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Acoustic cavitation bubble and its production extreme physics such as shockwaves and micro-jets on a solid wall have attracted great interest in the application of ultrasound (e.g., ultrasonic medical, ultrasonic cleaning, and ultrasonic machining). However, the prediction and control of micro-jets induced by ultrasonic field have been a very challenging work, due to the complicated mechanisms of collapsing of cavitation bubbles. In order to determine the interaction of micro-jet with the key parameters that influence the acoustic cavitation, the dynamics of bubble growth and collapse near a rigid boundary in water is investigated. Using the method of mirror image, a revised bubble dynamics equation in radial oscillation for a bubble near a plane rigid wall is derived from the double-bubble equation (the Doinikov equation). In the present equation, the gas inside the bubble is assumed to be the van der Waals gas, and the weak compressibility of the liquid is also assumed. The revised equation is then employed to simulate numerically the dynamical behaviors of a bubble, using the fourth-order Runge-Kutta method with variable step size adaptive control. Numerical simulations of the motion characteristics and collapse velocities of a bubble near a rigid boundary or a free boundary have been performed, under various conditions of initial bubble radius, spacing between the center of the bubble and the wall, acoustic pressure and ultrasonic frequency, in order to explain the effects of these key parameters on the acoustic cavitation intensity. It is shown that, compared with free boundary, the effect of rigid boundary on the bubble plays a significant role in suppressing the bubble oscillation. The intensity of bubble collapsing is reduced as the increase of the initial bubble radius and ultrasonic frequency, and increased by enlarging the spacing between the center of the bubble and the wall. There exists an optimal acoustic pressure (almost 3.5 times bigger than the ambient pressure), at which the collapse of a bubble near a rigid wall can be the most violent. Furthermore, the relationship between the collapse velocity of a bubble near a rigid boundary and its micro-jet is described. Results demonstrate that the velocity of micro-jet is dependent on that of bubble collapse, and it can be controlled by adjusting the velocity of bubble collapse indirectly. Calculation results of the micro-jet in this paper are compared with some numerical and experimental results given in the literature and good apparent trends between them are obtained. These results will give important implications for further understanding the dynamics of cavitation bubble on a solid wall induced by the ultrasonic field and its different requirements in engineering applications.
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Keywords:
- ultrasound field /
- cavitation bubble /
- rigid wall /
- micro-jet
[1] Benjamin T B, Ellis A T 1966 Phil.Trans. R. Soc. Lond. A 260 221
[2] Brujan E A, Matsumoto Y 2012 Microfluid Nanofluid 13 957
[3] Brujan E A, Ikeda T, Matsumoto Y 2008 Exp. Thermal Fluid Sci. 32 1188
[4] Vignoli L L, Barros A L, Thom R C, et al. 2013 Eur. J. Phys. 34 679
[5] Merouani S, Hamdaoui O, Rezgui Y, et al. 2014 Ultrasonic 54 227
[6] Wang Y C, Yao M C 2013 Ultrason. Sonochem. 20 565
[7] Zarepour H, Yeo S H 2012 Int. J. Mach. Tools Manufact. 62 13
[8] Tsuboi R, Kakinuma Y, Aoyama T, et al. 2012 Procedia CIRP 1 342
[9] Grossmann S, Hilgenfeldt S, Lohse D 1997 J. Acoust. Soc. Am. 102 1223
[10] Behnia S, Sojahrood A J, Soltanpoor W, et al. 2009 Ultrason. Sonochem. 16 502
[11] Mahdi M, Ebrahimi R, Sham M 2011 Phys. Lett. A 375 2348
[12] Doinikov A A, Zhao S K, Dayton P A 2009 Ultrasonics 49 195
[13] Mettin R, Doinikov A A 2009 Appl. Acoust. 70 1330
[14] Wang L, Tu J, Guo X S, et al. 2014 Chin. Phys. B 23 124302
[15] Wang C H 2010 Ph. D. Dissertation (Xi'an: Shaanxi Normal University) (in Chinese) [王成会 2010 博士学位论文 (西安: 陕西师范大学)]
[16] Doinikov A A 2001 Phys. Rev. E 64 026301
[17] Wang C H, Cheng J C 2013 Sci. China: Phys. Mech. Astron. 56 1246
[18] Ida M 2009 Phys. Rev. E 79 016307
[19] Li F C, Cai J, Huai X L, Liu B 2013 J. Thermal Sci. 22 242
[20] Shen Z Z, Lin S Y 2011 Acta Phys. Sin 60 104302 (in Chinese) [沈壮志, 林书玉 2011 60 104302]
[21] Qian M L, Cheng Q, Ge C Y 2002 Acta Acustica 27 289 (in Chinese) [钱梦騄, 程茜, 葛曹燕 2002 声学学报 27 289]
[22] Hegedűs F, Klapcsik K 2015 Ultrason. Sonochem. 27 153
[23] Chen H S, Li J, Chen D, Wang J D 2008 Wear 265 692
[24] Chen X G, Yan J C, Gao F, et al. 2013 Ultrason. Sonochem. 20 144
[25] Wang X F 2009 Cavitating and Supercavitating Flows Theory and Applications (Beijing: National Defence Industry Press) p29 (in Chinese) [王献孚 2009 空化泡和超空化泡流动理论及应用 (北京: 国防工业出版社) 第29页]
[26] Blake J R, Gibson D C 1987 Ann. Rev. Fluid Mech. 19 99
[27] Ohl C, Arora M, Ikink R, et al. 2006 Biophys. J. 91 4285
[28] Tzanakis I, Hadfield M, Henshaw I 2011 Exp. Thermal Fluid Sci. 35 1544
[29] Rayleigh L 1917 Phil. Mag. 34 94
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[1] Benjamin T B, Ellis A T 1966 Phil.Trans. R. Soc. Lond. A 260 221
[2] Brujan E A, Matsumoto Y 2012 Microfluid Nanofluid 13 957
[3] Brujan E A, Ikeda T, Matsumoto Y 2008 Exp. Thermal Fluid Sci. 32 1188
[4] Vignoli L L, Barros A L, Thom R C, et al. 2013 Eur. J. Phys. 34 679
[5] Merouani S, Hamdaoui O, Rezgui Y, et al. 2014 Ultrasonic 54 227
[6] Wang Y C, Yao M C 2013 Ultrason. Sonochem. 20 565
[7] Zarepour H, Yeo S H 2012 Int. J. Mach. Tools Manufact. 62 13
[8] Tsuboi R, Kakinuma Y, Aoyama T, et al. 2012 Procedia CIRP 1 342
[9] Grossmann S, Hilgenfeldt S, Lohse D 1997 J. Acoust. Soc. Am. 102 1223
[10] Behnia S, Sojahrood A J, Soltanpoor W, et al. 2009 Ultrason. Sonochem. 16 502
[11] Mahdi M, Ebrahimi R, Sham M 2011 Phys. Lett. A 375 2348
[12] Doinikov A A, Zhao S K, Dayton P A 2009 Ultrasonics 49 195
[13] Mettin R, Doinikov A A 2009 Appl. Acoust. 70 1330
[14] Wang L, Tu J, Guo X S, et al. 2014 Chin. Phys. B 23 124302
[15] Wang C H 2010 Ph. D. Dissertation (Xi'an: Shaanxi Normal University) (in Chinese) [王成会 2010 博士学位论文 (西安: 陕西师范大学)]
[16] Doinikov A A 2001 Phys. Rev. E 64 026301
[17] Wang C H, Cheng J C 2013 Sci. China: Phys. Mech. Astron. 56 1246
[18] Ida M 2009 Phys. Rev. E 79 016307
[19] Li F C, Cai J, Huai X L, Liu B 2013 J. Thermal Sci. 22 242
[20] Shen Z Z, Lin S Y 2011 Acta Phys. Sin 60 104302 (in Chinese) [沈壮志, 林书玉 2011 60 104302]
[21] Qian M L, Cheng Q, Ge C Y 2002 Acta Acustica 27 289 (in Chinese) [钱梦騄, 程茜, 葛曹燕 2002 声学学报 27 289]
[22] Hegedűs F, Klapcsik K 2015 Ultrason. Sonochem. 27 153
[23] Chen H S, Li J, Chen D, Wang J D 2008 Wear 265 692
[24] Chen X G, Yan J C, Gao F, et al. 2013 Ultrason. Sonochem. 20 144
[25] Wang X F 2009 Cavitating and Supercavitating Flows Theory and Applications (Beijing: National Defence Industry Press) p29 (in Chinese) [王献孚 2009 空化泡和超空化泡流动理论及应用 (北京: 国防工业出版社) 第29页]
[26] Blake J R, Gibson D C 1987 Ann. Rev. Fluid Mech. 19 99
[27] Ohl C, Arora M, Ikink R, et al. 2006 Biophys. J. 91 4285
[28] Tzanakis I, Hadfield M, Henshaw I 2011 Exp. Thermal Fluid Sci. 35 1544
[29] Rayleigh L 1917 Phil. Mag. 34 94
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