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Ultrasonics Sonochemistry 15 (2008) 618–628

Shock-wave model of acoustic cavitation Sergei L. Peshkovsky, Alexey S. Peshkovsky *

Industrial Sonomechanics, LLC, 1505 St. Nicholas Ave., Suite 5B, New York, NY 10033, USA

Received 8 December 2006; received in revised form 5 July 2007; accepted 22 July 2007 Available online 7 August 2007

Shock-wave model of liquid cavitation due to an acoustic wave was developed, showing how the primary energy of an acoustic radiator is absorbed in the cavitation region owing to the formation of spherical shock-waves inside each gas bubble. The model is based on the concept of a hypothetical spatial wave moving through the cavitation region. It permits using the classical system of Rankine–Hugoniot equations to calculate the total energy absorbed in the cavitation region. Additionally, the model makes it possible to explain some newly discovered properties of acoustic cavitation that occur at extremely high oscillatory velocities of the radiators, at which the mode of bub- ble oscillation changes and the bubble behavior approaches that of an empty Rayleigh cavity. Experimental verification of the proposed model was conducted using an acoustic calorimeter with a set of barbell horns. The maximum amplitude of the oscillatory velocity of the horns’ radiating surfaces was 17 m/s. Static pressure in the calorimeter was varied in the range from 1 to 5 bars. The experimental data and the results of the calculations according to the proposed model were in good agreement. Simple algebraic expressions that follow from the model can be used for engineering calculations of the energy parameters of the ultrasonic radiators used in sonochemical reactors.

Ó 2007 Elsevier B.V. All rights reserved.

PACS: 43.35+d

Keywords: Acoustic cavitation; Acoustic wave; Cavitation bubble; Shock-wave; Shock-wave theory; Acoustic horn; Ultrasonic cavitation; Ultrasonic

radiator; Ultrasonics

1. Introduction

In the design and calculation of powerful ultrasonic sources for sonochemical reactors, it is necessary to know the exact value of the intensity of the acoustic energy radi- ated into the working liquid. This information is usually obtained experimentally because no adequate physical model of acoustic cavitation that would allow one to obtain such data through calculation so far exists. The development of an adequate model of acoustic cavitation, although of great importance, has in the past been severely restricted by considerable mathematical difficulties con- nected with the necessity of finding numerical solutions of nonlinear equations describing the cavitation region

* Corresponding author. Tel.: +1 (646) 267 2890.

E-mail address: (A.S. Peshkovsky).

1350-4177/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ultsonch.2007.07.006

(the visible region of large cavitation bubble population) [1]. Direct analytical solutions of these equations in differ- ent approximations do not give practical results suitable for the design of ultrasonic equipment [2,3].

Current literature on acoustic cavitation mainly tends to involve numerical models of spatio-temporal characteristics of the cavitation region [4–6]. Large number of theoretical acoustic cavitation models has been developed along with the corresponding methods of numerical analysis of such models. Further computer simulation-based investigations of acoustic cavitation have also been proposed, involving complex nonlinear physicomathematical models and including many aspects of spatial movement of cavitation bubbles in an acoustic field, spatial distribution of the characteristics of these fields in a liquid, interaction between the bubbles themselves, properties of acoustical flow, etc. [7–10]. Water is most frequently used for the experimental verification of such theoretical models.

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