Formulation of multibubble cavitation

Evolutionary mechanism of Y-branches in acoustic Lichtenberg figures just below the water surface

The acoustic Lichtenberg figure (ALF) in an ultrasonic cleaner with a frequency of 28 kHz at different power levels was observed using high-speed photography. The nonlinear response of the cavitation structure was analyzed by the entropy spectrum in the ALF images, which showed the modulation influence of the primary acoustic field, exhibiting the fluctuations of the bubble distribution with time. Typical Y-branches predict the paths by which surrounding bubbles are attracted and converge into the structure, the branches are curved due to bubble-bubble interactions, and the curvature increases as the bubbles are approaching the main chain. The average travelling speed of bubbles along the branches is about 1.1 m/s, almost independent of power level of the ultrasonic cleaner. A theoretical model consisting of free bubbles and a straight bubble chain of finite length was developed to explore the evolutionary mechanism of branching. It was found that the bubble trajectories showed a bending tendency similar to the experimentally observed Y-branches, and the stationary straight bubble chain parallel to the main chain could evolve into a curved chain and eventually become a branch of the main chain. The theoretical predictions agree well with the experimental results, verifying the evolutionary mechanism of Y-branches in ALF.

Effect of tissue viscoelasticity and adjacent phase-changed microbubbles on vaporization process and direct growth threshold of nanodroplet in an ultrasonic field

Understanding the behavior of nanodroplets converted into microbubbles with applied ultrasound is an important problem in tumor therapeutical and diagnostic applications. In this study, a comprehensive model is proposed to investigate the vaporization process and the direct growth threshold of the nanodroplet by following the vapor bubble growth, especially attention devoted to the effect of tissue viscoelasticity and adjacent phase-changed microbubbles (PCMBs). It is shown that the ultrasonic energy must be sufficiently strong to counterbalance the natural condensation of the vapor bubble and the tissue stiffness-inhibitory effect. The softer tissue with a lower shear modulus favors the vaporization process, and the nanodroplet has a lower direct growth threshold in the softer tissue. Moreover, the adjacent PCMBs show a suppression effect on the vaporization process due to the negative value of the secondary Bjerknes force, implying an attractive force, preventing the nanodroplet from escaping from the constraint of the adjacent PCMBs. However, according to the linear scattering theory, the attractive force signifies that the constraint is weak, causing the direct growth threshold to increase in the range of 0.09-0.24 MPa. The weak increase in threshold demonstrates that the direct growth threshold is relatively unaffected by the adjacent PCMBs. The prediction results of our model are in good agreement with the experiment results obtained by the echo enhancement method, in which the threshold is relatively independent of the intermediate concentration. The findings presented here provide physical insight that will be further helpful in understanding the complex behavior of the nanodroplet responses to ultrasound in practical medical applications.

Cavitation bubble structures below a soft boundary in an ultrasonic field

We studied the layer structure of bubbles just below water/air and water/EPE (Expand aple poly ephylene) interfaces using high-speed photography. The layer structure was generated by floating spherical clusters, the source bubbles of which were identified to come from the attachment of bubble nuclei at the interface, the floating of bubbles in the bulk liquid, or bubbles generated on the surface of the ultrasonic transducer. The boundary shape affected the layer structure, which assumed a similar profile below the water/EPE interface. We developed a simplified model composed of a bubble column and bubble chain to describe interface impacts and the interaction of bubbles in a typical branching structure. We found that the resonant frequency of the bubbles is smaller than that of an isolated single bubble. Moreover, the primary acoustic field plays an important role in the generation of the structure. A higher acoustic frequency and pressure were found to shorten the distance between the structure and the interface. A hat-like layer structure of bubbles was more likely to exist in the low-frequency (28 and 40 kHz) intense inertial cavitation field, in which bubbles oscillate violently. By contrast, structures composed of discrete spherical clusters were more likely to form in the relatively weak cavitation field at 80 kHz, in which stable and inertial cavitation coexisted. The theoretical predictions were in good agreement with the experimental observations.

Dynamics of three cavitation bubbles with pulsation and symmetric deformation

A new system of dynamical equations was obtained by using the perturbation and potential flow theory to couple the pulsation and surface deformation of the second-order Legendre polynomials (P₂) of three bubbles in a line. The feasibility and effectiveness of the model were verified by simulating the radial oscillations, surface deformation with P₂, and shape evolution of three bubbles. The spherical radial pulsation and surface deformation of the three bubbles exhibit periodic behavior. The maximum secondary Bjerknes forces (SBFs) on the three bubbles are found not to depend on the system's resonance frequency. Within a stable region, the SBFs of the three bubbles increase with increasing sound pressure amplitude but decrease with increasing distance between the bubbles. The primary Bjerknes force (PBF) on a bubble is significantly higher than the SBF on it.

Theoretical prediction of the scattering of spherical bubble clusters under ultrasonic excitation

Due to the nonlinear vibration of ultrasound contrast agent bubbles, a nonlinear scattered sound field will be generated when bubbles are driven by ultrasound. A bubble cluster consists of numerous bubbles gathering in a spherical space. It has been noted that the forward scattering of a bubble cluster is larger than its backscattering, and some studies have experimentally found the angular dependence of a bubble cluster's scattering signal. In this paper, a theory is proposed to explain the difference of acoustic scattering at different directions of a bubble cluster when it is driven by ultrasound, and predicts the angular distribution of scattered acoustic pressure under different parameters. The theory is proved to be correct under circumstances of small clusters and weak interactions by comparing theoretical results with numerical simulations. This theory not only sheds light on the physics of bubble cluster scattering, but also may contribute to the improvement of ultrasound imaging technology, including ultrasonic harmonic imaging and contrast-enhanced ultrasonography.

Interactions of bubbles in acoustic Lichtenberg figure

The evolution of acoustic Lichtenberg figure (ALF) in ultrasound fields is studied using high-speed photography. It is observed that bubbles travel along the branch to the aggregation region of an ALF, promoting the possibility of large bubble or small cluster formation. Large bubbles move away from the aggregation region while surrounding bubbles are attracted into this structure, and a bubble transportation cycle arises in the cavitation field. A simplified model consisting of a spherical cluster and a chain of bubbles is developed to explain this phenomenon. The interaction of the two units is analyzed using a modified expression for the secondary Bjerknes force in this system. The model reveals that clusters can attract bubbles on the chain within a distance of 2 mm, leading to a bubble transportation process from the chain to the bubble cluster. Many factors can affect this process, including the acoustic pressure, frequency, bubble density, and separation distance. The larger the bubble in the cluster, the broader the attraction region. Therefore, the presence of large bubbles might enhance the process in this system. Local disturbances in bubble density could destroy the ALF structure. The predictions of the model are in good agreement with the experimental phenomena.

Numerical simulations for sonochemistry

Numerical simulations for sonochemistry are reviewed including single-bubble sonochemistry, influence of ultrasonic frequency and bubble size, acoustic field, and sonochemical synthesis of nanoparticles. The theoretical model of bubble dynamics including the effect of non-equilibrium chemical reactions inside a bubble has been validated from the study of single-bubble sonochemistry. By the numerical simulations, it has been clarified that there is an optimum bubble temperature for the production of oxidants inside an air bubble such as OH radicals and H2O2 because at higher temperature oxidants are strongly consumed inside a bubble by oxidizing nitrogen. Unsolved problems are also discussed.

Multibubble Sonoluminescence from a Theoretical Perspective

In the present review, complexity in multibubble sonoluminescence (MBSL) is discussed. At relatively low ultrasonic frequency, a cavitation bubble is filled mostly with water vapor at relatively high acoustic amplitude which results in OH-line emission by chemiluminescence as well as emissions from weakly ionized plasma formed inside a bubble at the end of the violent bubble collapse. At relatively high ultrasonic frequency or at relatively low acoustic amplitude at relatively low ultrasonic frequency, a cavitation bubble is mostly filled with noncondensable gases such as air or argon at the end of the bubble collapse, which results in relatively high bubble temperature and light emissions from plasma formed inside a bubble. Ionization potential lowering for atoms and molecules occurs due to the extremely high density inside a bubble at the end of the violent bubble collapse, which is one of the main reasons for the plasma formation inside a bubble in addition to the high bubble temperature due to quasi-adiabatic compression of a bubble, where "quasi" means that appreciable thermal conduction takes place between the heated interior of a bubble and the surrounding liquid. Due to bubble-bubble interaction, liquid droplets enter bubbles at the bubble collapse, which results in sodium-line emission.

Nonlinear oscillation and acoustic scattering of bubbles

The scattered acoustic pressure and scattered cross section of bubbles is studied using the scattered theory of bubbles. The nonlinear oscillations of bubbles and the scattering acoustic fields of a spherical bubble cluster are numerically simulated based on the bubble dynamic and fluid dynamic. The influences of the interaction between bubbles on scattering acoustic field of bubbles are researched. The results of numerical simulation show that the oscillation phases of bubbles are delayed to a certain extent at different positions in the bubble cluster, but the radii of bubbles during oscillation do not differ too much at different positions. Furthermore, directivity of the acoustic scattering of bubbles is obvious. The scattered acoustic pressures of bubbles are different at the different positions inside and outside of the bubble cluster. The scattering acoustic fields of a spherical bubble cluster depend on the driving pressure amplitude, driving frequency, the equilibrium radii of bubbles, bubble number and the radius of the spherical bubble cluster. These theoretical predictions provide a further understanding of physics behind ultrasonic technique and should be useful for guiding ultrasonic application.

The role of the bubble-bubble interaction on radial pulsations of bubbles

Using a model that with or without considering the interaction between bubbles through the radiated pressure waves, numerical simulations of cavitation bubbles have been performed in order to study the effect of the bubble-bubble interaction on radial pulsations of bubbles. Comparing the results obtained by with or without considering the bubble-bubble interaction, it is suggested that the suppression or enlargement property of expansion ratios of bubbles due to the bubble-bubble interaction largely depends on the ultrasound parameters, the ambient bubble radii, the distances between bubbles and the number of bubbles (in multi-bubble environment, the last two aspects can be expressed using the coupling strength). The frequency response curve of expansion ratio decreases and shifts to left due to the bubble-bubble interaction and the larger the coupling strength is, the more the left-shifting is.

Low and High-Intensity Ultrasound in Dairy Products: Applications and Effects on Physicochemical and Microbiological Quality

Milk and dairy products have a major role in human nutrition, as they contribute essential nutrients for child development. The nutritional properties of dairy products are maintained despite applying traditional processing techniques. Nowadays, so-called emerging technologies have also been implemented for food manufacture and preservation purposes. Low- and high-intensity ultrasounds are among these technologies. Low-intensity ultrasounds have been used to determine, analyze and characterize the physical characteristics of foods, while high-intensity ultrasounds are applied to accelerate particular biological, physical and chemical processes during food product handling and transformation. The objective of this review is to explain the phenomenology of ultrasounds and to detail the differences between low and high-intensity ultrasounds, as well as to present the advantages and disadvantages of each one in terms of the processing, quality and preservation of milk and dairy products. Additionally, it reviews the rheological, physicochemical and microbiological applications in dairy products, such as raw milk, cream, yogurt, butter, ice cream and cheese. Finally, it explains some methodologies for the generation of emulsions, homogenates, crystallization, etc. Currently, low and high-intensity ultrasounds are an active field of study, and they might be promising tools in the dairy industry.

A simple model of bubble cluster dynamics in an acoustic field

The dynamics of bubble clouds induced by ultrasound field are investigated in a regime where the cloud size is much smaller than the ultrasound wavelength. Two frequently used models describing the dynamics of individual bubbles inside a bubble cluster in an acoustic field are studied, one based on the homogeneity assumption, and the other based on the simultaneous motion assumption. A modified formula of the homogenization-based model is presented, and an inherent distinction in bubble-bubble interaction term is found in comparison to the simultaneous motion model. To gain insight into the mechanisms of such distinction, a reduced model unifying these two models is presented, and such distinction is explained by the spatial dependence of the bubble-bubble interaction in a bubble cluster accordingly. To validate the reduced model, the normalized distance γ_bb and the cloud interaction parameter B₀ are used as two scaling parameters, and the comparison between the present model and the coupled Rayleigh-Plesset type equations is made. A conclusion is that, in the weak bubble-bubble interaction case (γ_bb>10), the reduced model can well reproduce the radial motion of bubbles in the cluster during the growth stage and the collapse stage in each acoustic cycle; in the strong bubble-bubble interaction case (γ_bb<10), the growth phase of bubbles in the cluster can be accurately predicted by the reduced model only if B₀ or the amplitude of driving field is small.

Study on Bubble Cavitation in Liquids for Bubbles Arranged in a Columnar Bubble Group

In liquids, bubbles usually exist in the form of bubble groups. Due to their interaction with other bubbles, the resonance frequency of bubbles decreases. In this paper, the resonance frequency of bubbles in a columnar bubble group is obtained by linear simplification of the bubbles’ dynamic equation. The correction coefficient between the resonance frequency of the bubbles in the columnar bubble group and the Minnaert frequency of a single bubble is given. The results show that the resonance frequency of bubbles in the bubble group is affected by many parameters such as the initial radius of bubbles, the number of bubbles in the bubble group, and the distance between bubbles. The initial radius of the bubbles and the distance between bubbles are found to have more significant influence on the resonance frequency of the bubbles. When the distance between bubbles increases to 20 times the bubbles’ initial radius, the coupling effect between bubbles can be ignored, and after that the bubbles’ resonance frequency in the bubble group tends to the resonance frequency of a single bubble’s resonance frequency. Fluent software is used to simulate the bubble growth, shrinkage, and collapse of five and seven bubbles under an ultrasonic field. The simulation results show that when the bubble breaks, the two bubbles at the outer field first begin to break and form a micro-jet along the axis line of the bubbles. Our methods and conclusions will provide a reference for further simulations and indicate the significance of the prevention or utilization of cavitation.

Stable tridimensional bubble clusters in multi-bubble sonoluminescence (MBSL)

In the present work, stable clusters made of multiple sonoluminescent bubbles are experimentally and theoretically studied. Argon bubbles were acoustically generated and trapped using bi-frequency driving within a cylindrical chamber filled with a sulfuric acid aqueous solution (SA85w/w). The intensity of the acoustic pressure field was strong enough to sustain, during several minutes, a large number of positionally and spatially fixed (without pseudo-orbits) sonoluminescent bubbles over an ellipsoidally-shaped tridimensional array. The dimensions of the ellipsoids were studied as a function of the amplitude of the applied low-frequency acoustic pressure (PAc(LF)) and the static pressure in the fluid (P0). In order to explain the size and shape of the bubble clusters, we performed a series of numerical simulations of the hydrodynamic forces acting over the bubbles. In both cases the observed experimental behavior was in excellent agreement with the numerical results. The simulations revealed that the positionally stable region, mainly determined by the null primary Bjerknes force (F→Bj), is defined as the outer perimeter of an axisymmetric ellipsoidal cluster centered in the acoustic field antinode. The role of the high-frequency component of the pressure field and the influence of the secondary Bjerknes force are discussed. We also investigate the effect of a change in the concentration of dissolved gas on the positional and spatial instabilities through the cluster dimensions. The experimental and numerical results presented in this paper are potentially useful for further understanding and modeling numerous current research topics regarding multi-bubble phenomena, e.g. forces acting on the bubbles in multi-frequency acoustic fields, transient acoustic cavitation, bubble interactions, structure formation processes, atomic and molecular emissions of equal bubbles and nonlinear or unsteady acoustic pressure fields in bubbly media.

Hydrodynamic approach to multibubble sonoluminescence

The velocity profile and radiation pressure field of a bubble cluster containing several thousand micro bubbles were obtained by solving the continuity and momentum equations for the bubbly mixture. In this study, the bubbles in the cluster are assumed to be generated and collapsed synchronously with an applied ultrasound. Numerical calculations describing the behavior of a micro bubble in a cluster included the effect of the radiation pressure field from the synchronizing motion of bubbles in the cluster. The radiation pressure generated from surrounding bubbles affects the bubble's behavior by increasing the effective mass of the bubble so that the bubble expands slowly to a smaller maximum size. The light pulse width and spectral radiance from a bubble in a cluster subjected to ultrasound were calculated by adding a radiation pressure term to the Keller-Miksis equation, and the values were compared to experimental values of the multibubble sonoluminescence condition. There was close agreement between the calculated and observed values.

Instability of a bubble chain

Based on the theory of shape instability and diffusive instability for single bubbles, we have studied the instability of an individual bubble in a bubble chain and found that its stable area enlarges the narrower the distance between bubbles. The spatial stability of the bubble chain is due to the secondary Bjerknes force between bubbles. Numerical calculations show the tension of the bubble chain varies with bubble distance and maxima appear at certain distances which could correspond to the stable states of the bubble chain.

Nonlinear bubble dynamics of cavitation

For cavitation clouds generated in a standing sound wave driven by an ultrasonic horn, the nonlinear acoustic wave equation governing cavitation dynamics is numerically solved together with the bubble motion equation under an approximation. This conceptual calculation can qualitatively reproduce the observed characteristics of cavitation.