The bubble cloud as an N-degree of freedom harmonic oscillator

Acoustic tokamak with strongly coupled toroidal bubbles

Gas bubbles stabilized in toroidal 3D-printed cages are good acoustic resonators with an unusual topology. We arrange them in a circular array to obtain what we call an "acoustic tokamak" because of the torus shape of the whole array. We demonstrate experimentally and theoretically that the system features several acoustic modes resulting from the acoustic interaction between tori. The fundamental acoustic mode has a much lower frequency than that of the individual bubbles. The acoustic field along the circle inside the acoustic tokamak is remarkably homogeneous, as shown by our 3D simulations.

Modeling frequency shifts of collective bubble resonances with the boundary element method

Increasing the number of closely packed air bubbles immersed in water changes the frequency of the Minnaert resonance. The collective interactions between bubbles in a small ensemble are primarily in the same phase, causing them to radiate a spherically symmetric field that peaks at a frequency lower than the Minnaert resonance for a single bubble. In contrast, large periodic arrays include bubbles that are further apart than half of the wavelength such that collective resonances have bubbles oscillating in opposite phases, ultimately creating a fundamental resonance at a frequency higher than the single-bubble Minnaert resonance. This work investigates the transition in resonance behavior using a modal analysis of a mass-spring system and a boundary element method. The computational complexity of the full-wave solver is significantly reduced to a linear dependence on the number of bubbles in a rectangular array. The simulated acoustic fields confirm the initial downshift in resonance frequency and the strong influence of collective resonances when the array has hundreds of bubbles covering more than half of the wavelength. These results are essential in understanding the low-frequency resonance characteristics of bubble ensembles, which have important applications in diverse fields such as underwater acoustics, quantum physics, and metamaterial design.

Amplification of Acoustic Forces Using Microbubble Arrays Enables Manipulation of Centimeter-Scale Objects

Manipulation of macroscale objects by sound is fundamentally limited by the wavelength and object size. Resonant subwavelength scatterers such as bubbles can decouple these requirements, but typically the forces are weak. Here we show that patterning bubbles into arrays leads to geometric amplification of the scattering forces, enabling the precise assembly and manipulation of cm-scale objects. We rotate a 1 cm object continuously or position it with 15  μm accuracy, using sound with a 50 cm wavelength. The results are described well by a theoretical model. Our results lay the foundation for using secondary Bjerknes forces in the controlled organization and manipulation of macroscale structures.

Acoustic interaction between 3D-fabricated cubic bubbles

Spherical bubbles are notoriously difficult to hold in specific arrangements in water and tend to dissolve over time. Here, using stereolithographic printing, we built an assembly of millimetric cubic frames overcoming these limitations. Indeed, each of these open frames holds an air bubble when immersed into water, resulting in bubbles that are stable for a long time and are still able to oscillate acoustically. Several bubbles can be placed in any wanted spatial arrangement, thanks to the fabrication process. We show that bubbles are coupled acoustically when disposed along lines, planes or in 3D arrangements, and that their collective resonance frequency is shifted to much lower values, especially for 3D arrangements where bubbles have a higher number of close neighbours. Considering that these cubic bubbles behave acoustically as spherical bubbles of the same volume, we develop a theory allowing one to predict the acoustical emission of any arbitrary group of bubbles, in agreement with experimental results.

Extraction of bubble size and number data from an acoustically-excited bubble chain

The passive-acoustic measurement of bubbly flows could potentially deliver data useful to many industrial and environmental applications. However, acoustic interactions between bubbles complicate interpretations of measured frequencies in terms of the bubble sizes that are of practical interest. Experiments were undertaken on the emissions of a bubble chain when a just-formed bubble at one end of the chain created a sound pulse. This is an idealised paradigm for many applications. The chain was a one-dimensional line of bubbles fixed with known bubble sizes and inter-bubble spacings. Frequencies naturally emitted by the chain were measured for various bubble sizes and spacings, including cases such that the bubbles were close to touching. Semi-empirical fits were found relating the bubble size and number to the lowest and highest-measurable peak frequencies. It was found that all data collapsed onto two curves, one for the lowest-peak and one for the highest-peak frequency. This was confirmed by running numerical simulations for wider ranges of parameters than available experimentally. The results suggest that for a bubble chain, measurements of two peak frequencies could be used to determine the bubble size and also the number of interacting bubbles.

Acoustics of Cubic Bubbles: Six Coupled Oscillators

We introduce cubic bubbles that are pinned to 3D printed millimetric frames immersed in water. Cubic bubbles are more stable over time and space than standard spherical bubbles, while still allowing large oscillations of their faces. We find that each face can be described as a harmonic oscillator coupled to the other ones. These resonators are coupled by the gas inside the cube but also by acoustic interactions in the liquid. We provide an analytical model and 3D numerical simulations predicting the resonance with very good agreement. Acoustically, cubic bubbles prove to be good monopole subwavelength emitters, with nonemissive secondary surface modes.

Eigenmodal resonances of polydisperse bubble systems on a rigid boundary

This paper presents theory and experimental data on the resonance frequency of systems consisting of different-sized air bubbles attached to a rigid wall. Effects of the change in resonant frequency with bubble size and distance between the bubbles were studied. It was found that the symmetric mode resonance frequency of the bubble system decreased with increasing r=R(02)/R(01), where R(01) and R(02) are the equilibrium radii of bubbles in the system. Both the symmetric and antisymmetric modes of oscillation were detected in the experiments, with the resonant frequency of the symmetric mode dominant at small bubble separation and the frequency of the antisymmetric mode dominant when the bubbles were farther apart. A linear coupled-oscillator theoretical model was used to describe the oscillations of the bubble system, in which the method of images was used to approximate the effects of the wall. It was found that there was fair to good agreement between the predictions of the coupled-oscillator model with the experimental data.

Transmission of ultrasound through a single layer of bubbles

We investigate, both experimentally and theoretically, the effect of coupling between resonant scatterers on the transmission coefficient of a model system of isotropic scatterers. The model system consists of a monodisperse layer of bubbles, which exhibit a strong monopole scattering resonance at low ultrasonic frequencies. The layer was a true 2D structure obtained by injecting very monodisperse bubbles (with radius a approximately 100 microm) into a yield-stress polymer gel. Even for a layer with a low concentration of bubbles (areal fraction, n pi a(2), of 10-20%, where n is the number of bubbles per unit area), the ultrasonic transmission was found to be significantly reduced by the presence of bubbles (-20 to -50 dB) and showed a sharp minimum at a particular frequency. Interestingly, this frequency did not correspond to the resonance frequency of the individual, isolated bubbles, but depended markedly on the concentration. This frequency shift is an indication of strong coupling between the bubbles. We propose a simple model, based on a self-consistent relation, which takes into account the coupling between the bubbles and gives good agreement with the measured transmission coefficient.

Ultrasound contrast microbubbles in imaging and therapy: physical principles and engineering

Microbubble contrast agents and the associated imaging systems have developed over the past 25 years, originating with manually-agitated fluids introduced for intra-coronary injection. Over this period, stabilizing shells and low diffusivity gas materials have been incorporated in microbubbles, extending stability in vitro and in vivo. Simultaneously, the interaction of these small gas bubbles with ultrasonic waves has been extensively studied, resulting in models for oscillation and increasingly sophisticated imaging strategies. Early studies recognized that echoes from microbubbles contained frequencies that are multiples of the microbubble resonance frequency. Although individual microbubble contrast agents cannot be resolved-given that their diameter is on the order of microns-nonlinear echoes from these agents are used to map regions of perfused tissue and to estimate the local microvascular flow rate. Such strategies overcome a fundamental limitation of previous ultrasound blood flow strategies; the previous Doppler-based strategies are insensitive to capillary flow. Further, the insonation of resonant bubbles results in interesting physical phenomena that have been widely studied for use in drug and gene delivery. Ultrasound pressure can enhance gas diffusion, rapidly fragment the agent into a set of smaller bubbles or displace the microbubble to a blood vessel wall. Insonation of a microbubble can also produce liquid jets and local shear stress that alter biological membranes and facilitate transport. In this review, we focus on the physical aspects of these agents, exploring microbubble imaging modes, models for microbubble oscillation and the interaction of the microbubble with the endothelium.

Nanometer-resolved collective micromeniscus oscillations through optical diffraction

We study the dynamics of periodic arrays of micrometer-sized liquid-gas menisci formed at superhydrophobic surfaces immersed into water. By measuring the intensity of optical diffraction peaks in real time, we are able to resolve nanometer-scale oscillations of the menisci with submicrosecond time resolution. Upon driving the system with an ultrasound field at variable frequency, we observe a pronounced resonance at a few hundred kilohertz, depending on the exact geometry. By modeling the system using the unsteady Stokes equation, we find that this low resonance frequency is caused by a collective mode of the acoustically coupled oscillating menisci.