Mathematical Model of Multibubble Cavitation into Sonochemical Reactor

Sergey D. Shestakov^1,

¹The Technological Management Institute, Moscow state university of Technologies and Management, Russian Acoustical Society, Moscow, Russia

Cite this paper:
Sergey D. Shestakov. Mathematical Model of Multibubble Cavitation into Sonochemical Reactor. American Journal of Modeling and Optimization. 2014; 2(2):60-68. doi: 10.12691/ajmo-2-2-3

Abstract

The research described in this paper shows that main parameter of acoustic cavitation which should be used for practical applications this phenomenon, are not the temperatures of plasma into the cavitation bubbles (the intensity of son luminescence), but the power of pressure pulses, which they produce, and which cause destruction of phases existing in a liquid (the intensity of erosion). The distribution of the density power of erosion in space can be the subject of numerically simulated, if it is assumed that process of multibubble cavitation is an ergodic process. For this the integral of pressure superposition from all bubbles of cavitation field at any point in space, must be approximated by the function of the pressure pulse on the surface of a single cavitation bubble, that pulsate with a period equal to the period of oscillations of the harmonic wave. This superposition of pressure can be described using a two metrics of space, which are belongs to this point. The first – the average distance from this a point until all points of the cavitation region. It determines the average time of arrival into this point of a total perturbation of pressure from all bubbles. The second – the average harmonic distance – determines the average coefficient of attenuation of this perturbation. The results of computational and laboratory experiments illustrate the adequacy and the applicability of model. The model makes it possible to quantitatively compare the results of physical and chemical effects of cavitation in the any liquids in the reactors of any size. The model also gives a sufficient degree of accuracy and reliability of performing the technical calculations for the design of such devices and the possibility to make comparative assessments of different reactors.

Keywords:
ergodic process mathematical model single-bubble cavitations multibubble cavitations cavitational areas erosive power

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References:

[1]	Mettin R., et al., 1997. Bjerknes forces between small cavitation bubbles in a strong acoustic field. Phys. Rev. 56, 3, 2924-2931.
[2]	Mettin R., Koch Ph., & Lauterborn W., 2006. Modeling acoustic cavitation with bubble redistribution 6-th International Symposium on Cavitation, Wageningen.
[3]	Shestakov S., 2001. The basic technology of cavitation disintegration. Mоskow: EVA-Press (in Russian).
[4]	Shestakov S., 2009. Management of hydration the food biopolymers. In V. Panfilov (Eds.). Theoretical Foundations of Food Technology. Moskow: ColosS, (in Russian).
[5]	Margulis M., 1997. Patent RU 2096934.
[6]	Dezhkunov N., et al., 2000. Enhancement of sonoluminescence emission from a multibabble cavitation zone. Ultrasonics Sonochemistry, V 7, 1, 19-24.
[7]	Margulis M., 2000. Sonoluminescence. Physics-Uspekhi, 170, 263-287 (in Russian).
[8]	Matula T., et al., 1995. Comparison of Multibubble and Single-Bubble Sonoluminescence Spectra. Phys. Rev. Lett., 75, 2602-2605.
[9]	Flannigan D., Suslik K., 2005. Plasma formation and temperature measurement during single-bubble cavitation. Letters to Nature, 434, 52-55.
[10]	Shestakov S., 2008. Research of an opportunity to strengthen the nonparametric multibubble cavitation. Applied Physics, 6, 18-24 (in Russian).
[11]	Flynn H., 1982. Patent US 4333796.
[12]	Putterman S. et al., 1994. Patent US 5659173.
[13]	Taleyarkhan R. et al., 2002. Evidence for Nuclear Emissions During Acoustic Cavitation. Science, V. 295, 1868-1873.
[14]	Taleyarkhan R. et al., 2004. Additional evidence of nuclear emissions during acoustic cavitation. Physical Review, V. 69, 036109.
[15]	Nigmatulin R., 2005. Nano-scale thermonuclear fusion in imploding vapor bubbles. Nuclear Engineering and Design, V. 235, 1079-1091.
[16]	Lahey R., Taleyarkhan R., & Nigmatulin R., 2007. Sonofusion technology revisted. Nuclear Engineering and Design, V. 237, 1571-1585.
[17]	Khavroshkin O., Bystrov V., 2007. Sonoluminescence and Sono-fusion. Applied Physics, 5, 7-14 (in Russian).
[18]	Shestakov S., 2007. Patent EP 1810744.
[19]	Dezhkunov N., Ignatenko P., & Kotukhov A., 2007. Optimization of the activity of cavitation generated by pulsed ultrasound. Electronic Journal “Technical Acoustics”. http://www.ejta.org, 2007, 16 (in Russian).
[20]	Lanin V., Dezhkunov N. & Tomal V., 2008. Instrumentation for measurement of ultrasonic effects in processes. Technology and design of electronic equipment, 2, 51-55 (in Russian).
[21]	Krefting D., Mettin R. & Lauterborn W., 2004. High-speed observation of acoustic cavitation erosion in multibubble systems. Ultrasonics Sonochemistry, 11, 119-123.
[22]	Shestakov S., & Krasulya O., 2010. Sonochemical technologies in food industry. Electronic Journal “Technical Acoustics”, http://www.ejta.org, 2010, 10 (in Russian).
[23]	Rogov I., & Shestakov S., 2004. Epithermal change the thermodynamic equilibrium of water and aqueous solutions: Delusion and Reality. Storage and Processing of Farm Products, 4, 17-20; 10, 9-13 (in Russian).
[24]	Ashokkumar M., Rink R., & Shestakov S., 2011. Hydrodynamic cavitation – an alternative to ultrasonic food processing. Electronic Journal “Technical Acoustics”. http://www.ejta.org, 2011, 9.
[25]	Jinesh K. & Frenken J., 2008. Experimental Evidence for Ice Formation at Room Temperature. Physical Review Letters, 101, 036101.
[26]	Mawson R., & Knoerzer K., 2007. A brief history of the application of ultrasonics in food processing. 19-th ICA Congress, Madrid.
[27]	Knapp R., Daily J., & Hammitt F., 1970. Cavitation. NY: McGraw Book Company.
[28]	Rozenberg L. (Eds.), 1968. Physics and technology of high-intensity ultrasound. Moskow: Nauka, (in Russian).
[29]	Podobriy G. M. et al., 1969. Theoretical foundations of torpedo weapons. Moscow: Military (in Russian).
[30]	Klotz A., & Hynynen K., 2010. Simulations of the Devin and Zudin modified Rayleigh-Plesset equations to model bubble dynamics in a tube. Electronic Journal “Technical Acoustics”, http://www.ejta.org, 2010, 11.
[31]	Melnikov P., Makarenko V. & Makarenko M., 2004. Achievement of high temperatures during compression vapor bubble. J. of Appl. Mechanics and Tech. Physics, V 45, 4, 13-25 (in Russian).
[32]	Gaitan D., Tessien R., & Hiller R., 2007. Pressure pulses from transient cavitation in high-q resonators. 19-th ICA Congress, Madrid.
[33]	Mettin R., Koch Ph. & Lauterborn W., 2006. Modeling acoustic cavitation with bubble redistribution 6-th International Symposium on Cavitation, Wageningen.
[34]	Shestakov S., & Befus A., 2008. The formulation of the criterion of similarity sonochemical reactors processing environments that do not ensure acoustic resonance. Dep. VINITI, 840-B2008 (in Russian).
[35]	Lavrinenko O., Savina E. & Leonov G., 2007. Modeling mechanical-physical and chemical effects in the collapse of cavitation bubbles. Polzunov Bulletin, 3, 59-63 (in Russian).
[36]	Kedrinskiy V., 1975. Dynamics of the cavitation zone at underwater explosion near free surface. J. of Appl. Mechanics and Tech. Physics, 5, 68-78 (in Russian).
[37]	Rink R. & Shestakov S., 2012. Cavitational reactor with symmetric nonmonolithic oscillatory system of the acoustic cell for processes of food sonochemistry. Electronic Journal “Technical Acoustics”, http://www.ejta.org, 2012, 2.
[38]	Mettin R., et al., 1997. Bjerknes forces between small cavitation bubbles in a strong acoustic field. Phys. Rev. 56, 3, 2924-2931.
[39]	Patent application WO 2007111524, 2007.