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Research Papers: Heat and Mass Transfer

A General Approach for Rectified Mass Diffusion of Gas Bubbles in Liquids Under Acoustic Excitation

[+] Author and Article Information
Yuning Zhang

School of Engineering,
University of Warwick,
Coventry CV4 7AL, UK
e-mail: zhangyn02@gmail.com

Shengcai Li

School of Engineering,
University of Warwick,
Coventry CV4 7AL, UK

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 11, 2012; final manuscript received November 22, 2013; published online January 31, 2014. Assoc. Editor: James A. Liburdy.

J. Heat Transfer 136(4), 042001 (Jan 31, 2014) (8 pages) Paper No: HT-12-1655; doi: 10.1115/1.4026089 History: Received December 11, 2012; Revised November 22, 2013

Rectified mass diffusion serves as an important mechanism for dissolution or growth of gas bubbles under acoustic excitation with many applications in acoustical, chemical and biomedical engineering. In this paper, a general approach for predicting rectified mass diffusion phenomenon is proposed based on the equation of bubble motion with liquid compressibility. Nonuniform pressure inside gas bubbles is considered in the approach through employing a well-established framework relating with thermal effects during gas bubble oscillations. Energy dissipation mechanisms (i.e., viscous, thermal, and acoustic dissipation) and surface tension are also included in the approach. Comparing with previous analytical investigations, present approach mainly improves the predictions of rectified mass diffusion in the regions far above resonance and regions with frequencies megahertz and above. Mechanisms for the improvements are shown and discussed together with valid regions and limitations of present approach.

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Figures

Grahic Jump Location
Fig. 1

Comparisons of threshold of acoustic pressure amplitude of rectified mass diffusion predicted by Crum and Hansen [32], Crum and Mao [7] and ours (Present). ω = 107 s−1. Ci/C0 = 1.0.

Grahic Jump Location
Fig. 2

Comparisons of threshold of acoustic pressure amplitude of rectified mass diffusion predicted by Crum and Hansen [32], Crum and Mao [7] and ours (Present). ω = 5 × 107 s−1. Ci/C0 = 1.0.

Grahic Jump Location
Fig. 3

Comparisons of threshold of acoustic pressure amplitude of rectified mass diffusion predicted by Crum and Hansen [32], Crum and Mao [7] and ours (Present). ω = 108 s−1. Ci/C0 = 1.0.

Grahic Jump Location
Fig. 4

Predicted values of viscous (dashed line), thermal (dotted line), acoustic (dashed–dotted line), and total (solid line) damping constants. Open circle refers to the resonance. ω = 5 × 107 s−1.

Grahic Jump Location
Fig. 5

Influences of nonuniform pressure and liquid compressibility on the threshold of acoustic pressure amplitude of rectified mass diffusion. For details, readers are referred to the texts. Ci/C0 = 1.2.

Grahic Jump Location
Fig. 6

Comparisons of threshold of acoustic pressure amplitude of rectified mass diffusion predicted by Crum and Hansen [32], Crum and Mao [7] and ours (Present) with ω = 5 × 107 s−1 and Ci/C0 = 1.2.

Grahic Jump Location
Fig. 7

Comparisons of threshold of acoustic pressure amplitude of rectified mass diffusion predicted by Crum and Hansen [32], Crum and Mao [7] and ours (Present) with ω = 5 × 107 s−1 and Ci/C0 = 0.8.

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