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Growth-and-collapse dynamics of small bubble clusters near a wall

Published online by Cambridge University Press:  16 June 2015

A. Tiwari
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
C. Pantano
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
J. B. Freund*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
Email address for correspondence: jbfreund@illinois.edu

Abstract

The violent collapse of bubble clusters is thought to damage adjacent material in both engineering and biomedical applications. Yet the complexities of the root mechanisms have restricted theoretical descriptions to significantly simplified configurations. Reduced-physics models based upon either homogenization or arrays of idealized spherical bubbles do reproduce important gross cluster-scale features. However, these models neglect detailed local bubble–bubble interactions, which are expected to mediate damage mechanisms. To describe these bubble-scale interactions, we simulate the expansion and subsequent collapse of a hemispherical cluster of 50 bubbles adjacent to a plane rigid wall, explicitly representing both the asymmetric dynamics of each bubble within the cluster and the compressible-fluid mechanics of bubble–bubble interactions. Results show that the collapse propagates inward, as visualized in experiments, and that geometric focusing generates high impulsive pressures. This gross behaviour is nearly independent of the specific arrangement of bubbles within the cluster and matches predictions from the corresponding particle and homogenized models we consider. The peak pressure in the detailed simulations is associated with the centremost bubble, which causes a corresponding peak pressure on the nearby wall. However, the peak pressures in all cases are a small fraction – over a factor of ten times smaller in many cases – of those predicted in the corresponding reduced models. This is due to the enhanced focusing in the homogeneous model and the spherical constraint on each bubble in the particle models assessed. These would be important factors to consider in any subsequent predictions of wall damage based upon reduced models.

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Papers
Copyright
© 2015 Cambridge University Press 

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References

d’Agostino, L. & Brennen, C. E. 1989 Linearized dynamics of spherical bubble clouds. J. Fluid Mech. 199, 155176.CrossRefGoogle Scholar
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), 28052819.CrossRefGoogle Scholar
Ando, K., Colonius, T. & Brennen, C. E. 2011 Numerical simulation of shock propagation in a polydisperse bubbly liquid. Intl J. Multiphase Flow 37 (6), 596608.CrossRefGoogle Scholar
Arora, M., Ohl, C. D. & Lohse, D. 2007 Effect of nuclei concentration on cavitation cluster dynamics. J. Acoust. Soc. Am. 121 (6), 34323436.CrossRefGoogle ScholarPubMed
Baer, M. R. & Nunziato, J. W. 1986 A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Intl J. Multiphase Flow 12 (6), 861889.CrossRefGoogle Scholar
Bailey, M. R., Khokhlova, V. A., Sapozhnikov, O. A., Kargl, S. G. & Crum, L. A. 2003 Physical mechanisms of the therapeutic effect of ultrasound - (a review). Acoust. Phys. 49 (4), 369388.CrossRefGoogle Scholar
Best, J. P. 1993 The formation of toroidal bubbles upon the collapse of transient cavities. J. Fluid Mech. 251, 79107.CrossRefGoogle Scholar
Blake, J. R. & Gibson, D. C. 1987 Cavitation bubbles near boundaries. Annu. Rev. Fluid Mech. 19, 99123.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 (1751), 251267.CrossRefGoogle Scholar
Bremond, N., Arora, M., Ohl, C. D. & Lohse, D. 2006 Controlled multibubble surface cavitation. Phys. Rev. Lett. 96 (22), 224501.CrossRefGoogle ScholarPubMed
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.Google Scholar
Brennen, C. E. 2002 Fission of collapsing cavitation bubbles. J. Fluid Mech. 472, 153166.CrossRefGoogle Scholar
Brujan, E. A., Ikeda, T. & Matsumoto, Y. 2012 Shock wave emission from a cloud of bubbles. Soft Matt. 8 (21), 57775783.CrossRefGoogle Scholar
Brujan, E. A., Ikeda, T., Yoshinaka, K. & Matsumoto, Y. 2011 The final stage of the collapse of a cloud of bubbles close to a rigid boundary. Ultrason. Sonochem. 18 (1), 5964.CrossRefGoogle ScholarPubMed
Bui, T. T., Ong, E. T., Khoo, B. C., Klaseboer, E. & Hung, K. C. 2006 A fast algorithm for modeling multiple bubbles dynamics. J. Comput. Phys. 216 (2), 430453.CrossRefGoogle 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, 259273.CrossRefGoogle Scholar
Chahine, G. L. & Duraiswami, R. 1992 Dynamical interactions in a multi-bubble cloud. Trans. ASME: J. Fluids Engng 114 (4), 680686.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), 732746.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, 395420.CrossRefGoogle Scholar
Deiterding, R., Radovitzky, R., Mauch, S. P., Noels, L., Cummings, J. C. & Meiron, D. I. 2006 A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading. Engng Comput. 22 (3–4), 325347.CrossRefGoogle Scholar
Delale, C. F. & Tunc, M. 2004 A bubble fission model for collapsing cavitation bubbles. Phys. Fluids 16 (11), 42004203.CrossRefGoogle Scholar
Doinikov, A. A. 2004 Mathematical model for collective bubble dynamics in strong ultrasound fields. J. Acoust. Soc. Am. 116 (2), 821827.CrossRefGoogle Scholar
Esmaeeli, A. & Tryggvason, G. 2004a Computations of film boiling. Part I: numerical method. Intl J. Heat Mass Transfer 47 (25), 54515461.CrossRefGoogle Scholar
Esmaeeli, A. & Tryggvason, G. 2004b Computations of film boiling. Part II: multi-mode film boiling. Intl J. Heat Mass Transfer 47 (25), 54635476.CrossRefGoogle Scholar
Freund, J. B., Colonius, T. & Evan, A. P. 2007 A cumulative shear mechanism for tissue damage initiation in shock-wave lithotripsy. Ultrasound Med. Biol. 33 (9), 14951503.CrossRefGoogle ScholarPubMed
Freund, J. B., Shukla, R. K. & Evan, A. P. 2009 Shock-induced bubble jetting into a viscous fluid with application to tissue injury in shock-wave lithotripsy. J. Acoust. Soc. Am. 126 (5), 27462756.CrossRefGoogle ScholarPubMed
Fuster, D. & Colonius, T. 2011 Modelling bubble clusters in compressible liquids. J. Fluid Mech. 688, 352389.CrossRefGoogle Scholar
Fuster, D., Dopazo, C. & Hauke, G. 2011 Liquid compressibility effects during the collapse of a single cavitating bubble. J. Acoust. Soc. Am. 129 (1), 122131.CrossRefGoogle ScholarPubMed
Gottlieb, S. & Shu, C. W. 1988 Total variation diminishing Runge–Kutta schemes. Maths Comput. 67, 7385.CrossRefGoogle Scholar
Hansson, I. & Mørch, K. A. 1980 The dynamics of cavity clusters in ultrasonic (vibratory) cavitation erosion. J. Appl. Phys. 51 (9), 46514658.CrossRefGoogle Scholar
Hardt, S. & Wondra, F. 2008 Evaporation model for interfacial flows based on a continuum-field representation of the source terms. J. Comput. Phys. 227 (11), 58715895.CrossRefGoogle 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), 786795.CrossRefGoogle Scholar
Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202228.CrossRefGoogle Scholar
Johnsen, E. & Colonius, T. 2006 Implementation of WENO schemes in compressible multicomponent flow problems. J. Comput. Phys. 219 (2), 715732.CrossRefGoogle Scholar
Johnsen, E. & Colonius, T. 2009 Numerical simulations of non-spherical bubble collapse. J. Fluid Mech. 629, 231262.CrossRefGoogle ScholarPubMed
Kameda, M. & Matsumoto, Y. 1996 Shock waves in a liquid containing small gas bubbles. Phys. Fluids 8 (2), 322335.CrossRefGoogle Scholar
Kameda, M., Shimaura, N., Higashino, F. & Matsumoto, Y. 1998 Shock waves in a uniform bubbly flow. Phys. Fluids 10 (10), 26612668.CrossRefGoogle Scholar
Keller, J. B. & Miksis, M. 1980 Bubble oscillations of large-amplitude. J. Acoust. Soc. Am. 68 (2), 628633.CrossRefGoogle Scholar
Konno, A., Kato, H., Yamaguchi, H. & Maeda, M. 2002 On the collapsing behavior of cavitation bubble clusters. JSME Intl J. B 45 (3), 631637.CrossRefGoogle Scholar
Kornfeld, M. & Suvorov, L. 1944 On the destructive action of cavitation. J. Appl. Phys. 15, 495506.CrossRefGoogle Scholar
Krefting, D., Mettin, R. & Lauterborn, W. 2004 High-speed observation of acoustic cavitation erosion in multibubble systems. Ultrason. Sonochem. 11, 119123.CrossRefGoogle ScholarPubMed
Kubota, A., Kato, H. & Yamaguchi, H. 1992 A new modelling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section. J. Fluid Mech. 240, 5996.CrossRefGoogle Scholar
Lauer, E., Hu, X. Y., Hickel, S. & Adams, N. A. 2012 Numerical investigation of collapsing cavity arrays. Phys. Fluids 24 (5), 052104.CrossRefGoogle Scholar
Lauterborn, W. & Kurz, T. 2010 Physics of bubble oscillations. Rep. Prog. Phys. 73 (10), 106501.CrossRefGoogle Scholar
Lindau, O. & Lauterborn, W. 2003 Cinematographic observation of the collapse and rebound of a laser-produced cavitation bubble near a wall. J. Fluid Mech. 479, 327348.CrossRefGoogle Scholar
Matsumoto, Y., Allen, J. S., Yoshizawa, S., Ikeda, T. & Kaneko, Y. 2005 Medical ultrasound with microbubbles. Exp. Therm. Fluid Sci. 29 (3), 255265.CrossRefGoogle Scholar
Matsumoto, Y. & Yoshizawa, S. 2005 Behaviour of a bubble cluster in an ultrasound field. Intl J. Numer. Meth. Fluids 47, 591601.CrossRefGoogle Scholar
Menikoff, R. & Plohr, B. J. 1989 The Riemann problem for fluid-flow of real materials. Rev. Mod. Phys. 61 (1), 75130.CrossRefGoogle Scholar
Mettin, R., Akhatov, I., Parlitz, U., Ohl, C. D. & Lauterborn, W. 1997 Bjerknes forces between small cavitation bubbles in a strong acoustic field. Phys. Rev. E 56 (3), 29242931.CrossRefGoogle Scholar
Omta, R. 1987 Oscillations of a cloud of bubbles of small and not so small amplitude. J. Acoust. Soc. Am. 82 (3), 10181033.CrossRefGoogle Scholar
Parlitz, U., Mettin, R., Luther, S., Akhatov, I., Voss, M. & Lauterborn, W. 1999 Spatio-temporal dynamics of acoustic cavitation bubble clouds. Phil. Trans. R. Soc. Lond. A 357 (1751), 313334.CrossRefGoogle Scholar
Pelekasis, N. A., Gaki, A., Doinikov, A. & Tsamopoulos, J. A. 2004 Secondary Bjerknes forces between two bubbles and the phenomenon of acoustic streamers. J. Fluid Mech. 500, 313347.CrossRefGoogle Scholar
Philipp, A. & Lauterborn, W. 1998 Cavitation erosion by single laser-produced bubbles. J. Fluid Mech. 361, 75116.CrossRefGoogle Scholar
Pishchalnikov, Y. A., McAteer, J. A., Williams, J. C., Pishchalnikova, I. V. & Vonderhaar, R. J. 2006 Why stones break better at slow shockwave rates than at fast rates: in vitro study with a research electrohydraulic lithotripter. J. Endourol. 20 (8), 537541.CrossRefGoogle Scholar
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9, 145185.CrossRefGoogle Scholar
Popinet, S. & Zaleski, S. 1999 A front-tracking algorithm for accurate representation of surface tension. Intl J. Numer. Meth. Fluids 30 (6), 775793.3.0.CO;2-#>CrossRefGoogle Scholar
Popinet, S. & Zaleski, S. 2002 Bubble collapse near a solid boundary: a numerical study of the influence of viscosity. J. Fluid Mech. 464, 137163.CrossRefGoogle Scholar
Prosperetti, A. & Lezzi, A. 1986 Bubble dynamics in a compressible liquid. Part 1. First-order theory. J. Fluid Mech. 168, 457478.CrossRefGoogle Scholar
Rayleigh, Lord 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 9498.CrossRefGoogle Scholar
Reisman, G. E., Wang, Y. C. & Brennen, C. E. 1998 Observations of shock waves in cloud cavitation. J. Fluid Mech. 355, 255283.CrossRefGoogle Scholar
Roberts, W. W., Hall, T. L., Ives, K., Wolf, J. S., Fowlkes, J. B. & Cain, C. A. 2006 Pulsed cavitational ultrasound: A noninvasive technology for controlled tissue ablation (histotripsy) in the rabbit kidney. J. Urol. 175 (2), 734738.CrossRefGoogle ScholarPubMed
Rossinelli, D., Hejazialhosseini, B., Hadjidoukas, P., Bekas, C., Curioni, A., Bertsch, A., Futral, S., Schmidt, S., Adams, N. & Koumoutsakos, P.2013 11 PFLOP/s simulations of cloud cavitation collapse. In Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (Supercomputing 2013, SC13). Article no. 3. ACM.Google Scholar
Sapozhnikov, O. A., Khokhlova, V. A., Bailey, M. R., Williams, J. C., McAteer, J. A., Cleveland, R. O. & Crum, C. A. 2002 Effect of overpressure and pulse repetition frequency on cavitation in shock wave lithotripsy. J. Acoust. Soc. Am. 112 (3), 11831195.CrossRefGoogle ScholarPubMed
Saurel, R. & Abgrall, R. 1999a A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150 (2), 425467.CrossRefGoogle Scholar
Saurel, R. & Abgrall, R. 1999b A simple method for compressible multifluid flows. SIAM J. Sci. Comput. 21 (3), 11151145.CrossRefGoogle Scholar
Seo, J. H., Lele, S. K. & Tryggvason, G. 2010 Investigation and modeling of bubble–bubble interaction effect in homogeneous bubbly flows. Phys. Fluids 22 (6), 063302.CrossRefGoogle 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), 380385.CrossRefGoogle Scholar
Smereka, P. 2002 A Vlasov equation for pressure wave propagation in bubbly fluids. J. Fluid Mech. 454, 287325.CrossRefGoogle Scholar
Titarev, V. A. & Toro, E. F. 2004 Finite-volume WENO schemes for three-dimensional conservation laws. J. Comput. Phys. 201 (1), 238260.CrossRefGoogle Scholar
Tiwari, A., Freund, J. B. & Pantano, C. 2013 A diffuse interface model with immiscibility preservation. J. Comput. Phys. 252, 290309.CrossRefGoogle Scholar
Toro, E. F. 2006 Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer.Google Scholar
Wang, Y. C. 1999 Effects of nuclei size distribution on the dynamics of a spherical cloud of cavitation bubbles. Trans. ASME: J. Fluids Engng 121 (4), 881886.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), 872880.Google Scholar
van Wijngaarden, L. 1968 On the equations of motion for mixtures of liquid and gas bubbles. J. Fluid Mech. 33 (3), 465474.CrossRefGoogle Scholar
van Wijngaarden, L. 1972 One-dimensional flow of liquids containing small gas bubbles. Annu. Rev. Fluid Mech. 4, 369396.CrossRefGoogle Scholar
Xu, Z., Fowlkes, J. B. & Cain, C. A. 2006 A new strategy to enhance cavitational tissue erosion using a high-intensity, initiating sequence. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53 (8), 14121424.Google ScholarPubMed
Xu, Z., Fowlkes, J. B., Ludomirsky, A. & Cain, C. A. 2005a Investigation of intensity thresholds for ultrasound tissue erosion. Ultrasound Med. Biol. 31 (12), 16731682.CrossRefGoogle ScholarPubMed
Xu, Z., Fowlkes, J. B., Rothman, E. D., Levin, A. M. & Cain, C. A. 2005b Controlled ultrasound tissue erosion: the role of dynamic interaction between insonation and microbubble activity. J. Acoust. Soc. Am. 117 (1), 424435.CrossRefGoogle ScholarPubMed
Xu, Z., Ludomirsky, A., Eun, L. Y., Hall, T. L., Tran, B. C., Fowlkes, J. B. & Cain, C. A. 2004 Controlled ultrasound tissue erosion. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51 (6), 726736.CrossRefGoogle ScholarPubMed
Xu, Z., Raghavan, M., Hall, T. L., Mycek, M.-A., Fowlkes, J. B. & Cain, C. A. 2008 Evolution of bubble clouds induced by pulsed cavitational ultrasound therapy – histotripsy. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 55 (5), 11221132.Google ScholarPubMed
Yasui, K., Iida, Y., Tuziuti, T., Kozuka, T. & Towata, A. 2008 Strongly interacting bubbles under an ultrasonic horn. Phys. Rev. E 77 (1), 016609.CrossRefGoogle ScholarPubMed
Zeravcic, Z., Lohse, D. & Van Saarloos, W. 2011 Collective oscillations in bubble clouds. J. Fluid Mech. 680, 114149.CrossRefGoogle Scholar
Zhang, D. Z. & Prosperetti, A. 1994 Ensemble phase-averaged equations for bubbly flows. Phys. Fluids 6 (9), 29562970.CrossRefGoogle Scholar
Zhang, S. G., Duncan, J. H. & Chahine, G. L. 1993 The final stage of the collapse of a cavitation bubble near a rigid wall. J. Fluid Mech. 257, 147181.CrossRefGoogle Scholar
Zhang, Y. L., Yeo, K. S., Khoo, B. C. & Wang, C. 2001 3D jet impact and toroidal bubbles. J. Comput. Phys. 166 (2), 336360.CrossRefGoogle Scholar
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 (1), 119134.CrossRefGoogle ScholarPubMed
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