Bubble Theory and its Applications in Underwater Explosion, Marine Cavitation, and Seismic Exploration

Abstract

Bubbles play crucial roles in various fields, including naval and ocean engineering, chemical engineering, and biochemical engineering. Numerous theoretical analyses, numerical simulations, and experimental studies have been conducted to reveal the mysteries of bubble motion and its mechanisms. These efforts have significantly advanced research in bubble dynamics, where theoretical study is an efficient method for bubble motion prediction. Since Lord Rayleigh introduced the theoretical model of single-bubble motion in incompressible fluid in 1917, theoretical studies have been pivotal in understanding bubble dynamics. This study provides a comprehensive review of the development and applicability of theoretical studies in bubble dynamics using typical theoretical bubble models across different periods as a focal point and an overview of bubble theory applications in underwater explosion, marine cavitation, and seismic exploration. This study aims to serve as a reference and catalyst for further advancements in theoretical analysis and practical applications of bubble theory across marine fields.

Keywords

Bubble theory / Underwater explosion / Marine cavitation / Seismic exploration

References

[1] AllenJS, RoyRA. Dynamics of gas bubbles in viscoelastic fluids. i. linear viscoelasticity. The Journal of the Acoustical Society of America, 2000, 107: 3167-3178

[2] AllenJS, RoyRA. Dynamics of gas bubbles in viscoelastic fluids. ii. nonlinear viscoelasticity. The Journal of the Acoustical Society of America, 2000, 108: 1640-1650

[3] ApfelRE. 7. acoustic cavitation. Methods in Experimental Physics, 1981, 19: 355-411

[4] BaetenG, ChavanD, KuvshinovB, Tan KroodeF, RonenS, ChelminskiS, Chelminski. A marine seismic source with enhanced low and reduced high frequency conten. 81st EAGE Conference and Exhibition 2019, 20191-52019

[5] BarashRMIce-breaking by explosives, 1966

[6] BaileyM, KhokhlovaV, SapozhnikovO, KarglS, CrumL. Physical mechanisms of the therapeutic effect of ultrasound (a review). Acoustical Physics, 2003, 49: 369-388

[7] BehzadipourA, AzimiAH, NetoIEL. Effects of air discharge on bubble dynamics in vertically discharged bubble plumes. Chemical Engineering Science, 2023, 268: 118440

[8] BremondN, AroraM, OhlCD, LohseD. Controlled multibubble surface cavitation. Physical Review Letters, 2006, 96: 224501

[9] BenjaminTB, EllisAT. The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries. Philosophical Transactions for the Royal Society of London. Series A, Mathematical and Physical Sciences, 1966, 260(1110): 221-240

[10] BrennenCE. Cavitation in medicine. Interface Focus, 2015, 5(5): 20150022

[11] BesantWHydrostatics and hydrodynamics art. 158, 1859, London, Cambridge University Press

[12] BetneyM, TullyB, HawkerN, VentikosY. Computational modelling of the interaction of shock waves with multiple gas-filled bubbles in a liquid. Physics of Fluids, 2015, 27: 036101

[13] BeylichAE, GülhanA. On the structure of nonlinear waves in liquids with gas bubbles. Physics of Fluids A: Fluid Dynamics, 1990, 2: 1412-1428

[14] BlakeJR, GibsonD. Cavitation bubbles near boundaries. Annual Review of Fluid Mechanics, 1987, 19: 99-123

[15] BlakeJR. The kelvin impulse: application to cavitation bubble dynamics. The ANZIAM Journal, 1988, 30(2): 127-146

[16] BrujanEA, NahenK, SchmidtP, VogelA. Dynamics of laser-induced cavitation bubbles near an elastic boundary. Journal of Fluid Mechanics, 2001, 433: 251-281

[17] ChahineGL. Pressures generated by a bubble cloud collapse. Chemical Engineering Communications, 1984, 28: 355-367

[18] ChahineG, PerdueT, TuckerCInteraction between an underwater explosion bubble and a solid submerged structure, 198889001-1

[19] ChelminskiS, WatsonLM, RonenS. Research note: Low-frequency pneumatic seismic sources. Geophysical Prospecting, 2019, 67: 1547-1556

[20] ChelminskiS, ChelminskiF, SteelG, RonenS, BaetenG, ChenTR, HuntK, KryvohuzM, KuehlH, KuvshinovB, MacintyreH, MaDonaldM, PerroneF, PlessixR-É, TangZ, ten KroodF. Sea trial of a low-frequency enhanced pneumatic source. First International Meeting for Applied Geoscience & Energy Expanded Abstracts Society of Exploration Geophysicists, 2021

[21] ChenH, QuanH, YuG, LiW, LiuY. A review of air-gun seismic source theory and technology. Physical Exploration Equipment, 2008, 18: 211

[22] Chen SQ, Hu JF, Zhang JQ (1981) Determination of residual ammonium in solid catalysts by ammonia gas gap electrode method. Petrochemicals 9

[23] ChenR, LiangW, ZhengJ, LiXY, LinYL. Experimental study on the interaction of three linearly arranged spark bubbles with controlled phase differences. Physics of Fluids, 2022, 34: 037105

[24] ChenYApplication of Cavitation Gain on Super-Vacuum Weapons, 2011, Harbin, Harbin Engineering University

[25] ColeRH, WellerR. Underwater explosions. Maryland: American Institute of Physics, 1948, 1(6): 35

[26] CoussiosCC, RoyRA. Applications of acoustics and cavitation to noninvasive therapy and drug delivery. Annual Review of Fluid Mechanics, 2008, 40: 395-420

[27] CoxE, PearsonA, BlakeJ, OttoS. Comparison of methods for modelling the behaviour of bubbles produced by marine seismic airguns. Geophysical Prospecting, 2004, 52(5): 451-477

[28] CuiP, ZhangAM, WangS, KhooBC. Ice breaking by a collapsing bubble. Journal of Fluid Mechanics, 2018, 84: 287-309

[29] CunhaF, AlbernazD. Oscillatory motion of a spherical bubble in a non-newtonian fluid. Journal of Non-Newtonian fluid mechanics, 2013, 191: 35-44

[30] De GraafK, BrandnerP, PenesisI. Bubble dynamics of a seismic airgun. Experimental Thermal and Fluid Science, 2014, 55: 228-238

[31] De GraafK, PenesisI, BrandnerP. Modelling of seismic airgun bubble dynamics and pressure field using the gilmore equation with additional damping factors. Ocean Engineering, 2014, 76: 32-39

[32] De GraafK, BrandnerP, PenesisI. The pressure field generated by a seismic airgun. Experimental Thermal and Fluid Science, 2014, 55: 239-249

[33] DoinikovAA. Translational motion of two interacting bubbles in a strong acoustic field. Physical Review E, 2001, 64: 026301

[34] DolletB, MarmottantP, GarbinV. Bubble dynamics in soft and biological matter. Annual Review of Fluid Mechanics, 2019, 51: 331-355

[35] DuY, XieZG, LiG, ZhaoYC, LiuWT. Numerical simulation analysis of variety linear jet penetrating ice. Yellow River, 2021, 43(12): 53-56

[36] DuZ, ZhangL, ChenY, HuaH. Scaling experimental study on the protection mechanism of foam cover layer against underwater explosive bubble jet. Applied Mathematics and Mechanics, 2022, 43: 569-576

[37] DuanRZ, CaoYF, FengZW. Acoustic emission process during bubble bursting in free space. Journal of Applied Acoustics, 2024, 43(1): 204-212

[38] DuclauxV, CailleF, DuezC, YbertC, BocquetL, ClanetC. Dynamics of transient cavities. Journal of Fluid Mechanics, 2007, 591: 1-19

[39] EpsteinD, KellerJB. Expansion and contraction of planar, cylindrical, and spherical underwater gas bubbles. The Journal of the Acoustical Society of America, 1972, 52: 975-980

[40] FengZ, LealL. Nonlinear bubble dynamics. Annual Review of Fluid Mechanics, 1997, 29: 201-243

[41] FoglerS. The influence of reacting gases on the motion of collapsing cavities. Chemical Engineering Science, 1969, 24: 1043-1054

[42] FongSW, AdhikariD, KlaseboerE, KhooBC. Interactions of multiple spark-generated bubbles with phase differences. Experiments in Fluids, 2009, 46: 705-724

[43] FoglerHS, GoddardJD. Collapse of spherical cavities in viscoelastic fluids. Physics of Fluids, 1970, 13: 1135-1141

[44] FlintEB, SuslickKS. The temperature of cavitation. Science, 1991, 253: 1397-1399

[45] FujikawaS, AkamatsuT. Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid. Journal of Fluid Mechanics, 1980, 97(3): 481-512

[46] FujikawaS, TakahiraH. A theoretical study on the interaction between two spherical bubbles and radiated pressure waves in a liquid. Acta Acustica United with Acustica, 1986, 61(3): 188-199

[47] GeL, ZhangAM, ZhangZY, WangSP. Numerical simulation of compressible multifluid flows using an adaptive positivity-preserving rkdg-gfm approach. International Journal for Numerical Methods in Fluids, 2019, 91: 615-636

[48] GeersTL, HunterKS. An integrated wave-effects model for an underwater explosion bubble. The Journal of the Acoustical Society of America, 2002, 111(4): 1584-1601

[49] GeersT, ZhangP. Doubly asymptotic approximations for submerged structures with internal fluid volumes: formulation. Journal of Applied Mechanics, 1994, 61(4): 893-899

[50] GibsonD, BlakeJR. The growth and collapse of bubbles near deformable surfaces. Applied Scientific Research, 1982, 38: 215-224

[51] GilmoreFRThe growth or collapse of a spherical bubble in a viscous compressible liquid Vol. 26, 1952, Pasadena, CA, California Institute of Technology2626-4

[52] GisbonD, BlakeJGrowth and collapse of cavitation bubbles near flexible boundarie, 1980, Australia, Institution of Engineers: 283-286

[53] HanR, ZhangAM, TanS, LiS. Interaction of cavitation bubbles with the interface of two immiscible fluids on multiple time scales. Journal of Fluid Mechanics, 2022, 932: A8

[54] HanW, XuZT, HaoYJ, RenJL, LiWX, GuZY. Study on the dynamic characteristics of the impact loads in a near-wall double-cavitation bubble collapse. Processes, 2023, 11(6): 1805

[55] HanR, TaoL, ZhangAM, LiS. Experimental and numerical investigation of the dynamics of a coalesced oscillating bubble near a free surface. Ocean Engineering, 2019, 186: 106096

[56] HaoY, ProsperettiA. The effect of viscosity on the spherical stability of oscillating gas bubbles. Physics of Fluids, 1999, 11: 1309-1317

[57] HerringCTheory of the pulsations of the gas bubble produced by an underwater explosion, 1941, New York, Columbia Univ. Division of National Defense Research

[58] HicksAEffect of bubble migration on explosion-induced whipping in ships, 19703301

[59] HigdonCE. Water barrier ship self defense lethality. Naval Engineers Journal, 2000, 112: 121-135

[60] HiroseT, OkuyamaM. Mechanics on the cavitation produced by ultrasonics (ii) conditions for cavitation and stationary cavitation. The Journal of the Acoustical Society of Japan, 1957, 13(1): 14-20

[61] HongTYCharacterization of Near-Wall Microbubble Collapse in Ultrasonic Field, 2020, Hangzhou, China Jiliang University

[62] HowkinsS. Measurements of the resonant frequency of a bubble near a rigid boundary. The Journal of the Acoustical Society of America, 1965, 37: 504-508

[63] HuangXT, SunPM, PengYX, LiuNN, XiongZM, QiuYY. Numerical simulation of underwater explosion shock wave and bubble motion based on a novel axisymmetric meshless method. Journal of Tongji University (Natural Science Edition), 2023, 51: 818-826

[64] IchiharaM, OhkunitaniH, IdaY, KamedaM. Dynamics of bubble oscillation and wave propagation in viscoelastic liquids. Journal of Volcanology and Geothermal Research, 2004, 129(1–3): 37-60

[65] Jiménez FernándezJ, CrespoA. Bubble oscillation and inertial cavitation in viscoelastic fluids. Ultrasonics, 2005, 43(8): 643-651

[66] JinLA, HeSY, ZhangZY, YuanZJ. Characterization of bubble uplift in water under the influence of heat and mass transfer coupling. Journal of Engineering Thermophysics, 2019, 40: 1143-1150

[67] JinWG. Composition and application of offshore airgun vibriosis system. Science, Technology and Enterprise, 2015, 1: 197

[68] John GambleK, HansABThe pressure wave produced by an underwater explosion, 1942, New York, Columbia Univ. Division of National Defense Research

[69] JuL, SuYM, ZhaoJX, LiuYB, CuiT. Steady interaction numerical simulation of cavitating turbulent flow between ship hull and propeller. Chuan Bo Li Xue/Journal of Ship Mechanics, 2012, 16: 593-602

[70] KellerJB, MiksisM. Bubble oscillations of large amplitude. The Journal of the Acoustical Society of America, 1980, 68: 628-633

[71] KellerJB, KolodnerII. Damping of underwater explosion bubble oscillations. Journal of Applied Physics, 1956, 27(10): 1152-1161

[72] KimC. Collapse of spherical bubbles in maxwell fluids. Journal of Non-Newtonian Fluid Mechanics, 1994, 55: 37-58

[73] KlaseboerE, HungKC, WangC, WangCW, KhooBC, BoyceP, DebonoS, CharlierH. Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure. Journal of Fluid Mechanics, 2005, 537: 387-413

[74] KlaseboerE, KhooBC, HungKC. Dynamics of an oscillating bubble near a floating structure. Journal of Fluids and Structures, 2005, 21: 395-412

[75] KodamaT, TakayamaK, NagayasuN. The dynamics of two air bubbles loaded by an underwater shock wave. Journal of Applied Physics, 1996, 80: 5587-5592

[76] KudryashovNA, SinelshchikovDI. Analytical solutions of the rayleigh equation for empty and gas-filled bubble. Journal of Physics A: Mathematical and Theoretical, 2014, 47(40): 405202

[77] LandrøM, SollieR. Source signature determination by inversion. Geophysics, 1992, 57(12): 1633-1640

[78] LauterbornW. Numerical investigation of nonlinear oscillations of gas bubbles in liquids. The Journal of the Acoustical Society of America, 1976, 59: 283-293

[79] LauterbornW, KurzT. Physics of bubble oscillations. Reports on Progress in Physics, 2010, 73: 106501

[80] LawsR, HattonL, HaartsenM. Computer Modelling of Clustured Airguns. First Break, 1990, 8: 331-338

[81] LezziA, ProsperettiA. Bubble dynamics in a compressible liqui. part 2. second-order theory. Journal of Fluid Mechanics, 1987, 185: 289-321

[82] LiangJF, ChenWZ, ShaoWH, QiSB. Aspherical oscillation of two interacting bubbles in an ultrasound field. Chinese Physics Letters, 2012, 29(7): 074701

[83] LiS, ProsperettiA, van der MeerD. Dynamics of a toroidal bubble on a cylinder surface with an application to geophysical exploration. International Journal of Multiphase Flow, 2020, 129: 103335

[84] LiSM, LiuXB, TangH. Multi-cycle dynamics of underwater explosion bubbles: An experimental investigation. Physics of Fluids, 2024, 36: 093309

[85] LiSM, ZhangAM, CuiP, LiS, LiuYL. Vertically neutral collapse of a pulsating bubble at the corner of a free surface and a rigid wall. Journal of Fluid Mechanics, 2023, 962: A28

[86] LiS, ZhangAM, HanR. Fluid field pressure and velocity induced during multi-periodic motion of bubbles. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46: 533-543

[87] LiS, van der MeerD, ZhangAM, ProsperettiA, LohseD. Modelling large scale airgunbubble dynamics with highly non-spherical features. International Journal of Multiphase Flow, 2020, 122: 103143

[88] LiS, ZhangAM, HanR, CuiP. Experimental and numerical study of two underwater explosion bubbles: Coalescence, fragmentation and shock wave emission. Ocean Engineering, 2019, 190: 106414

[89] LiS, SaadeY, van der MeerD, LohseD. Comparison of boundary integral and volume-of-fluid methods for compressible bubble dynamics. International Journal of Multiphase Flow, 2021, 145: 103834

[90] LiS, KhooBC, ZhangAM, WangS. Bubble-sphere interaction beneath a free surface. Ocean Engineering, 2018, 169: 469-483

[91] LiHJ, GaoB, LinYF, SongDQ, GaoZH. Excitation mechanism and design of low-frequency airgun. Physical Exploration Equipment, 2022, 32: 300-305

[92] LiHJ, GaoB, SongDQ, LiXL, ZhaoQ. Current status and development direction of marine low-frequency seismic sources. Proceedings of the 2021 Symposium on Physical Exploration Technology of the Chinese Petroleum Society, 20211254-1257

[93] LiMK, WangSP, ZhangS, SagarH. Experimental study of underwater explosions below a free surface: Bubble dynamics and pressure wave emission. Physics of Fluids, 2023, 35: 083313

[94] LiYJ, ZhangXC, WuYS, ChenQF. Whip-like motion of ship hull excited by underwater explosion bubbles. China Shipbuilding, 2001, 42: 1-7

[95] LiGF, CaoMQ, ChenHL, NiCZ, GuoSL. Influence of muzzle throttling and thermal conduction on sub-waves of gas lance for offshore exploration. Specialty Hydrocarbon Reservoirs, 2011, 18: 1

[96] LiuJHTheory and application of non-contact underwater explosion dynamics for ships, 2002, Wuxi, China Ship Scientific Research Center

[97] LiuNN, ZhangA, CuiP, WangSP, LiS. Interaction of two out-of-phase underwater explosion bubbles. Physics of Fluids, 2021, 33(10): 106103

[98] LiuHB, LiHJ, QuanHY, YuGP, LiuYY. Development and application of ‘seal’ series of shallow water air-gun seismic vessel. Petroleum Instruments, 2007, 21: 10-12

[99] LiuM, LiuG, LamK, ZongZ. Smoothed particle hydrodynamics for numerical simulation of underwater explosion. Computational mechanics, 2003, 30: 106-118

[100] Longuet HigginsMS. Monopole emission of sound by asymmetric bubble oscillation. part 1. normal modes. Journal of Fluid Mechanics, 1989, 201: 525-541

[101] Longuet HigginsMS. Monopole emission of sound by asymmetric bubble oscillation. part 2. an initial-value problem. Journal of Fluid Mechanics, 1989, 201: 543-565

[102] Longuet HigginsMS, KermanBR, LundeK. The release of air bubbles from an underwater nozzle. Journal of Fluid Mechanics, 1991, 230: 365-390

[103] LvK, ZouJJ, ChenY, YanS, LiS, ZhangAM. Study on the interaction and jet enhancement effect of two out-of-phase bubbles near a rigid boundary. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(8): 1605-1617

[104] MellorMBreaking ice with explosives, 198282-40

[105] MinnaertM. Xvi. on musical air-bubbles and the sounds of running water. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1933, 16: 235-248

[106] MoriokaM. Theory of natural frequencies of two pulsating bubbles in infinite liquid. Journal of Nuclear Science and Technology, 1974, 11(12): 554-560

[107] NasibullaevaES, AkhatovI. Bubble cluster dynamics in an acoustic field. The Journal of the Acoustical Society of America, 2013, 133: 3727-3738

[108] NaudeCF, EllisATOn the mechanism of cavitation damage by nonhemispherical cavities collapsing in contact with a solid boundary, 1960, Pasadena, Hydrodynamics LaboratoryE-108.7

[109] NaudeJ, MendezF. Periodic and chaotic acoustic oscillations of a bubble gas immersed in an upper convective maxwell fluid. Journal of Non-Newtonian Fluid Mechanics, 2008, 155(1–2): 30-38

[110] NeppirasE, NoltingkB. Cavitation produced by ultrasonics: theoretical conditions for the onset of cavitation. Proceedings of the Physical Society. Section B, 1951, 64(12): 1032

[111] NeppirasEA. Acoustic cavitation. Physics Reports, 1980, 61: 159-251

[112] NiBY, GuoPJ, XueYZ. Experimental study on the mechanism of bubble-assisted icebreaking system in an ice-water tank. Journal of Harbin Engineering University, 2020, 41: 777-783

[113] NikolaevSCutting sea ice by directed blasting, 19731971

[114] NoltingkBE, NeppirasEA. Cavitation produced by ultrasonics. Proceedings of the Physical Society. Section B, 1950, 63(9): 674

[115] ParsonsCA, CookSS. Experiments on the compression of liquids at high pressures. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1911, 85(579): 332-348

[116] ParsonsCA, CookSS. Investigations into the causes of corrosion or erosion of propellers. Journal of the American Society for Naval Engineers, 1919, 31: 536-541

[117] Pan H, Yin QZ, Gao WS (2008) Influence of air gap size on partial discharge process in solid insulation. High Voltage Technology 39–42

[118] PhilippA, LauterbornW. Cavitation erosion by single laser-produced bubbles. Journal of Fluid Mechanics, 1998, 361: 75-116

[119] PlessetMS, ChapmanRB. Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary. Journal of Fluid Mechanics, 1971, 47: 283-290

[120] PlessetMS, ZwickSA. The growth of vapor bubbles in superheated liquids. Journal of Applied Physics, 1994, 25: 493-500

[121] PlessetMDaviesrBubble dynamics in cavitation in realliquids, 1964, Cambridge, Cambridge University Press

[122] PlessetMS. The dynamics of cavitation bubbles. Journal of Applied Mechanics, 1949, 16(3): 277-282

[123] ProsperettiA. Viscous effects on perturbed spherical flows. Quarterly of Applied Mathematics, 1977, 34: 339-352

[124] ProsperettiA, LezziA. Bubble dynamics in a compressible liqui. part 1. first-order theory. Journal of Fluid Mechanics, 1986, 168: 457-478

[125] PumphreyHC, ElmorePA. The entrainment of bubbles by drop impacts. Journal of Fluid Mechanics, 1990, 220: 539-567

[126] QiTC, WuSY, ZhangHX. Study on the noise characteristics of cavitation propeller. Equipment Manufacturing Technology, 2022, 4: 4-8

[127] QianZW. Large-amplitude vibration of bubbles and its application to acoustic luminescence and cavitation fusion. Physics, 2004, 33(4): 266-271

[128] RambarzinF, Shervani TabarM, Taeibi RahniM. Numerical study on a bubble dynamic generated by ultrasound waves in liquid-saturated porous media. Mechanics, 2016, 22: 504-509

[129] RattrayMPerturbation effects in cavitation bubble dynamics, 1951, Los Angeles, California Institute of Technology

[130] RayleighL. VIII. On the pressure developed in a liquid during the collapse of a spherical cavity. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1917, 34(200): 94-98

[131] ReuterF, ZengQ, OhlCD. The Rayleigh prolongation factor at small bubble to wall stand-off distances. Journal of Fluid Mechanics, 2022, 944: id.A11

[132] RonenS, ChelminskiS. Tuned pulse source-a new low frequency seismic source. 2017 SEG International Exposition and Annual Meeting, 2017, Houston, SEGSEG-2017-W16-04

[133] Rossell’oJM, OhlCD. On-demand bulk nanobubble generation through pulsed laser illumination. Physical Review Letters, 2021, 127(4): 044502

[134] RungsiyaphornratS, KlaseboerE, KhooB, YeoK. The merging of two gaseous bubbles with an application to underwater explosions. Computers & Fluids, 2003, 32(8): 1049-1074

[135] SafarM. Efficient design of air-gun arrays. Geophysical Prospecting, 1976, 24: 773-787

[136] SagarHJ, HankeS, UnderbergM, FengCJ, el MonctarO, KaiserSA. Experimental and numerical investigation of damage on an aluminum surface by single-bubble cavitation. Materials Performance and Characterization, 2018, 7(5): 985-1003

[137] SagarHJ, el MoctarO. Dynamics of a cavitation bubble near a solid surface and the induced damage. Journal of Fluids and Structures, 2020, 92: 102799

[138] Schulze GattermannR. Physical aspects of the “airpulser” as a seismic energy source. Geophysical Prospecting, 1972, 20(1): 155-192

[139] SchmidmayerK, BryngelsonSH, ColoniusT. An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics. Journal of Computational Physics, 2020, 402: 109080

[140] ShenY, YasuiK, ZhuT, AshokkumarM. A model for the effect of bulk liquid viscosity on cavitation bubble dynamics. Physical Chemistry Chemical Physics, 2017, 19(13): 20635-20640

[141] ShiZF, LinSY. Application of ultrasonic cavitation in medical treatment. Technical Acoustics, 2009, 28(2): 79-80

[142] ShimaA, TomitaY. The behavior of a spherical bubble near a solid wall in a compressible liquid. Ing. Arch, 1981, 51: 243-255

[143] ShimaA. The natural frequency of a bubble oscillating in a viscous compressible liquid. Journal of Fluids Engineering, 1970, 92(3): 555-561

[144] Shervani TabarMT, FarzanehB, AhrabiR, RazaviSE. Numerical study on the impulsive growth of a gaseous plug inside a cylindrical vein with compliant coating. BioImpacts, 2018, 8(4): 271-279

[145] ShimaA. The natural frequencies of two spherical bubbles oscillating in water. Journal of Fluids Engineering, 1971, 93(3): 426-431

[146] SolimanW, NakanoT, TakadaN, SasakiK. Modification of rayleigh-plesset theory for reproducing dynamics of cavitation bubbles in liquid-phase laser ablation. Japanese Journal of Applied Physics, 2010, 49: 116202

[147] SohW. An energy approach to cavitation bubbles near compliant surfaces. Applied Mathematical Modelling, 1992, 16: 263-268

[148] SunX, LiuJT, JiL, WangGC, ZhaoS, YoonJY, ChenSY. A review on hydrodynamic cavitation disinfection: The current state of knowledge. Science of the Total Environment, 2020, 737: 139606

[149] SunPN, LiYB, MingFR. Smooth particle hydrodynamics simulation of the kinematic properties of freely floating bubbles. Acta Physica Sinica, 2015, 64: 174701

[150] SunX, LiuS, ManickamS, TaoY, YoonJY, XuanXX. Intensification of biodiesel production by hydrodynamic cavitation: A critical review. Renewable and Sustainable Energy Reviews, 2023, 179: 113277

[151] StrasbergM. The pulsation frequency of nonspherical gas bubbles in liquids. The Journal of the Acoustical Society of America, 1953, 25: 536-537

[152] SzeriAJ, StoreyBD, PearsonA, BlakeJR. Heat and mass transfer during the violent collapse of nonspherical bubbles. Physics of Fluids, 2003, 15: 2576-2586

[153] TanasawaI, YangWJ. Dynamic behavior of a gas bubble in viscoelastic liquids. Journal of Applied Physics, 1970, 41: 4526-4531

[154] TangH, LiuYL, FengJT, JuXY, ZhangAM. Euler finite element numerical simulation of the dynamics of heterogeneous bubbles in underwater explosions. Applied Mathematics and Mechanics, 2023, 44(8): 895-908

[155] TomitaY, ShimaA, OhnoT. Collapse of multiple gas bubbles by a shock wave and induced impulsive pressure. Journal of Applied Physics, 1984, 56: 125-131

[156] TrillingL. The collapse and rebound of a gas bubble. Journal of Applied Physics, 1952, 23: 14-17

[157] Van der KleyJThe use of explosives for clearing ice, 19657

[158] VenerusDC, YalaN, BernsteinB. Analysis of diffusion-induced bubble growth in viscoelastic liquids. Journal of Non-Newtonian Fluid Mechanics, 1998, 75(1): 55-75

[159] WangQX, YeoKS, KhooBC, LamKY. Nonlinear interaction between gas bubble and free surface. Computers & Fluids, 1996, 25(7): 607-628

[160] WangQ, YeoK, KhooB, LamK. Strong interaction between a buoyancy bubble and a free surface. Theoretical and Computational Fluid Dynamics, 1996, 8: 73-88

[161] WangSP, WangQ, ZhangAM, StrideE. Experimental observations of the behaviour of a bubble inside a circular rigid tube. International Journal of Multiphase Flow, 2019, 121: 103096

[162] WangCH, MoRY, HuJ, ChenS. Coupled vibrations of bubbles within a spherical bubble cluster. Acta Physica Sinica, 2015, 64: 234301

[163] WangYJ, ZhangSD, LiH, ZhouHB. Uncertain parameters of the Jones-Wilkins-Lee equation of state for explosive blast products. Acta Physica Sinica, 2016, 65(10): 241-246

[164] WehnerD, LandrøM, AmundsenL. On low frequencies emitted by air guns at very shallow depths—an experimental study. Geophysics, 2019, 84(5): 61-71

[165] WuXY, LiangJF. Translation and nonspherical oscillation of single bubble in ultrasound field. Acta Physica Sinica, 2021, 70(18): 184301

[166] WangSS, LiM, MaF. Dynamics of the interaction between explosion bubble and free surface. Acta Physica Sinica, 2014, 63(19): 194703

[167] WangPH. Application of cavitation jet in pipeline cleaning. Electric Power Science and Engineering, 2002, 18: 21-24

[168] WangWMApplication of Hydro-Cavitation Technology to Inactivate Algae in Eutrophic Water Bodies, 2009, Yangzhou, Yangzhou University

[169] WebsterKGInvestigation of close proximity underwater explosion effects on a ship-like structure using the multi-material arbitrary Lagrangian Eulerian finite element method, 2007, Blacksburg, Virginia Tech

[170] WhiteFM, XueHFluid mechanics, 2006, New York, McGraw Hill

[171] WuAF, GouXL, LiP. Ultrasonic degradation mechanism of wastewater and numerical simulation of cavitation bubble motion process. Electromechanical Equipment, 2008, 25: 37-40

[172] XuRZ, HaoT, LiSM, WangSP. Study on the influence of migration character parameters for underwater explosion bubbles based on the unified equation for bubble dynamics. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(9): 2544-2554

[173] YangGL, YangJ, TangJH, LiuZ. Research and application of ultrasound-targeted microbubble destruction technology in the era of precision medicine. Medical Review, 2021, 27: 4939-4945

[174] YangWJ, YehHC. Theoretical study of bubble dynamics in purely viscous fluids. AIChE Journal, 1966, 12: 927-931

[175] YasuiK. Effect of non-equilibrium evaporation and condensation on bubble dynamics near the sonoluminescence threshold. Ultrasonics, 1998, 36: 575-580

[176] ZhaoD, XuR, ZhangS, LiS. Improved model for high-pressure airgun bubble dynamics and its application. Chinese Journal of Geophysics, 2024, 67(3): 1108-1119

[177] ZhangA, SunP, MingF. An SPH modeling of bubble rising and coalescing in three dimensions. Computer Methods in Applied Mechanics and Engineering, 2015, 294: 189-209

[178] ZhangAM, YangWS, HuangC, MingFR. Numerical simulation of column charge underwater explosion based on sph and bem combination. Computers & Fluids, 2013, 71: 169-178

[179] ZhangAM, NiBY. Influences of different forces on the bubble entrainment into a stationary gaussian vortex. Science China Physics, Mechanics and Astronomy, 2013, 56: 2162-2169

[180] ZhangAM, WangSP, HuangC, WangB. Influences of initial and boundary conditions on underwater explosion bubble dynamics. European Journal of Mechanics-B/Fluids, 2013, 42: 69-91

[181] ZhangAM, CuiP, CuiJ, WangQX. Experimental study on bubble dynamics subject to buoyancy. Journal of Fluid Mechanics, 2015, 776: 137-160

[182] ZhangA, LiS, CuiJ. Study on splitting of a toroidal bubble near a rigid boundary. Physics of Fluids, 2015, 27: 062102

[183] ZhangAM, MingFR, LiuYL, LiS, WangSP. Review of researche on underwater explosion related to load characteristics and ship damage and protection. Chinese Journal of Ship Research, 2023, 18(3): 139-154

[184] ZhangY, LiuL, WangJ, LiH, TangK. Damage characteristics of underwater explosion shock wave and bubble load on typical cylindrical shell Structure. Acta Armamentarii, 2023, 44: 345-359

[185] ZhangAM, LiSM, CuiP, LiS, LiuYL. A unified theory for bubble dynamics. Physics of Fluids, 2023, 35: 033323

[186] ZhangAM, LiSM, CuiP, LiS, LiuYL. Theoretical study on bubble dynamics under hybrid-boundary and multi-bubble conditions using the unified equation. Science China Physics, Mechanics & Astronomy, 2023, 66: 124711

[187] ZhangAM, LiSM, CuiP, LiS, LiuYL. Interactions between a central bubble and a surrounding bubble cluster. Theoretical and Applied Mechanics Letters, 2023, 13(3): 100438

[188] ZhangGP, WangHS, WangQP, LinYZ, ZhangSJ, JinX. The simulation of large volume air-gun excited in land area and analysis of its influence factors. Journal of Geodesy and Geodynamics, 2019, 39(12): 1243-1248

[189] ZhongX, EshraghiJ, VlachosP, DabiriS, ArdekaniAM. A model for a laser-induced cavitation bubble. International Journal of Multiphase Flow, 2020, 132: 103433

[190] ZhangY, ChenT, LiuS. Critical issues in the study of ultrasonic cavitation vacuoles as gene or drug carriers. Journal of Biomedical Engineering, 2009, 26: 1129

[191] ZhangZ, LiangX, XuW. Numerical analysis of effect of different charge position on ice blasting. Blasting, 2015, 32: 118-127

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