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Bubble Dynamics

Chapter
Part of the SpringerBriefs in Molecular Science book series (BRIEFSMOLECULAR)

Abstract

Bubble pulsation is mathematically described by the Rayleigh–Plesset equation and by Keller equation. Derivation of the equations is fully described herein. Using the Rayleigh–Plesset equation, the violent collapse of a bubble is discussed. A method of numerical simulations of bubble pulsation is also described. In relation to numerical simulations, non-equilibrium evaporation and condensation of water vapor at the bubble wall, the variation in liquid temperature at the bubble wall, the gas diffusion across the bubble wall, and the chemical reactions inside a bubble are discussed. Comparison between numerical results and experimental data for a single-bubble system is shown. The main oxidants created inside a bubble are described based upon numerical simulations data. Linear and nonlinear resonance radius of a bubble is discussed as well as the analytical solution of the linearized equation of bubble pulsation. The mechanism of shock wave emission from a bubble into surrounding liquid is discussed. Inside a collapsing bubble, a shock wave is seldom formed due to lower temperature near the bubble wall. A liquid jet penetrates into a collapsing bubble near the solid surface. The bubble pulsation is influenced by the acoustic emissions from the surrounding bubbles, which is called bubblebubble interaction. The origin of acoustic cavitation noise is discussed based upon results of numerical simulations. It is shown that surfactants and salts strongly retard bubble–bubble coalescence.

Keywords

Rayleigh–Plesset equation Keller equation Rayleigh collapse Resonance radius Shock wave Jetting Primary and secondary Bjerkens forces Bubble–bubble interaction Acoustic cavitation noise Acoustic streaming 

References

  1. 1.
    Atkins P, de Paula J (2010) Atkins’ physical chemistry, 9th edn. Oxford University Press, OxfordGoogle Scholar
  2. 2.
    Yasui K (2015) Dynamics of acoustic bubbles. In: Grieser F, Choi PK, Enomoto N, Harada H, Okitsu K, Yasui K (eds) Sonochemistry and the acoustic bubble. Elsevier, AmsterdamGoogle Scholar
  3. 3.
    Yasui K (2016) Mechanism for stability of ultrafine bubbles. Jpn J Multiph Flow 30:19–26 (in Japanese)Google Scholar
  4. 4.
    Keller JB, Miksis M (1980) Bubble oscillations of large amplitude. J Acoust Soc Am 68:628–633. doi: 10.1121/1.384720 CrossRefGoogle Scholar
  5. 5.
    Prosperetti A, Lezzi A (1986) Bubble dynamics in a compressible liquid. Part 1. First-order theory. J Fluid Mech 168:457–478. doi: 10.1017/S0022112086000460 CrossRefGoogle Scholar
  6. 6.
    Yasui K (1996) Variation of liquid temperature at bubble wall near the sonoluminescence threshold. J Phys Soc Jpn 65:2830–2840. doi: 10.1143/JPSJ.65.2830 CrossRefGoogle Scholar
  7. 7.
    Pozrikidis C (2017) Fluid dynamics, 3rd edn. Springer, New YorkCrossRefGoogle Scholar
  8. 8.
    Storey BD, Szeri AJ (1999) Mixture segregation within sonoluminescence bubbles. J Fluid Mech 396:203–221. doi: 10.1017/S0022112099005984 CrossRefGoogle Scholar
  9. 9.
    Yasui K (2001) Effect of liquid temperature on sonoluminescence. Phys Rev E 64:016310. doi: 10.1103/PhysRevE.64.016310 CrossRefGoogle Scholar
  10. 10.
    Kundu PK (1990) Fluid mechanics. Academic Press, San DiegoGoogle Scholar
  11. 11.
    Akhatov I, Lindau O, Topolnikov A, Mettin R, Vakhitova N, Lauterborn W (2001) Collapse and rebound of a laser-induced cavitation bubble. Phys Fluids 13:2805–2819. doi: 10.1063/1.1401810 CrossRefGoogle Scholar
  12. 12.
    Muller S, Bachmann M, Kroninger D, Kurz T, Helluy P (2009) Comparison and validation of compressible flow simulations of laser-induced cavitation bubbles. Comput Fluid 38:1850–1862. doi: 10.1016/j.compfluid.2009.04.004 CrossRefGoogle Scholar
  13. 13.
    Gould H, Tobochnik J, Christian W (2007) An introduction to computer simulation methods, applications to physical systems, 3rd edn. Pearson, Addison Wesley, San FranciscoGoogle Scholar
  14. 14.
    Yasui K (1997) Alternative model of single-bubble sonoluminescence. Phys Rev E 56:6750–6760. doi: 10.1103/PhysRevE.56.6750 CrossRefGoogle Scholar
  15. 15.
    Yasui K (1996) A new formulation of bubble dynamics for sonoluminescence. Ph.D. thesis, Waseda University, JapanGoogle Scholar
  16. 16.
    Yasui K, Tuziuti T, Kanematsu W (2016) Extreme conditions in a dissolving air nanobubble. Phys Rev E 94:013106. doi: 10.1103/PhysREvE.94.013106 CrossRefGoogle Scholar
  17. 17.
    Yasui K, Tuziuti T, Sivakumar M, Iida Y (2005) Theoretical study of single-bubble sonochemistry. J Chem Phys 122:224706. doi: 10.1063/1.1925607 CrossRefGoogle Scholar
  18. 18.
    Toegel R, Lohse D (2003) Phase diagrams for sonoluminescing bubbles: a comparison between experiment and theory. J Chem Phys 118:1863–1875. doi: 10.1063/1.1531610 CrossRefGoogle Scholar
  19. 19.
    Storey BD, Szeri AJ (2001) A reduced model of cavitation physics for use in sonochemistry. Proc R Soc Lond A 457:1685–1700. doi: 10.1098/rspa.2001.0784 CrossRefGoogle Scholar
  20. 20.
    Lohse D, Brenner MP, Dupont TF, Hilgenfeldt S, Johnston B (1997) Sonoluminescing air bubbles rectify argon. Phys Rev Lett 78:1359–1362. doi: 10.1103/PhysRevLett.78.1359 CrossRefGoogle Scholar
  21. 21.
    Brenner MP, Hilgenfeldt S, Lohse D (2002) Single-bubble sonoluminescence. Rev Mod Phys 74:425–484. doi: 10.1103/RevModPhys.74.425 CrossRefGoogle Scholar
  22. 22.
    Yasui K, Tuziuti T, Sivakumar M, Iida Y (2004) Sonoluminescence. Appl Spectrosc Rev 39:399–436. doi: 10.1081/ASR-200030202 CrossRefGoogle Scholar
  23. 23.
    Storey BD, Szeri AJ (2000) Water vapour, sonoluminescence and sonochemistry. Proc R Soc Lond A 456:1685–1709. doi: 10.1098/rspa.2000.0582 CrossRefGoogle Scholar
  24. 24.
    Yasui K (2001) Single-bubble sonoluminescence from noble gases. Phys Rev E 63:035301. doi: 10.1103/PhysRevE.63.035301
  25. 25.
    Yasui K (2002) Segregation of vapor and gas in a sonoluminescing bubble. Ultrasonics 40:643–647. doi: 10.1016/S0041-624X(02)00190-7 CrossRefGoogle Scholar
  26. 26.
    Schrage RW (1953) A theoretical study of interphase mass transfer. Columbia University Press, New YorkGoogle Scholar
  27. 27.
    Fujikawa S, Akamatsu T (1980) Effects of the no-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid. J Fluid Mech 97:481–512. doi: 10.1017/S0022112080002662 CrossRefGoogle Scholar
  28. 28.
    Matsumoto M (1996) Molecular dynamics simulation of interphase transport at liquid surfaces. Fluid Phase Equilib 125:195–203. doi: 10.1016/S0378-3812(96)03123-8 CrossRefGoogle Scholar
  29. 29.
    Yasui K (1998) Effect of non-equilibrium evaporation and condensation on bubble dynamics near the sonoluminescence threshold. Ultrasonics 36:575–580. doi: 10.1016/S0041-6244(97)00107-8 CrossRefGoogle Scholar
  30. 30.
    Suslick KS, Hammerton DA, Cline RE Jr (1986) The sonochemical hot spot. J Am Chem Soc 108:5641–5642. doi: 10.1021/ja00278a055 CrossRefGoogle Scholar
  31. 31.
    Hua I, Hochemer RH, Hoffmann MR (1995) Sonolytic hydrolysis of p-nitrophenyl acetate: the role of supercritical water. J Phys Chem 99:2335–2342. doi: 10.1021/j100008a015 CrossRefGoogle Scholar
  32. 32.
    Moriwaki H, Takagi Y, Tanaka M, Tsuruho K, Okitsu K, Maeda Y (2005) Sonochemical decomposition of perfluorooctane sulfonate and perfluorooctanoic acid. Environ Sci Technol 39:3388–3392. doi: 10.1021/es040342v CrossRefGoogle Scholar
  33. 33.
    Yasui K (2016) Unsolved problems in acoustic cavitation. In: Ashokkumar M, Cavalieri F, Chemat F, Okitsu K, Sambandam A, Yasui K, Zisu B (eds) Handbook of ultrasonics and sonochemistry. Springer, SingaporeGoogle Scholar
  34. 34.
    Vuong VQ, Szeri AJ (1996) Sonoluminescence and diffusive transport. Phys Fluids 8:2354–2364. doi: 10.1063/1.869020 CrossRefGoogle Scholar
  35. 35.
    Kamath V, Prosperetti A, Egolfopoulos FN (1993) A theoretical study of sonoluminescence. J Acoust Soc Am 94:248–260. doi: 10.1121/1.407083 CrossRefGoogle Scholar
  36. 36.
    Shen Y, Yasui K, Sun Z, Mei B, You M, Zhu T (2016) Study on the spatial distribution of the liquid temperature near a cavitation bubble wall. Ultrason Sonochem 29:394–400. doi: 10.1016/j.ultsonch.2015.10.015 CrossRefGoogle Scholar
  37. 37.
    Eller A, Flynn HG (1965) Rectified diffusion during nonlinear pulsations of cavitation bubbles. J Acoust Soc Am 37:493–503. doi: 10.1121/1.1909357 CrossRefGoogle Scholar
  38. 38.
    Yasui K (2002) Influence of ultrasonic frequency on multibubble sonoluminescence. J Acoust Soc Am 112:1405–1413. doi: 10.1121/1.1502898 CrossRefGoogle Scholar
  39. 39.
    Leighton TG (1994) The acoustic bubble. Academic Press, LondonGoogle Scholar
  40. 40.
    Leong T, Ashokkumar M, Kentish S (2016) The growth of bubbles in an acoustic field by rectified diffusion. In: Ashokkumar M, Cavalieri F, Chemat F, Okitsu K, Sambandam A, Yasui K, Zisu B (eds) Handbook of ultrasonics and sonochemistry. Springer, SingaporeGoogle Scholar
  41. 41.
    Crum LA (1980) Measurements of the growth of air bubbles by rectified diffusion. J Acoust Soc Am 68:203–211. doi: 10.1121/1.384624 CrossRefGoogle Scholar
  42. 42.
    Louisnard O, Gomez F (2003) Growth by rectified diffusion of strongly acoustically forced gas bubbles in nearly saturated liquids. Phys Rev E 67:036610. doi: 10.1103/PhysRevE.67.036610 CrossRefGoogle Scholar
  43. 43.
    Yasui K, Tuziuti T, Lee J, Kozuka T, Towata A, Iida Y (2008) The range of ambient radius for an active bubble in sonoluminescence and sonochemical reactions. J Chem Phys 128:184705. doi: 10.1063/1.2919119 CrossRefGoogle Scholar
  44. 44.
    Yasui K (1997) Chemical reactions in a sonoluminescing bubble. J Phys Soc Jpn 66:2911–2920. doi: 10.1143/JPSJ.66.2911 CrossRefGoogle Scholar
  45. 45.
    Yasui K, Tuziuti T, Iida Y, Mitome H (2003) Theoretical study of the ambient-pressure dependence of sonochemical reactions. J Chem Phys 119:346–356. doi: 10.1063/1.1576375 CrossRefGoogle Scholar
  46. 46.
    Didenko YT, Suslick KS (2002) The energy efficiency of formation of phtons, radicals and ions during single-bubble cavitation. Nature (London) 418:394–397. doi: 10.1038/nature00895 CrossRefGoogle Scholar
  47. 47.
    Matula TJ, Crum LA (1998) Evidence for gas exchange in single-bubble sonoluminescence. Phys Rev Lett 80:865–868. doi: 10.1103/PhysRevLett.80.865 CrossRefGoogle Scholar
  48. 48.
    Yasui K, Tuziuti T, Kozuka T, Towata A, Iida Y (2007) Relationship between the bubble temperature and main oxidant created inside an air bubble under ultrasound. J Chem Phys 127:154502. doi: 10.1063/1.2790420 CrossRefGoogle Scholar
  49. 49.
    Yasui K, Tuziuti T, Iida Y (2004) Optimum bubble temperature for the sonochemical production of oxidants. Ultrasonics 42:579–584. doi: 10.1016/j.ultras.2003.12.005 CrossRefGoogle Scholar
  50. 50.
    Hart EJ, Henglein A (1985) Free radical and free atom reactions in the sonolysis of aqueous iodide and formate solutions. J Phys Chem 89:4342–4347. doi: 10.1021/j100266a038 CrossRefGoogle Scholar
  51. 51.
    Yasui K (2002) Effect of volatile solutes on sonoluminescence. J Chem Phys 116:2945–2954. doi: 10.1063/1.1436122 CrossRefGoogle Scholar
  52. 52.
    Ashokkumar M, Crum LA, Frensley CA, Grieser F, Matula TJ, McNamara WB III, Suslick KS (2000) Effect of solutes on single-bubble sonoluminescence in water. J Phys Chem 104:8462–8465. doi: 10.1021/jp000463r CrossRefGoogle Scholar
  53. 53.
    Guan J, Matula TJ (2003) Time scales for quenching single-bubble sonoluminescence in the presence of alcohols. J Phys Chem B 107:8917–8921. doi: 10.1021/jp026494z CrossRefGoogle Scholar
  54. 54.
    Kinsler LE, Frey AR, Coppens AB, Sanders JV (1982) Fundamentals of acoustics, 3rd edn. Wiley, New YorkGoogle Scholar
  55. 55.
    Landau LD, Lifshitz EM (1987) Fluid mechanics, 2nd edn. (trans: Sykes JB, Reid WH). Elsevier, AmsterdamGoogle Scholar
  56. 56.
    Holzfuss J, Ruggeberg M, Billo A (1998) Shock wave emissions of a sonoluminescing bubble. Phys Rev Lett 81:5434–5437. doi: 10.1103/PhysRevLett.81.5434 CrossRefGoogle Scholar
  57. 57.
    Hickling R, Plesset MS (1964) Collapse and rebound of a spherical bubble in water. Phys Fluids 7:7–14. doi: 10.1063/1.1711058 CrossRefGoogle Scholar
  58. 58.
    Wu CC, Roberts PH (1993) Shock-wave propagation in a sonoluminescing gas bubble. Phys Rev Lett 70:3424–3427. doi: 10.1103/PhysRevLett.70.3424 CrossRefGoogle Scholar
  59. 59.
    Moss WC, Clarke DB, White JW, Young DA (1994) Hydrodynamic simulations of bubble collapse and picosecond sonoluminescence. Phys Fluids 6:2979–2985. doi: 10.1063/1.868124 CrossRefGoogle Scholar
  60. 60.
    Nigmatulin RI, Akhatov IS, Topolnikov AS, Bolotnova RK, Vakhitova NK, Lahey RT Jr, Taleyarkhan RP (2005) Theory of supercompression of vapor bubbles and nanoscale thermonuclear fusion. Phys Fluids 17:107106. doi: 10.1063/1.2104556 CrossRefGoogle Scholar
  61. 61.
    Yuan L, Cheng HY, Chu MC, Leung PT (1998) Physical parameters affecting sonoluminescence: a self-consistent hydrodynamic study. Phys Rev E 57:4265–4280. doi: 10.1103/PhysRevE.57.4265 CrossRefGoogle Scholar
  62. 62.
    Cheng HY, Chu MC, Leung PT, Yuan L (1998) How important are shock waves to single-bubble sonoluminescence? Phys Rev E 58:R2705–R2708. doi: 10.1103/PhysRevE.58.R2705 CrossRefGoogle Scholar
  63. 63.
    Yuan L (2005) Sonochemical effects on single-bubble sonoluminescence. Phys Rev E 72:046309. doi: 10.1103/PhysRevE.72.046309 CrossRefGoogle Scholar
  64. 64.
    An Y (2006) Mechanism of single-bubble sonoluminescence. Phys Rev E 74:026304. doi: 10.1103/PhysRevE.74.026304 CrossRefGoogle Scholar
  65. 65.
    An Y, Li C (2008) Spectral lines of OH radicals and Na atoms in sonoluminescence. Phys Rev E 78:046313. doi: 10.1103/PhysRevE.78.046313 CrossRefGoogle Scholar
  66. 66.
    Vuong VQ, Szeri AJ, Young DA (1999) Shock formation within sonoluminescence bubbles. Phys Fluids 11:10–17. doi: 10.1063/1.869920 CrossRefGoogle Scholar
  67. 67.
    Ohl CD, Arora M, Dijkink R, Janve V, Lohse D (2006) Surface cleaning from laser-induced cavitation bubbles. Appl Phys Lett 89:074102. doi: 10.1063/1.2337506 CrossRefGoogle Scholar
  68. 68.
    Plesset MS, Chapman RB (1971) Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary. J Fluid Mech 47:283–290. doi: 10.1017/S0022112071001058 CrossRefGoogle Scholar
  69. 69.
    Lamminen MO, Walker HW, Weavers LK (2004) Mechanism and factors influencing the ultrasonic cleaning of particle-fouled ceramic membranes. J Membr Sci 237:213–223. doi: 10.1016/j.memsci.2004.02.031 CrossRefGoogle Scholar
  70. 70.
    Bremond N, Arora M, Dammer SM, Lohse D (2006) Interaction of cavitation bubbles on a wall. Phys Fluids 18:121505. doi: 10.1063/1.2396922 CrossRefGoogle Scholar
  71. 71.
    Calvisi ML, Lindau O, Blake JR, Szeri AJ (2007) Shape stability and violent collapse of microbubbles in acoustic traveling waves. Phys Fluids 19:047101. doi: 10.1063/1.2716633 CrossRefGoogle Scholar
  72. 72.
    Mettin R (2005) Bubble structures in acoustic cavitation. In: Doinikov AA (ed) Bubble and particle dynamics in acoustic fields: modern trends and applications. Research Signpost, TrivandrumGoogle Scholar
  73. 73.
    Matula TJ, Cordry SM, Roy RA, Crum LA (1997) Bjerknes force and bubble levitation under single-bubble sonoluminescence conditions. J Acoust Soc Am 102:1522–1527. doi: 10.1121/1.420065 CrossRefGoogle Scholar
  74. 74.
    Yasui K, Iida Y, Tuziuti T, Kozuka T, Towata A (2008) Strongly interacting bubbles under an ultrasonic horn. Phys Rev E 77:016609. doi: 10.1103/PhysRevE.77.016609 CrossRefGoogle Scholar
  75. 75.
    Mettin R, Akhatov I, Parlitz U, Ohl CD, Lauterborn W (1997) Bjerknes forces between small cavitation bubbles in a strong acoustic field. Phys Rev E 56:2924–2931. doi: 10.1103/PhysRevE.56.2924 CrossRefGoogle Scholar
  76. 76.
    Firouzi M, Howes T, Nguyen AV (2015) A quantitative review of the transition salt concentration for inhibiting bubble coalescence. Adv Colloid Interface Sci 222:305–318. doi: 10.1016/j.cis.2014.07.005 CrossRefGoogle Scholar
  77. 77.
    Prince MJ, Blanch HW (1990) Transition electrolyte concentrations for bubble coalescence. AIChE J 36:1425–1429. doi: 10.1002/aic.690360915 CrossRefGoogle Scholar
  78. 78.
    Prince MJ, Blanch HW (1990) Bubble coalescence and break-up in air-sparged bubble columns. AIChE J 36:1485–1499. doi: 10.1002/aic.690361004 CrossRefGoogle Scholar
  79. 79.
    Craig VSJ, Ninham BW, Pashley RM (1993) Effect of electrolytes on bubble coalescence. Nature (London) 364:317–319. doi: 10.1038/364317a0 CrossRefGoogle Scholar
  80. 80.
    Christenson HK, Yaminsky VV (1995) Solute effects on bubble coalescence. J Phys Chem 99:10420. doi: 10.1021/j100025a052 CrossRefGoogle Scholar
  81. 81.
    Oolman TO, Blanch HW (1986) Bubble coalescence in stagnant liquids. Chem Eng Commun 43:237–261. doi: 10.1080/00986448608911334 CrossRefGoogle Scholar
  82. 82.
    Lee JC, Meyrick DL (1970) Gas-liquid interfacial areas in salt solutions in an agitated tank. Trans Inst Chem Eng 48:T37–T45Google Scholar
  83. 83.
    Marrucci G (1969) A theory of coalescence. Chem Eng Sci 24:975–985. doi: 10.1016/0009-2509(69)87006-5 CrossRefGoogle Scholar
  84. 84.
    Iida Y, Ashokkumar M, Tuziuti T, Kozuka T, Yasui K, Towata A, Lee J (2010) Bubble population phenomena in sonochemical reactor: I estimation of bubble size distribution and its number density with pulsed sonication—laser diffraction method. Ultrason Sonochem 17:473–479. doi: 10.1016/j.ultsonch.2009.08.018 CrossRefGoogle Scholar
  85. 85.
    Iida Y, Ashokkumar M, Tuziuti T, Kozuka T, Yasui K, Towata A, Lee J (2010) Bubble population phenomena in sonochemical reactor: II. Estimation of bubble size distribution and its number density by simple coalescence model calculation. Ultrason Sonochem 17:480–486. doi: 10.1016/j.ultsonch.2009.08.017 CrossRefGoogle Scholar
  86. 86.
    Ashokkumar M, Hall R, Mulvaney P, Grieser F (1997) Sonoluminescence from aqueous alcohol and surfactant solutions. J Phys Chem 101:10845–10850. doi: 10.1021/jp972477b CrossRefGoogle Scholar
  87. 87.
    Sunartio D, Ashokkumar M, Grieser F (2005) The influence of acoustic power on multibubble sonoluminescence in aqueous solution containing organic solutes. J Phys Chem B 109:20044–20050. doi: 10.1021/jp052747n CrossRefGoogle Scholar
  88. 88.
    Lee J, Ashokkumar M, Kentish S, Grieser F (2005) Determination of the size distribution of sonoluminescence bubbles in a pulsed acoustic field. J Am Chem Soc 127:16810–16811. doi: 10.1021/ja0566432 CrossRefGoogle Scholar
  89. 89.
    Yasui K, Lee J, Tuziuti T, Towata A, Kozuka T, Iida Y (2009) Influence of the bubble-bubble interaction on destruction of encapsulated microbubbles under ultrasound. J Acoust Soc Am 126:973–982. doi: 10.1121/1.3179677 CrossRefGoogle Scholar
  90. 90.
    Yasui K, Towata A, Tuziuti T, Kozuka T, Kato K (2011) Effect of static pressure on acoustic energy radiated by cavitation bubbles in viscous liquids under ultrasound. J Acoust Soc Am 130:3233–3242. doi: 10.1121/1.3626130 CrossRefGoogle Scholar
  91. 91.
    Yasui K, Kato K (2012) Bubble dynamics and sonoluminescence from helium or xenon in mercury and water. Phys Rev E 86:036320. doi: 10.1103/PhysRevE.86.036320. Erratum. Phys Rev E 86:069901. doi: 10.1103/PhysRevE.86.069901
  92. 92.
    Guedra M, Cornu C, Inserra C (2017) A derivation of the stable cavitation threshold accounting for bubble-bubble interactions. Ultrason Sonochem 38:168–173. doi: 10.1016/j.ultsonch.2017.03.010 CrossRefGoogle Scholar
  93. 93.
    Matula TJ, Hallaj IM, Cleveland RO, Crum LA, Moss WC, Roy RA (1998) The acoustic emissions from single-bubble sonoluminescence. J Acoust Soc Am 103:1377–1382. doi: 10.1121/1.421279 CrossRefGoogle Scholar
  94. 94.
    Yasui K, Tuziuti T, Lee J, Kozuka T, Towata A, Iida Y (2010) Numerical simulations of acoustic cavitation noise with the temporal fluctuation in the number of bubbles. Ultrason Sonochem 17:460–472. doi: 10.1016/j.ultsonch.2009.08.014 CrossRefGoogle Scholar
  95. 95.
    Hilgenfeldt S, Lohse D, Brenner MP (1996) Phase diagrams for sonoluminescing bubbles. Phys Fluids 8:2808–2826. doi: 10.1063/1.869131 CrossRefGoogle Scholar
  96. 96.
    Luther S, Sushchik M, Parlitz U, Akhatov I, Lauterborn W (2000) Is cavitation noise governed by a low-dimensional chaotic attractor? AIP Conf Proc 524:355–358CrossRefGoogle Scholar
  97. 97.
    Ashokkumar M, Hodnett M, Zeqiri B, Grieser F, Price GJ (2007) Acoustic emission spectra from 515 kHz cavitation in aqueous solutions containing surface-active solutes. J Am Chem Soc 129:2250–2258. doi: 10.1021/ja067960r CrossRefGoogle Scholar
  98. 98.
    Lauterborn W, Mettin R (2015) Acoustic cavitation: bubble dynamics in high-power ultrasonic fields. In: Gallego-Juarez JA, Graff KF (eds) Power ultrasonics—applications of high-intensity ultrasound. Woodhead Publishing, Cambridge (Elsevier, Amsterdam)Google Scholar
  99. 99.
    Manasseh R (2016) Acoustic bubbles, acoustic streaming, and cavitation microstreaming. In: Ashokkumar M, Cavalieri F, Chemat F, Okitsu K, Sambandam A, Yasui K, Zisu B (eds) Handbook of ultrasonics and sonochemistry. Springer, SingaporeGoogle Scholar
  100. 100.
    Beyer RT (1997) Nonlinear acoustics. Acoustical Society of America, New YorkGoogle Scholar
  101. 101.
    Yasui K, Izu N (2017) Effect of evaporation and condensation on a thermoacoustic engine: a Lagrangian simulation approach. J Acoust Soc Am 141:4398–4407. doi: 10.1121/1.4985385 CrossRefGoogle Scholar
  102. 102.
    Nyborg WL (1958) Acoustic streaming near a boundary. J Acoust Soc Am 30:329–339. doi: 10.1121/1.1909587 CrossRefGoogle Scholar
  103. 103.
    Elder SA (1959) Cavitation microstreaming. J Acoust Soc Am 31:54–64. doi: 10.1121/1.1907611 CrossRefGoogle Scholar
  104. 104.
    Mettin R, Cairos C (2016) Bubble dynamics and observations. In: Ashokkumar M, Cavalieri F, Chemat F, Okitsu K, Sambandam A, Yasui K, Zisu B (eds) Handbook of ultrasonics and sonochemistry. Springer, SingaporeGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.National Institute of Advanced Industrial Science and Technology (AIST)Moriyama-ku, NagoyaJapan

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