Void fraction, number density of acoustic cavitation bubbles, and acoustic frequency: A numerical investigation

Abstract

The present paper consists of a numerical study attempting to characterize the bubble population within a sonochemical reactor through modeling and simulating the number density of bubbles and the void fraction. In a first step, both previous parameters were estimated under 1.52 bar and various acoustic frequencies ranging from 20 to 1000 kHz in function of normalized time. The results showed that the average number density of bubbles, varying within the interval 2.8104−1.4 × 1012 bubbles dm−3, follows a clear monotonous evolving trend as the frequency increases, while the average void fraction, comprised between 9.05 × 10−5 and 1.95 × 10−4, demonstrates no dependency of acoustic conditions. In a second step, an energy analysis was performed at microscopic and macroscopic scales, which led the authors to figure out that the evolution of the number density of bubbles in function of acoustic frequency is mainly governed by the energy required to maintain oscillating the single cavitation bubble.

Numerical simulations for sonochemistry

“…In usual experiments of sonochemistry which is a multibubble system, not only chemical reaction-rates in each bubble but also spatial distribution of number density of bubbles and acoustic amplitude are relevant to the total sonochemical activity [47] , [48] , [49] , [50] , [51] , [52] , [53] . In this section, numerical simulations of an acoustic field (spatial distribution of acoustic amplitude) are discussed [53] .…”

Numerical Characterization of Acoustic Cavitation Bubbles with Respect to the Bubble Size Distribution at Equilibrium

“…The probability of occurrence of each ambient radius in terms of number densities of bubbles is known by the resolution of the iterative algorithm. The number density related to each homogeneous sub-population is retrieved by the application of microscopic and macroscopic energy balances based on Equation (9) [57] and (10) [16,17,44], respectively. Equation (9) represents the energy balance applied on a single acoustic cavitation bubble of a radius R evolving in water under an oxygen atmosphere, within which 45 elementary chemical equations [13] are supposed to emerge, giving rise to 9 chemical species, as shown in Table 1.…”

“…Most of the numerical works that investigated the acoustic cavitation phenomenon were limited in scale to the single acoustic cavitation bubble [11][12][13][14]. Some researcher attempted to numerically explore the multibubble dimension by investigating parameters such as the number density of bubbles [15][16][17], bubble-bubble interaction [18][19][20], and bubble size distribution [21]. Some examples of multibubble approaches are found in the studies of Yasui [22], Colonius et al [23] and Ida [24].…”

“…The present paper is presented in the perspective of improvement of a first work of modeling the number density of bubbles within a homogenous population [16,17,44]. The passage from a homogeneous model to a heterogeneous one in terms of the size distribution within the bubble population at equilibrium is performed numerically using an incremental statistical approach.…”

Multibubble Sonoluminescence from a Theoretical Perspective

“…MBSL intensity is determined not only by the light intensity from a bubble but also by number of active bubbles in SL. The number of active bubbles in MBSL has not yet been fully studied either experimentally or theoretically [ 89 , 90 , 91 ]. Further studies are required on the brightest MBSL.…”