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FEM simulation of a sono-reactor accounting for vibrations of the boundaries.

O. Louisnard a,1, J. Gonzalez Garcia b, I. Tudela b, J. Klima c, V. Saez b, Y. Vargas d, aLaboratoire de G ́enie des Proc ́ed ́es des Solides Divis ́es,

UMR CNRS 2392, E ́cole des Mines d’Albi-Carmaux,

Campus Jarlard, 81013 Albi Cedex 09, France

bDepartamento de Qu ́ımica F ́ısica e Instituto Universitario de Electroqu ́ımica, Universidad de Alicante, Spain.

cJ. Herovsky Institute of Physical Chemistry Academy of Sciences of the Czech Republic, 18223 Prague 8, Czech Republic. dLaboratorio de Ultrasonidos, USACH, Casilia 307, Santiago 2, Chile

Abstract

The chemical effects of acoustic cavitation are obtained in sono-reactors built-up from a vessel and an ultrasonic source. In this paper, simulations of an existing sono-reactor are carried out, using a linear acoustics model, accounting for the vibrations of the solid walls. The available frequency range of the generator (19 kHz-21 kHz) is systematically scanned. Global quantities are plotted as a function of frequency in order to obtain response curves, exhibiting several resonance peaks. The attenuation coefficient of the wave is taken as a variable parameter, in absence of the precise knowledge of the bubble size distribution, and its influence is studied. The concepts of acoustic energy, intensity and active power are recalled, along with the general balance equation for acoustic energy. The latter is used as a convergence check of the simulations. Finally, it is shown that the interface between the liquid and the solid walls cannot be correctly represented by the simple approximations of either infinitely soft, or infinitely hard boundaries. Moreover, the liquid-solid coupling allows the cooling jacket to receive a noticeable part of the input power, although it is not in direct contact with the sonotrode. It may therefore undergo cavitation and this feature opens the perspective to design sono-reactors which avoid direct contact between the working liquid and the sonotrode.

Key words: finite elements, ultrasound, linear acoustics, bubble, cavitation, PACS: 47.57.ef

PACS: 47.55.dd

PACS: 68.55.Ac

1. Introduction

When a liquid is irradiated by a high-power ul- trasonic wave, numerous radially oscillating micron- sized bubbles appear. The phenomenon is known as acoustic cavitation [1, 2]. The strong collapse, fol- lowing the explosive expansion of these bubbles, in- duces extreme conditions inside or near the bubbles,

Email address: louisnar@enstimac.fr (O. Louisnard). 1 Corresponding author

Preprint submitted to Elsevier

which are responsible for a specific chemistry, known as sonochemistry [3].

Various experimental devices can be used to pro- duce this phenomenon. The most common one is a horn transducer, diving in the liquid and creating large acoustic pressure in its vicinity. Other systems involve a transducer with larger emitting area, from the bottom (sometimes referred as “cup-horn reac- tors”), or various transducers sticked to plane walls, the latter system being commonly known as ultra- sonic bath.

29 February 2008

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