Acoustical scattering cross section of gas bubbles under dual-frequency acoustic excitation

Mass transfer of microbubble in liquid under multifrequency acoustic excitation - A theoretical study

Microbubble's mass transfer under external acoustic excitation holds immense potential across various technological fields. However, the current state of acoustic technology faces limitations due to inadequate control over bubble size in liquids under external excitation. Here, we conducted numerical investigations of the mass transfer behavior of microbubbles in liquids under multifrequency acoustic excitations with different frequencies (in the MHz range), pressure amplitudes (in the range of several atmospheric pressures), and amplitude ratios. We identified various pressure threshold regions for the growth of gas bubbles (radii range from a few microns to tens of microns) and observed common intersections between single and multifrequency excitations that enable effective control of the growth intervals and final size of bubbles by adjusting the ratio of pressure amplitude and frequency value. Allocating power to the lower frequency component of multifrequency acoustic excitation is recommended to facilitate mass transfer or diffusion, as small-frequency acoustic excitation has a more significant effect than the higher frequency in the growth region. Our study provides a better understanding of the dynamics of bubbles under complex excitations and has practical implications for developing methods to control and promote bubble-related processes.

Multi-frequency therapeutic ultrasound: A review

Focused ultrasound is a noninvasive, radiation-free and real-time therapeutic approach to treat deep-seated targets, which benefits numerous diseases otherwise requiring surgeries. Treatment efficiency is one of the key factors determining therapeutic outcomes, but improving it solely by increasing the total power can be limited by the performance of general ultrasound devices. To address this, multi-frequency therapeutic ultrasound, using additional ultrasound waves of different frequencies on top of the standard single-frequency wave, provides a promising method for treatment efficiency enhancement with limited power. Several applications and numerical works have demonstrated its superiority on treatment enhancement. This paper presents an overview of the mechanisms, implementations, applications and decisive parameters of the multi-frequency therapeutic ultrasound, which could help to pave the way for better understanding and further developing this technology in the future.

Multi-bubble scattering acoustic fields in viscoelastic tissues under dual-frequency ultrasound

Bubbles are widely used in the medical field due to their strong acoustic scattering properties, and the interaction between bubbles affects the scattering acoustic field caused by the bubble cluster. In this study, the dynamic equations of bubbles oscillating in viscoelastic tissues are solved numerically. The effect of bubble interaction on the scattered acoustic pressure under dual-frequency ultrasound is analyzed. In addition, the frequency spectra of the scattered acoustic waves due to the bubbles with and without considering the interaction are compared. The results show that the suppression or enlargement of the scattered sound pressure caused by the interaction between bubbles is related to the bubble radius and the incident frequency. Moreover, when the incident frequency is equal to the resonant frequency of the bubble with equilibrium radius R0, the effect of resonant bubbles is stronger than that of non-resonant bubbles. Meanwhile, for the multi-bubble system with a small bubble number density, the total response of the bubble cluster can be approximated as an algebraic sum of the dynamical behavior of individual bubbles.

A single oscillating bubble in liquids with high Mach number

The oscillation characteristics of a single bubble and its induced radiation pressure and the dissipated power are essential for a wide range of applications. For bubble oscillations with high Mach number, the influence of the liquid compressibility is significantly strong and should be fully considered. In the present paper, the bubble wall motion equation with the second-order Mach number is employed for investigating a free oscillating bubble in the liquid with numerical and experimental verifications. For the purpose of comparisons, the revised Keller-Miksis equation up to the first-order Mach number is solved with the same conditions (e.g. the initial conditions and the ambient pressure). Through our simulations, comparing with the predictions by the first-order equation, we find that: (1) The bubble radius, the bubble wall radial velocity and the bubble wall radial acceleration predicted by the second-order equation with high Mach number are significantly different respectively, and the dimensionless differences increase with the increase of the Mach number. (2) The valid prediction range of the second-order equation is much larger. (3) The dissipated power predicted by the second-order equation with high Mach number is smaller.

Ultrasound-assisted transesterification of soybean oil using low power and high frequency and no external heating source

In this work, high frequency and low power ultrasound without external heating source and mechanical stirring in biodiesel production were studied. Transesterification of soybean oil with methanol and catalyzed by KOH was investigated using ultrasound equipment and ultrasonic transducer. The effect of ultrasonic output power (3 W-9 W), ultrasonic frequency (1 MHz and 3 MHz), and alcohol to oil molar ratio (6:1 and 8:1) have been investigated. The increase in ultrasonic power provided higher conversion rates. In addition, higher conversion rates were obtained by increasing the ultrasonic frequency from 1 MHz to 3 MHz (48.7% to 79.5%) for the same reaction time. Results also indicate that the speed of sound can be used to evaluate the produced biodiesel qualitatively. Further, the ultrasound system presented electric consumption (46.2W∙h) four times lower than achieved using the conventional method (211.7W∙h and 212.3W∙h). Thus, biodiesel production using low power ultrasound in the MHz frequency range is a promising technology that could contribute to biodiesel production processes.

Nonlinear dynamics and bifurcation structure of ultrasonically excited lipid coated microbubbles

In many applications, microbubbles (MBs) are encapsulated by a lipid coating to increase their stability. However, the complex behavior of the lipid coating including buckling and rupture sophisticates the dynamics of the MBs and as a result the dynamics of the lipid coated MBs (LCMBs) are not well understood. Here, we investigate the nonlinear behavior of the LCMBs by analyzing their bifurcation structure as a function of acoustic pressure. We show that, the LC can enhance the generation of period 2 (P2), P3, higher order subharmonics (SH), superharmonics and chaos at very low excitation pressures (e.g. 1 kPa). For LCMBs sonicated by their SH resonance frequency and in line with experimental observations with increasing pressure, P2 oscillations exhibit three stages: generation at low acoustic pressures, disappearance and re-generation. Within non-destructive oscillation regimes and by pressure amplitude increase, LCMBs can also exhibit two saddle node (SN) bifurcations resulting in possible abrupt enhancement of the scattered pressure. The first SN resembles the pressure dependent resonance phenomenon in uncoated MBs and the second SN resembles the pressure dependent SH resonance. Depending on the initial surface tension of the LCMBs, the nonlinear behavior may also be suppressed for a wide range of excitation pressures.

GPU accelerated study of a dual-frequency driven single bubble in a 6-dimensional parameter space: The active cavitation threshold

The active cavitation threshold of a dual-frequency driven single spherical gas bubble is studied numerically. This threshold is defined as the minimum intensity required to generate a given relative expansion (R_max-R_E)/R_E, where R_E is the equilibrium size of the bubble and R_max is the maximum bubble radius during its oscillation. The model employed is the Keller-Miksis equation that is a second order ordinary differential equation. The parameter space investigated is composed by the pressure amplitudes, excitation frequencies, phase shift between the two harmonic components and by the equilibrium bubble radius (bubble size). Due to the large 6-dimensional parameter space, the number of the parameter combinations investigated is approximately two billion. Therefore, the high performance of graphics processing units is exploited; our in-house code is written in C++ and CUDA C software environments. The results show that for (R_max-R_E)/R_E=2, the best choice of the frequency pairs depends on the bubble size. For small bubbles, below 3μm, the best option is to use just a single frequency of a low value in the giant response region. For medium sized bubbles, between 3μm and 6μm, the optimal choice is the mixture of low frequency (giant response) and main resonance frequency. For large bubbles, above 6μm, the main resonance dominates the active cavitation threshold. Increasing the prescribed relative expansion value to (R_max-R_E)/R_E=3, the optimal choice is always single frequency driving with the lowest value (20kHz here). Thus, in this case, the giant response always dominates the active cavitation threshold. The phase shift between the harmonic components of the dual-frequency driving (different frequency values) has no effect on the threshold.

Recent advances in ultrasound-based transdermal drug delivery

The transdermal transport of pharmaceuticals possesses various advantageous properties over conventional drug administration techniques such as oral delivery and hypodermic injections. However, the stratum corneum persists as the main barrier, which impedes percutaneous transport. The ultrasound-based transdermal delivery of therapeutics is one of the techniques that are being investigated to overcome this obstacle. This review outlines the background information pertaining to sonophoresis and then discusses the individual sections of sonophoretic research. These areas include the sonophoretic application of various drugs, dual-frequency sonophoresis, synergistic combinations of transdermal drug delivery techniques, and the use of nanosized carriers in ultrasound-based transdermal delivery. The various challenges associated with sonophoretic drug delivery and trends of future research are also highlighted.

Numerical investigation of the inertial cavitation threshold by dual-frequency excitation in the fluid and tissue

Inertial cavitation thresholds, which are defined as bubble growth by 2-fold from the equilibrium radius, by two types of ultrasonic excitation (at the classical single-frequency mode and dual-frequency mode) were calculated. The effect of the dual-frequency excitation on the inertial cavitation threshold in the different surrounding media (fluid and tissue) was studied, and the paramount parameters (driving frequency, amplitude ratio, phase difference, and frequency ratio) were also optimized to maximize the inertial cavitation. The numerical prediction confirms the previous experimental results that the dual-frequency excitation is capable of reducing the inertial cavitation threshold in comparison to the single-frequency one at the same output power. The dual-frequency excitation at the high frequency (i.e., 3.1 + 3.5 MHz vs. 1.1 + 1.3 MHz) is preferred in this study. The simulation results suggest that the same amplitudes of individual components, zero phase difference, and large frequency difference are beneficial for enhancing the bubble cavitation. Overall, this work may provide a theoretical model for further investigation of dual-frequency excitation and guidance of its applications for a better outcome.

Numerical investigation of the inertial cavitation threshold under multi-frequency ultrasound

Through the introduction of multi-frequency sonication in High Intensity Focused Ultrasound (HIFU), enhancement of efficiency has been noted in several applications including thrombolysis, tissue ablation, sonochemistry, and sonoluminescence. One key experimental observation is that multi-frequency ultrasound can help lower the inertial cavitation threshold, thereby improving the power efficiency. However, this has not been well corroborated by the theory. In this paper, a numerical investigation on the inertial cavitation threshold of microbubbles (MBs) under multi-frequency ultrasound irradiation is conducted. The relationships between the cavitation threshold and MB size at various frequencies and in different media are investigated. The results of single-, dual and triple frequency sonication show reduced inertial cavitation thresholds by introducing additional frequencies which is consistent with previous experimental work. In addition, no significant difference is observed between dual frequency sonication with various frequency differences. This study, not only reaffirms the benefit of using multi-frequency ultrasound for various applications, but also provides a possible route for optimizing ultrasound excitations for initiating inertial cavitation.

Chaotic oscillations of gas bubbles under dual-frequency acoustic excitation

Chaotic oscillation of bubbles in liquids reduces the efficiency of the sonochemical system and should be suppressed in the practical applications. In the present paper, a chaos control method based on the dual-frequency approach is numerically investigated and is proved to be an effective method even for cases with intensive energy input. It was found that the chaos could be successfully suppressed by the application of dual-frequency approach in a wide range of parameter zone (even with high acoustic pressure amplitude). Furthermore, influences of power allocation between two waves on the chaos control are quantitatively discussed with clear descriptions of the routes from stable oscillations to chaos.

Effects of mass transfer on damping mechanisms of vapor bubbles oscillating in liquids

The damping mechanisms play an important role in the behavior of vapor bubbles. In the present paper, effects of mass transfer on the damping mechanisms of oscillating vapor bubbles in liquids are investigated within a wide range of parameter zone (e.g. in terms of frequency and bubble Péclet number). Results of the vapor bubbles are also compared with those of the gas bubbles. Our findings reveal that the damping mechanisms of vapor bubbles are significantly affected by the mass transfer especially in the regions with small and medium bubble Péclet number. Comparing with the gas bubbles, the contributions of the mass-transfer damping mechanism for the vapor bubble case are quite significant, being the dominant damping mechanism in a wide region.

Intensification of biodiesel production using dual-frequency counter-current pulsed ultrasound

Biodiesel production from soybean oil deodorizer distillate intensified by dual-frequency counter-current pulsed ultrasound and the kinetics were studied. Results indicated that the biodiesel conversions enhanced by single-frequency were lower than those enhanced by dual-frequency. For dual-frequency, the biodiesel conversion of SMM was higher than those of SQM. The biodiesel conversion of the combination of 20/28kHz is the highest. The effects of 20/28kHz SMM on biodiesel production were studied and optimal conditions were: methanol to triglyceride molar ratio 8:1, catalyst content 1.8%, the water content in feedstock should be less than 0.4%, the acid value of feedstock should be less than 2mgKOH·g^-1, the biodiesel conversion could reach 96.3%. The kinetics of SMM and SSPU were studied and results showed that the transesterification reaction was pseudo-second order and the energy activation obtained by SMM and SSPU were 18.122kJ·mol^-1 and 26.034kJ·mol^-1, respectively. These results showed that transesterification reaction intensified by SMM is easier to take place than SSPU.

Combination and simultaneous resonances of gas bubbles oscillating in liquids under dual-frequency acoustic excitation

The multi-frequency acoustic excitation has been employed to enhance the effects of oscillating bubbles in sonochemistry for many years. In the present paper, nonlinear dynamic oscillations of bubble under dual-frequency acoustic excitation are numerically investigated within a broad range of parameters. By investigating the power spectra and the response curves of oscillating bubbles, two unique features of bubble oscillations under dual-frequency excitation (termed as "combination resonance" and "simultaneous resonance") are revealed and discussed. Specifically, the amplitudes of the combination resonances are quantitatively compared with those of other traditional resonances (e.g. main resonances, harmonics). The influences of several paramount parameters (e.g., the bubble radius, the acoustic pressure amplitude, the energy allocation between two component waves) on nonlinear bubble oscillations are demonstrated.

The secondary Bjerknes force between two gas bubbles under dual-frequency acoustic excitation

The secondary Bjerknes force is one of the essential mechanisms of mutual interactions between bubbles oscillating in a sound field. The dual-frequency acoustic excitation has been applied in several fields such as sonochemistry, biomedicine and material engineering. In this paper, the secondary Bjerknes force under dual-frequency excitation is investigated both analytically and numerically within a large parameter zone. The unique characteristics (i.e., the complicated patterns of the parameter zone for sign change and the combination resonances) of the secondary Bjerknes force under dual-frequency excitation are revealed. Moreover, the influence of several parameters (e.g., the pressure amplitude, the bubble distance and the phase difference between sound waves) on the secondary Bjerknes force is also investigated numerically.