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Chin. Phys. B Vol. 24, No. 10 (2015) 104301

Quantitative calculation of reaction performance in sonochemical

reactor by bubble dynamics∗

Xu Zheng(徐 峥)a)b), Yasuda Keiji(安田启司)b), and Liu Xiao-Jun(刘晓峻)c)†

a)School of Physics Science and Engineering, Tongji University, Shanghai 200092, China b)Department of Chemical Engineering, Nagoya University, Nagoya 464-8603, Japan c)School of Physics, Nanjing University, Nanjing 210093, China

(Received 12 March 2015; revised manuscript received 24 April 2015; published online 20 August 2015)

In order to design a sonochemical reactor with high reaction efficiency, it is important to clarify the size and intensity of the sonochemical reaction field. In this study, the reaction field in a sonochemical reactor is estimated from the distribution of pressure above the threshold for cavitation. The quantitation of hydroxide radical in a sonochemical reactor is obtained from the calculation of bubble dynamics and reaction equations. The distribution of the reaction field of the numerical simulation is consistent with that of the sonochemical luminescence. The sound absorption coefficient of liquid in the sonochemical reactor is much larger than that attributed to classical contributions which are heat conduction and shear viscosity. Under the dual irradiation, the reaction field becomes extensive and intensive because the acoustic pressure amplitude is intensified by the interference of two ultrasonic waves.

Keywords: reaction field, cavitation, bubble dynamics, hydroxide radical

PACS: 43.35.+d, 43.38.+n 1. Introduction

Ultrasound and the ultrasonic effect have been widely investigated. [1–6] Ultrasound irradiation at frequencies rang- ing from 20 kHz to a few MHz can result in a cavitation due to the sonochemical reaction.[1,2] The cavitation is induced at acoustic pressure above the minimum pressure necessary to initiate bubble growth, i.e., the cavitation threshold. Cavitation bubbles are generated when the “negative” pressure during the rarefaction phase of ultrasound is sufficiently large to disrupt the liquid.[3] Each bubble repeats expansion and contraction due to the acoustic cycle. Finally, the bubble undergoes an implosive collapse, and a high temperature and pressure field is generated by the adiabatic compression of the gas-phase in- side bubbles. In this field, a solute in solution is decomposed at high temperature or reacts with radical species generated by the pyrolysis of the solute and the solvent.[4]

The sonochemical process offers various possibilities for industrial applications, for instance, chemical synthesis, ex- traction, crystallization, and nano-technology.[7] It is widely used in chemistry and chemical engineering because the oper- ation is simple and safe, and secondary pollutants are difficult to form.[8] A major problem of designing sonochemical reac- tors is the non-uniform distribution of the reaction field which suppresses its reaction rate. This problem becomes serious in a large reactor for industrial applications.[9]

In order to extend the reaction field throughout the whole reactor, a superposition of ultrasonic fields by using multi- ple transducers has been widely investigated.[10–14] Feng et

DOI: 10.1088/1674-1056/24/10/104301

al. reported that irradiation from three transducers at 28 kHz, 1 MHz, and 1.87 MHz enhanced the sonochemical reactions of potassium iodide and terephthalate ion.[11] Koda et al. inves- tigated the effect of frequency on the sonochemical reaction rate of terephthalate ion. The frequencies of two transducers were individually changed from 176 kHz to 635 kHz, since the sonochemical reaction rate of potassium iodide by using one transducer had maximum values in a frequency range from 200 kHz to 600 kHz.[15] The sonochemical reaction rate had a maximum value when the frequencies of the bottom and side transducers were 422 kHz and 472 kHz, respectively.[14] The visualization of sonochemical reaction fields was also per- formed. A luminescence reaction of a luminal solution was employed, and the expansion of reaction fields was observed by dual irradiation. To evaluate the reaction performance of a sonochemical reactor, researchers are becoming more and more aware of the importance of the depiction of reaction fields. However, measurement of the reaction field is diffi- cult. An ultrasonic hydrophone is damaged by cavitation. The quantitative analysis of reaction fields visualized by luminal solution is difficult.

Two factors are important to evaluate the performance of a sonochemical reactor: the area and the intensity of the reac- tion field. The area of reaction field is determined by the pres- sure distribution in a sonochemical reactor, which has been widely investigated.[16–21] Kl ́ıma et al. optimized the bound- ary conditions in a sonochemical reactor at 20 kHz.[16] To cal- culate the pressure distribution, Yasui et al.[17] and Servant et

∗Project supported by the National Natural Science Foundation of China (Grant Nos. 11404245, 11204129, and 11211140039). †Corresponding author. E-mail:

© 2015 Chinese Physical Society and IOP Publishing Ltd


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