American Journal of Modeling and Optimization
ISSN (Print): 2333-1143 ISSN (Online): 2333-1267 Website: Editor-in-chief: Dr Anil Kumar Gupta
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American Journal of Modeling and Optimization. 2014, 2(2), 60-68
DOI: 10.12691/ajmo-2-2-3
Open AccessArticle

Mathematical Model of Multibubble Cavitation into Sonochemical Reactor

Sergey D. Shestakov1,

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

Pub. Date: May 25, 2014

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


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.

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

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