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When the distances between bubbles are small enough, the pressure acting on the bubble is not the same as the external driving pressure, because of the radiation pressure wave of the neighboring bubbles. The force between two bubbles due to the bubble-radiated pressure waves by the neighboring bubbles is called the secondary Bjerknes force. Considering the bubble-radiated pressure waves and using the modified Keller-Miksis equation and van der Waals equation, the changes of the radius, the secondary Bjerknes force and the temperature of the double bubbles, which have different sizes, interspaces in between, and noble gases, in the process of ultrasonic cavitation are calculated. The calculations are based on the assumption that the locations of double bubbles stay unchanged in the oscillation process and their shapes always keep spherical. The double bubbles can also oscillate synchronously under the influence of the driving ultrasonic field. Because the sound propagation speed in water extremely fast, the time-delay effect on the secondary Bjerknes force is neglected. From the calculated results, the following conclusions can be drawn: when the sizes of double bubbles are different, the smaller bubble is more restrained and the temperature change is larger. When the sizes of double bubbles are the same, the Bjerknes force is negative, indicating that the coupled double bubbles are attracted to each other during the oscillation and the Bjerknes force has two radial oscillations in one driving period. As the interspace between double bubbles increases from 100 m to 1 cm, the secondary Bjerknes force decreases from 10-4 N to 10-8 N, indicating that the interaction between double bubbles increases with the decreasing of the distance between the bubbles. The coupling double bubbles with different noble gases have only a small difference in maximum radius in the stage of expansion, but have different oscillation patterns clearly in the stage of rebound. This is because the bubble expansion process can be seen as an isothermal process, the effective polytropic exponent is approximately equal to 1. The collapse process can be regarded as an adiabatic process, so the effective polytropic exponent of noble gas with large molecules changes rapidly, and the influence of the oscillation of the bubbles becomes large. Our work provides a theoretical basis for establishing the acoustic cavitation model of different-number bubbles, and calculating the interaction force between different-number bubbles.
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Keywords:
- secondary Bjerknes force /
- noble gas /
- temperature
[1] Rayleigh L 1917 Philos. Mag. 34 94
[2] Plesset M S 1949 J. Appl. Mech. 16 277
[3] Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628
[4] Kyuichi Y 2002 J. Acoust. Soc. Am. 112 1405
[5] Ida M, Naoe T, Futakawa M 2007 Phys. Rev. E 76 046309
[6] Wang C H, Mo R Y, Hu J, Chen S 2015 Acta Phys. Sin. 64 234301 (in Chinese) [王成会, 莫润阳, 胡静, 陈时 2015 64 234301]
[7] Mettin R, Akhatov I, Parlitz U, Ohl C D, Lauterborn W 1997 Phys. Rev. E 56 2924
[8] Lu Y G, Wu X H 2011 Acta Phys. Sin. 60 046202 (in Chinese) [卢义刚, 吴雄慧 2011 60 046202]
[9] Pu Z Q, Zhang W, Shi K R, Zhang J H, Wu Y L 2005 J. Tsinghua Univ. (Science and Technology) 45 1450 (in Chinese) [蒲中奇, 张伟, 施克仁, 张俊华, 吴玉林 2005 清华大学学报: 自然科学版 45 1450]
[10] Shirota M, Yamashita K, Inamura T 2012 AIP Conf. Proc. 1474 155
[11] Zhang W J, An Y 2013 Tech. Acoust. 32 125 (in Chinese) [张文娟, 安宇 2013 声学技术 32 125]
[12] Rasoul A, Rezaee N, Ebrahimi H, Mirheydari M 2010 Phys. Rev. E 82 016316
[13] Pelekasis N A, Tsanopoulos J A 1993 J. Fluid Mech. 254 467
[14] Pelekasis N A, Tsanopoulos J A 1993 J. Fluid Mech. 254 501
[15] Matula T J, Cordry S M, Roy R A 1997 J. Acoust. Soc. Am. 102 1522
[16] Ma Y, Lin S Y, Xian X J 2016 Acta Phys. Sin. 65 014301 (in Chinese) [马艳, 林书玉, 鲜晓军 2016 65 014301]
[17] Hu J, Lin S Y, Wang C H, Li J 2013 Acta Phys. Sin. 62 134303 (in Chinese) [胡静, 林书玉, 王成会, 李锦 2013 62 134303]
[18] Ma Y, Lin S Y, Xu J, Tang Y F 2017 Acta Phys. Sin. 66 014302 (in Chinese) [马艳, 林书玉, 徐洁, 唐一璠 2017 66 014302]
[19] Hilgenfeldt S, Grossmann S, Lohse D 1999 Phys. Fluids 11 1318
[20] Hiller R, Putterman S J, Barber B P 1992 Phys. Rev. Lett. 69 1182
[21] Zhou C, Chen W Z, Cui W C 2013 Acta Phys. Sin. 62 087805 (in Chinese) [周超, 陈伟中, 崔炜程 2013 62 087805]
[22] Gheshlaghi M 2015 Ext. J. Appl. Sci. 3 257
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[1] Rayleigh L 1917 Philos. Mag. 34 94
[2] Plesset M S 1949 J. Appl. Mech. 16 277
[3] Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628
[4] Kyuichi Y 2002 J. Acoust. Soc. Am. 112 1405
[5] Ida M, Naoe T, Futakawa M 2007 Phys. Rev. E 76 046309
[6] Wang C H, Mo R Y, Hu J, Chen S 2015 Acta Phys. Sin. 64 234301 (in Chinese) [王成会, 莫润阳, 胡静, 陈时 2015 64 234301]
[7] Mettin R, Akhatov I, Parlitz U, Ohl C D, Lauterborn W 1997 Phys. Rev. E 56 2924
[8] Lu Y G, Wu X H 2011 Acta Phys. Sin. 60 046202 (in Chinese) [卢义刚, 吴雄慧 2011 60 046202]
[9] Pu Z Q, Zhang W, Shi K R, Zhang J H, Wu Y L 2005 J. Tsinghua Univ. (Science and Technology) 45 1450 (in Chinese) [蒲中奇, 张伟, 施克仁, 张俊华, 吴玉林 2005 清华大学学报: 自然科学版 45 1450]
[10] Shirota M, Yamashita K, Inamura T 2012 AIP Conf. Proc. 1474 155
[11] Zhang W J, An Y 2013 Tech. Acoust. 32 125 (in Chinese) [张文娟, 安宇 2013 声学技术 32 125]
[12] Rasoul A, Rezaee N, Ebrahimi H, Mirheydari M 2010 Phys. Rev. E 82 016316
[13] Pelekasis N A, Tsanopoulos J A 1993 J. Fluid Mech. 254 467
[14] Pelekasis N A, Tsanopoulos J A 1993 J. Fluid Mech. 254 501
[15] Matula T J, Cordry S M, Roy R A 1997 J. Acoust. Soc. Am. 102 1522
[16] Ma Y, Lin S Y, Xian X J 2016 Acta Phys. Sin. 65 014301 (in Chinese) [马艳, 林书玉, 鲜晓军 2016 65 014301]
[17] Hu J, Lin S Y, Wang C H, Li J 2013 Acta Phys. Sin. 62 134303 (in Chinese) [胡静, 林书玉, 王成会, 李锦 2013 62 134303]
[18] Ma Y, Lin S Y, Xu J, Tang Y F 2017 Acta Phys. Sin. 66 014302 (in Chinese) [马艳, 林书玉, 徐洁, 唐一璠 2017 66 014302]
[19] Hilgenfeldt S, Grossmann S, Lohse D 1999 Phys. Fluids 11 1318
[20] Hiller R, Putterman S J, Barber B P 1992 Phys. Rev. Lett. 69 1182
[21] Zhou C, Chen W Z, Cui W C 2013 Acta Phys. Sin. 62 087805 (in Chinese) [周超, 陈伟中, 崔炜程 2013 62 087805]
[22] Gheshlaghi M 2015 Ext. J. Appl. Sci. 3 257
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