, A. & vanWijngaarden, L. 1984 Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J. Fluid Mech. 148, 301–318.Google Scholar
Bremond, N., Arora, M., Ohl, C.-D. & Lohse, D. 2006 Controlled multibubble surface cavitation. Phys. Rev. Lett. 96, 224501.Google Scholar
Brennen, C. E. 2002 Fission of collapsing cavitation bubbles. J. Fluid Mech. 472, 153–166.Google Scholar
Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L. 1985 Effective equations for wave propagation in bubbly liquids. J. Fluid Mech. 153, 259–273.Google Scholar
Canney, M. S., Bailey, M. R., Crum, L. A., Khokhlova, V. A. & Sapozhnikov, O. A. 2008 Acoustic characterization of high intensity focused ultrasound fields: a combined measurement and modeling approach. J. Acoust. Soc. Am. 124 (4), 2406–2420.Google Scholar
Carstensen, E. L. & Foldy, L. L. 1947 Propagation of sound through a liquid containing bubbles. J. Acoust. Soc. Am. 19 (3), 481–501.Google Scholar
Cash, J. R. & Karp, A. H. 1990 A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Trans. Math. Softw. 16 (3), 201–222.Google Scholar
Chahine, G. L. 1983 Cloud cavitation: theory. In Proc. 14th Symp. on Naval Hydrodynamics, Washington, DC, USA, pp. 165–194.Google 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 (2), 69–76.Google Scholar
Commander, K. W. & Prosperetti, A. 1989 Linear pressure waves in bubbly liquids: comparison between theory and experiments. J. Acoust. Soc. Am. 85 (2), 732–746.Google Scholar
Coralic, V. & Colonius, T. 2014 Finite-volume WENO scheme for viscous compressible multicomponent flows. J. Comput. Phys. 274, 95–121.Google Scholar
d’Agostino, L. & Brennen, C. E. 1989 Linearized dynamics of spherical bubble clouds. J. Fluid Mech. 199, 155–176.Google Scholar
Doinikov, A. A. 2004 Mathematical model for collective bubble dynamics in strong ultrasound fields. J. Acoust. Soc. Am. 116 (2), 821–827.Google Scholar
Fuster, D. & Colonius, T. 2011 Modelling bubble clusters in compressible liquids. J. Fluid Mech. 688, 352–389.Google Scholar
Ikeda, T., Yoshizawa, S., Masataka, T., Allen, J. S., Takagi, S., Ohta, N., Kitamura, T. & Matsumoto, Y. 2006 Cloud cavitation control for lithotripsy using high intensity focused ultrasound. Ultrasound Med. Biol. 32 (9), 1383–1397.Google Scholar
Ilinskii, Y. A., Hamilton, M. F. & Zabolotskaya, E. A. 2007 Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics. J. Acoust. Soc. Am. 121 (2), 786–795.Google Scholar
Ishimaru, A. 1978 Wave Propagation and scattering in Random Media, vol. 2. Academic Press.Google Scholar
Johnsen, E. & Colonius, T. 2009 Numerical simulations of non-spherical bubble collapse. J. Fluid Mech. 629, 231–262.Google Scholar
Kameda, M. & Matsumoto, Y. 1996 Shock waves in a liquid containing small gas bubbles. Phys. Fluids 8 (2), 322–335.Google Scholar
Keller, J. B. & Miksis, M. 1980 Bubble oscillations of large amplitude. J. Acoust. Soc. Am. 68 (2), 628–633.Google Scholar
Lu, Y., Katz, J. & Prosperetti, A. 2013 Dynamics of cavitation clouds within a high-intensity focused ultrasonic beam. Phys. Fluids 25 (7), 073301.Google Scholar
Ma, J., Chahine, G. L. & Hsiao, C.-T. 2015 Spherical bubble dynamics in a bubbly medium using an Euler–Lagrange model. Chem. Engng Sci. 128, 64–81.Google Scholar
Ma, J., Hsiao, C. H. & Chahine, G. L. 2018 Numerical study of acoustically driven bubble cloud dynamics near a rigid wall. Ultrasonics Sonochem. 40 (Part A), 944–954.Google Scholar
Maeda, K. & Colonius, T. 2017 A source term approach for generation of one-way acoustic waves in the Euler and Navier–Stokes equations. Wave Motion 75, 36–49.Google Scholar
Maeda, K. & Colonius, T. 2018 Eulerian–Lagrangian method for simulation of cloud cavitation. J. Comput. Phys. 371, 994–1017.Google Scholar
Maeda, K., Kreider, W., Maxwell, A., Cunitz, B., Colonius, T. & Bailey, M. 2015 Modeling and experimental analysis of acoustic cavitation bubbles for burst wave lithotripsy. J. Phys.: Conf. Ser. 656 (1), 012027.Google Scholar
Matsumoto, Y., Allen, J. S., Yoshizawa, S., Ikeda, T. & Kaneko, Y. 2005 Medical ultrasound with microbubbles. Exp. Therm. Fluid Sci. 29 (3), 255–265.Google Scholar
Matsumoto, Y. & Yoshizawa, S. 2005 Behaviour of a bubble cluster in an ultrasound field. Intl J. Numer. Meth. Fluids 47 (6–7), 591–601.Google Scholar
Maxwell, A. D., Cunitz, B. W., Kreider, W., Sapozhnikov, O. A., Hsi, R. S., Harper, J. D., Bailey, M. R. & Sorensen, M. D. 2015 Fragmentation of urinary calculi in vitro by burst wave lithotripsy. J. Urol. 193 (1), 338–344.Google Scholar
McAteer, J. A., Bailey, M. R., Williams, J. C. Jr, Cleveland, R. O. & Evan, A. P. 2005 Strategies for improved shock wave lithotripsy. Minerva urologica e nefrologica = The Italian Journal of Urology and Nephrology 57 (4), 271–287.Google Scholar
Menikoff, R. & Plohr, B. J. 1989 The Riemann problem for fluid flow of real materials. Rev. Mod. Phys. 61 (1), 75.Google Scholar
Miller, D. L., Smith, N. B., Bailey, M. R., Czarnota, G. J., Hynynen, K., Makin, I. R. S.& of the American Institute of Ultrasound in Medicine, Bioeffects Committee 2012 Overview of therapeutic ultrasound applications and safety considerations. J. Ultrasound Med. 31 (4), 623–634.Google Scholar
Mørch, K. A. 1980 On the collapse of cavity clusters in flow cavitation. In Cavitation and Inhomogeneities in Underwater Acoustics, pp. 95–100. Springer.Google Scholar
Mørch, K. A. 1982 Energy considerations on the collapse of cavity clusters. In Mechanics and Physics of Bubbles in Liquids, pp. 313–321. Springer.Google Scholar
Omta, R. 1987 Oscillations of a cloud of bubbles of small and not so small amplitude. J. Acoust. Soc. Am. 82 (3), 1018–1033.Google Scholar
Pishchalnikov, Y. A., Sapozhnikov, O. A., Bailey, M. R., Williams, J. C. Jr, Cleveland, R. O., Colonius, T., Crum, L. A., Evan, A. P. & McAteer, J. A. 2003 Cavitation bubble cluster activity in the breakage of kidney stones by lithotripter shockwaves. J. Endourol. 17 (7), 435–446.Google Scholar
Preston, A. T., Colonius, T. & Brennen, C. E. 2007 A reduced-order model of diffusive effects on the dynamics of bubbles. Phys. Fluids 19, 123302.Google Scholar
Prosperetti, A., Crum, L. A. & Commander, K. W. 1988 Nonlinear bubble dynamics. J. Acoust. Soc. Am. 83 (2), 502–514.Google Scholar
Rasthofer, U., Wermelinger, F., Hadijdoukas, P. & Koumoutsakos, P. 2017 Large scale simulation of cloud cavitation collapse. Procedia Comput. Sci. 108 (Supplement C), 1763–1772.Google Scholar
Reisman, G. E., Wang, Y.-C. & Brennen, C. E. 1998 Observations of shock waves in cloud cavitation. J. Fluid Mech. 355, 255–283.Google Scholar
Rossinelli, D., Hejazialhosseini, B., Hadjidoukas, P., Bekas, C., Curioni, A., Bertsch, A., Futral, S., Schmidt, S. J., Adams, N. A. & Koumoutsakos, P. 2013 11 pflop/s simulations of cloud cavitation collapse. In SC ’13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, pp. 1–13. IEEE.Google Scholar
Shimada, M., Matsumoto, Y. & Kobayashi, T. 2000 Influence of the nuclei size distribution on the collapsing behavior of the cloud cavitation. JSME Intl J. B 43 (3), 380–385.Google Scholar
Shyue, K.-M. 1998 An efficient shock-capturing algorithm for compressible multicomponent problems. J. Comput. Phys. 142 (1), 208–242.Google Scholar
Stride, E. P. & Coussios, C. C. 2010 Cavitation and contrast: the use of bubbles in ultrasound imaging and therapy. Proc. Inst. Mech. Engrs H: J. Engng Med. 224 (2), 171–191.Google Scholar
Takahira, H., Akamatsu, A. & Fujikawa, S. 1994 Dynamics of a cluster of bubbles in a liquid: theoretical analysis. JSME Intl J. B 37 (2), 297–305.Google Scholar
Tanguay, M.2003 Computation of bubbly cavitating flow in shock wave lithotripsy. PhD thesis, California Institute of Technology; http://resolver.caltech.edu/CaltechETD:etd-05282004-130028.Google Scholar
Tiwari, A., Pantano, C. & Freund, J. B. 2015 Growth-and-collapse dynamics of small bubble clusters near a wall. J. Fluid Mech. 775, 1–23.Google Scholar
Tomita, Y. & Shima, A. 1986 Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse. J. Fluid Mech. 169, 535–564.Google Scholar
vanWijngaarden, L. 1968 On the equations of motion for mixtures of liquid and gas bubbles. J. Fluid Mech. 33 (3), 465–474.Google Scholar
Wang, Y.-C. & Brennen, C. E. 1994 Shock wave development in the collapse of a cloud of bubbles. In Cavitation and Multiphase Flow, pp. 15–19. American Society of Mechanical Engineers.Google Scholar
Wang, Y.-C. & Brennen, C. E. 1999 Numerical computation of shock waves in a spherical cloud of cavitation bubbles. Trans. ASME J. Fluids Engng 121 (4), 872–880.Google Scholar
Yoshizawa, S., Ikeda, T., Ito, A., Ota, R., Takagi, S. & Matsumoto, Y. 2009 High intensity focused ultrasound lithotripsy with cavitating microbubbles. Med. Biol. Engng Comput. 47 (8), 851–860.Google Scholar
Zeravcic, Z., Lohse, D. & Van Saarloos, W. 2011 Collective oscillations in bubble clouds. J. Fluid Mech. 680, 114–149.Google Scholar