Holographic observation of period-doubled and chaotic bubble oscillations in acoustic cavitation

Cavitation erosion by shockwave self-focusing of a single bubble

The ability of cavitation bubbles to effectively focus energy is made responsible for cavitation erosion, traumatic brain injury, and even for catalyse chemical reactions. Yet, the mechanism through which material is eroded remains vague, and the extremely fast and localized dynamics that lead to material damage has not been resolved. Here, we reveal the decisive mechanism that leads to energy focusing during the non-spherical collapse of cavitation bubbles and eventually results to the erosion of hardened metals. We show that a single cavitation bubble at ambient pressure close to a metal surface causes erosion only if a non-axisymmetric energy self-focusing is at play. The bubble during its collapse emits shockwaves that under certain conditions converge to a single point where the remaining gas phase is driven to a shockwave-intensified collapse. We resolve the conditions under which this self-focusing enhances the collapse and damages the solid. High-speed imaging of bubble and shock wave dynamics at sub-picosecond exposure times is correlated to the shockwaves recorded with large bandwidth hydrophones. The material damage from several metallic materials is detected in situ and quantified ex-situ via scanning electron microscopy and confocal profilometry. With this knowledge, approaches to mitigate cavitation erosion or to even enhance the energy focusing are within reach.

Time-delayed interactions on acoustically driven bubbly screens

The influence of the compressibility effects is discussed, including the time delays on the dynamics of acoustically excited bubbly screens. In the linear regime, it is shown that the proposed model for the infinite bubbly screen recovers the results predicted by the effective medium theory (EMT) up to the second order without introducing any fitting parameter when the wavelength is large compared to the inter-bubble distance. However, the effect of boundaries on the finite bubbly screens is shown to lead to the appearance of multiple local resonances and characteristic periodic structures, which limit the applicability of the EMT. In addition, a local resonance phenomenon in the liquid spacings between the bubbles is observed for both the infinite and finite bubbly screens with crystal structures, and these effects vanish as the crystal structure is perturbed. In the nonlinear regime, the current model is treated with time-delay effects as a delay differential equation, which is directly solved numerically. The appearance of an optimal distance for the subharmonic emission for the crystal structures is shown, and the accuracy of the EMT in the strong nonlinear regime is discussed.

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.

Megahertz-rate shock-wave distortion cancellation via phase conjugate digital in-line holography

Holography is a powerful tool for three-dimensional imaging. However, in explosive, supersonic, hypersonic, cavitating, or ionizing environments, shock-waves and density gradients impart phase distortions that obscure objects in the field-of-view. Capturing time-resolved information in these environments also requires ultra-high-speed acquisition. To reduce phase distortions and increase imaging rates, we introduce an ultra-high-speed phase conjugate digital in-line holography (PCDIH) technique. In this concept, a coherent beam passes through the shock-wave distortion, reflects off a phase conjugate mirror, and propagates back through the shock-wave, thereby minimizing imaging distortions from phase delays. By implementing the method using a pulse-burst laser setup at up to 5 million-frames-per-second, time-resolved holograms of ultra-fast events are now possible. This technique is applied for holographic imaging through laser-spark plasma-generated shock-waves and to enable three-dimensional tracking of explosively generated hypersonic fragments. Simulations further advance our understanding of physical processes and experiments demonstrate ultra-high-speed PCDIH techniques for capturing dynamics.

Shock-waves in explosive, supersonic or ionizing environments impart phase distortions to holographic imaging. Here, the authors report an ultra-high-speed phase conjugate digital in-line holography technique where a laser passes through the shock-wave and is reflected back through the phase distortion, thus correcting phase delays.

Bubble dynamics and cavitation intensity in milli-scale channels under an ultrasonic horn

Under a vibrating ultrasonic horn device, intense cavitation occurs but is restricted to a small volume due to strong attenuation effects. In this study, milli-scale channels were introduced under the horn. The effect of this on the cavitation development and intensity within the channels were explored. High speed videography of up to 100,000 fps and acoustic signal acquisition through hydrophone were conducted. Cavitation intensity was observed to increase within the channels as compared to free field condition. Bubble density increased with a decrease in channel diameter and a rise in ultrasonic amplitude. Furthermore, an intriguing phenomenon of large bubble cluster formation near the channel exit (20 mm away from the horn surface) was detected. The oscillation behaviour of these clusters is dependent on both channel diameter and ultrasonic amplitude. At the maximum ultrasonic amplitude, the clusters reached maximum radiuses exceeding 3 mm and collapsed violently. Repetitive transient collapses near the exit region suggest that the introduction of milli-scale channels could extend the effective cavitation zone length and enhance the overall cavitation intensity under an ultrasonic horn.

Collective nonlinear behavior of interacting polydisperse microbubble clusters

Acoustically excited microbubbles (MBs) have shown to exhibit rich dynamics, enabling them to be employed in various applications ranging from chemistry to medicine. Exploiting the full potential of MBs for applications requires a good understanding of their complex dynamics. Improved understanding of MB oscillations can lead to further enhancement in optimizing their efficacy in many applications and also invent new ones. Oscillating MBs have been shown to generate secondary pressure waves that modify the dynamics of the MBs in their proximity. A modified Keller-Miksis equation is used to account for inter-bubble interactions. The oscillatory dynamics of each MB within clusters was computed by numerically solving the resulting system of coupled nonlinear second order differential equations in potential fluid flow. Frequency response analysis and bifurcation diagrams were employed to track the dynamics of interacting MBs. We start with investigating the effect of inter-bubble interactions for cases of three and four MBs over a wide range of acoustic and geometric parameters. Emergent collective behavior was observed which are dominated by the dynamics of the largest MB within the cluster. The emergent dynamics of smaller MBs within clusters can be characterized by constructive and destructive inter-bubble interactions. In constructive interactions, the radial oscillations of smaller MBs matched those of the largest MB and their oscillations are amplified. In destructive interactions, the oscillations of smaller bubbles are suppressed so that their oscillations match those of the largest MB. Furthermore, a special case of constructive interactions is presented where dominant MB (largest) can force smaller MBs into period doubling and subharmonic oscillations. The collective behavior is further investigated in large MB cluster and it is shown that largest MBs, even in small numbers can force smaller ones into period doubling and subharmonic oscillations.

Study of non-spherical bubble oscillations under acoustic irradiation in viscous liquid

The effect of dissipation on the shape stability of a harmonically excited bubble is investigated. The employed liquid is the highly viscous glycerine. The rate of the dissipation is controlled through the alteration of viscosity of the liquid by varying its temperature. The mean radius of the bubble during its radial oscillation is described by the Keller-Miksis equation. Two approaches are used to describe the surface oscillations. The first model solves the surface dynamics equations of each mode together with the transport equation of the vorticity in the liquid domain. The second model approximates the transport equation, which is a partial differential equation, with a boundary layer approximation reducing the required computational resources significantly. The comparison of the surface models shows qualitative agreement at low dissipation rate; however, at high viscosity the application of the full transport equation is mandatory. The results show that an increasing rate of dissipation can significantly extend the shape stable domains in the excitation frequency-pressure amplitude parameter plane. Nevertheless, the collapse strength is decreasing due to the highly damped oscillations. It has been found that an optimal range of dissipation rate in terms of temperature can be defined expressing a good compromise between the collapse strength and surface stability. The computations are carried out by an in-house GPU accelerated initial value problem solver.

Performance characterisation of a passive cavitation detector optimised for subharmonic periodic shock waves from acoustic cavitation in MHz and sub-MHz ultrasound

We describe the design, construction and characterisation of a broadband passive cavitation detector, with the specific aim of detecting low frequency components of periodic shock waves, with high sensitivity. A finite element model is used to guide selection of matching and backing layers for the shock wave passive cavitation detector (swPCD), and the performance is evaluated against a commercially available device. Validation of the model, and characterisation of the swPCD is achieved through experimental detection of laser-plasma bubble collapse shock waves. The final swPCD design is 20 dB more sensitive to the subharmonic component, from acoustic cavitation driven at 220 kHz, than the comparable commercial device. This work may be significant for monitoring cavitation in medical applications, where sensitive detection is critical, and higher frequencies are more readily absorbed by tissue.

An analysis of the acoustic cavitation noise spectrum: The role of periodic shock waves

Research on applications of acoustic cavitation is often reported in terms of the features within the spectrum of the emissions gathered during cavitation occurrence. There is, however, limited understanding as to the contribution of specific bubble activity to spectral features, beyond a binary interpretation of stable versus inertial cavitation. In this work, laser-nucleation is used to initiate cavitation within a few millimeters of the tip of a needle hydrophone, calibrated for magnitude and phase from 125 kHz to 20 MHz. The bubble activity, acoustically driven at f₀ = 692 kHz, is resolved with high-speed shadowgraphic imaging at 5 × 10⁶ frames per second. A synthetic spectrum is constructed from component signals based on the hydrophone data, deconvolved within the calibration bandwidth, in the time domain. Cross correlation coefficients between the experimental and synthetic spectra of 0.97 for the f₀/2 and f₀/3 regimes indicate that periodic shock waves and scattered driving field predominantly account for all spectral features, including the sub-harmonics and their over-harmonics, and harmonics of f₀.

Numerical 3D flow simulation of ultrasonic horns with attached cavitation structures and assessment of flow aggressiveness and cavitation erosion sensitive wall zones

As a contribution to a better understanding of cavitation erosion mechanisms, a compressible inviscid finite volume flow solver with barotropic homogeneous liquid-vapor mixture cavitation model is applied to ultrasonic horn set-ups with and without stationary specimen, that exhibit attached cavitation at the horn tip. Void collapses and shock waves, which are closely related to cavitation erosion, are resolved. The computational results are compared to hydrophone, shadowgraphy and erosion test data. At the horn tip, vapor volume and topology, subharmonic oscillation frequency as well as the amplitude of propagating pressure waves are in good agreement with experimental data. For the evaluation of flow aggressiveness and the assessment of erosion sensitive wall zones, statistical analyses of wall loads and of the multiplicity of distinct collapses in wall-adjacent flow regions are applied to the horn tip and the stationary specimen. An a posteriori projection of load collectives, i.e. cumulative collapse rate vs. collapse pressure, onto a reference grid eliminates the grid dependency effectively for attached cavitation at the horn tip, whereas a significant grid dependency remains at the stationary specimen. The load collectives show an exponential decrease towards higher collapse pressures. Erosion sensitive wall zones are well predicted for both, horn tip and stationary specimen, and load profiles are in good qualitative agreement with measured topography profiles of eroded duplex stainless steel samples after long-term runs. For the considered amplitude and gap width according to ASTM G32-10 standard, the analysis of load collectives reveals that the distinctive erosive ring shape at the horn tip can be attributed to frequent breakdown and re-development of a small portion of the tip-attached cavity. This partial breakdown of the attached cavity repeats at each driving cycle and is associated with relatively moderate collapse peak pressures, whereas the stationary specimen is rather unfrequently stressed at the end of each subharmonic oscillation cycle by the violent collapse of the complete cavity.

Effects of coupling, bubble size, and spatial arrangement on chaotic dynamics of microbubble cluster in ultrasonic fields

Microbubble clustering may occur when bubbles become bound to targeted surfaces or are grouped by acoustic radiation forces in medical diagnostic applications. The ability to identify the formation of such clusters from the ultrasound echoes may be of practical use. Nonlinear numerical simulations were performed on clusters of microbubbles modeled by the modified Keller-Miksis equations. Encapsulated bubbles were considered to mimic practical applications but the aim of the study was to examine the effects of inter-bubble spacing and bubble size on the dynamical behavior of the cluster and to see if chaotic or bifurcation characteristics could be helpful in diagnostics. It was found that as microbubbles were clustered closer together, their oscillation amplitude for a given applied ultrasound power was reduced, and for inter-bubble spacing smaller than about ten bubble radii nonlinear subharmonics and ultraharmonics were eliminated. For clustered microbubbles, as for isolated microbubbles, an increase in the applied acoustic power caused bifurcations and transition to chaos. The bifurcations preceding chaotic behavior were identified by Floquet analysis and confirmed to be of the period-doubling type. It was found that as the number of microbubbles in a cluster increased, regularization occurred at lower ultrasound power and more windows of order appeared.

Mathematical modeling of microbubble cavitation at 70 kHz and the importance of the subharmonic in drug delivery from micelles

In order to gain insight into the experimental observation of ultrasound-induced release of drugs from micelles, we modeled the dynamic oscillations of a 10-μm-diameter bubble insonated at 70kHz. The Parlitz modification of the Keller-Miksis model was employed to generate bubble dynamics over a wide range of mechanical index values. The resulting Poincaré maps and bifurcation diagram show that bubble oscillations bifurcate at a MI value of 0.32, then return apparently to a single mode before displaying a sudden onset of chaotic behavior at 0.35. The experimental release of drug from micelles occurs at a MI value of 0.37 and correlates with the intensity of the subharmonic in (μW/cm(2)) of the acoustic spectrum. The dynamic model shows the return to single mode at a MI value of 0.43, and bifurcation leading to chaos at values above 0.5. The correlation between the chaotic behavior predicted by the model and drug release hints at insonation conditions that could facilitate drug delivery.

Bubble population phenomena in sonochemical reactor: I estimation of bubble size distribution and its number density with pulsed sonication - laser diffraction method

To characterize the bubble populations (size and its number distribution) in a sonochemical reactor, a simple but powerful technique based on the Fraunhofer laser diffraction (LD) has been proposed. In this method, the acoustic wave disturbance to the laser probe in the sonochemical reaction field was eliminated by the temporal separation using pulsed sonication (pulsed LD). With this relatively simple strategy, the temporal development of the bubble size distribution could be evaluated by pulsed LD. A number density of bubbles was estimated by using a calibration data obtained with monosized standard particles. In addition, the effect of pulse length and a surfactant on the bubble population phenomena in a multibubble system are discussed.

Suppressing chaotic oscillations of a spherical cavitation bubble through applying a periodic perturbation

Nonlinear dynamics of a spherical cavitation bubble was studied. A method based on applying a periodic perturbation to suppress chaotic oscillations is introduced. The relation between this method and dual frequency ultrasonic irradiation is correlated to prove its applicability in applications involving cavitation phenomena. Results indicated its strong impact on reducing the chaotic oscillations to regular ones. The governing parameters are the secondary frequency value and the phase difference between the secondary frequency and the fundamental one. In the end, the possible application of this method in high intensity focused ultrasound tumor ablation as an instance, is discussed accounting for both free bubbles and microbubbles.

Inside a collapsing bubble: sonoluminescence and the conditions during cavitation

Acoustic cavitation, the growth and rapid collapse of bubbles in a liquid irradiated with ultrasound, is a unique source of energy for driving chemical reactions with sound, a process known as sonochemistry. Another consequence of acoustic cavitation is the emission of light [sonoluminescence (SL)]. Spectroscopic analyses of SL from single bubbles as well as a cloud of bubbles have revealed line and band emission, as well as an underlying continuum arising from a plasma. Application of spectrometric methods of pyrometry as well as tools of plasma diagnostics to relative line intensities, profiles, and peak positions have allowed the determination of intracavity temperatures and pressures. These studies have shown that extraordinary conditions (temperatures up to 20,000 K; pressures of several thousand bar; and heating and cooling rates of >10(12) K s(1)) are generated within an otherwise cold liquid.

Acoustic cavitation, bubble dynamics and sonoluminescence

Basic facts on the dynamics of bubbles in water are presented. Measurements on the free and forced radial oscillations of single spherical bubbles and their acoustic (shock waves) and optic (luminescence) emissions are given in photographic series and diagrams. Bubble cloud patterns and their dynamics and light emission in standing acoustic fields are discussed.

Evolution of an 1 MHz ultrasonic cavitation bubble field in a chopped irradiation mode

In this paper the evolution of an ultrasonic cavitation bubble field is studied by means of the void rate, the cavitation noise power and the electric power that feeds the ultrasonic transducer. The ultrasonic irradiation is performed in chopped mode. It is observed two kinds of evolution that differ respectively by a slow (A regime) and a fast (B regime) void rate increase. They correspond to cavitation regimes that are identified as respectively a stable cavitation and an inertial cavitation field. The beginning of the fast increase of the void rate is delayed from the irradiation start and this delay depends on the chopping frequency of the irradiation mode.

Alternative method to deduce bubble dynamics in single-bubble sonoluminescence experiments

In this paper we present an experimental approach that allows to deduce the important dynamical parameters of single sonoluminescing bubbles (pressure amplitude, ambient radius, radius-time curve). The technique is based on a few previously confirmed theoretical assumptions and requires the knowledge of quantities such as the amplitude of the electric excitation and the phase of the flashes in the acoustic period. These quantities are easily measurable by a digital oscilloscope, avoiding the cost of the expensive lasers or ultrafast cameras of previous methods. We show the technique in a particular example and compare the results with conventional Mie scattering. We find that within the experimental uncertainties these two techniques provide similar results.

Stable nonspherical bubble collapse including period doubling in sonoluminescence

We present observations of stable spherical symmetry broken states in single bubble sonoluminescence including observations of period doubled states. States observed involve both spatially oriented states and states with a tumbling symmetry axis. The observations are made using a fiber based four-channel correlation scheme. The measurements are made both with and without narrow band optical filters. The symmetry broken states are seen in all cases even using a 650+/-40-nm filter. This fact may be used to distinguish between different theories for the light emission. Prior to the measurements reported here, theoretical attempts to explain observations of period doubling bifurcation phenomena in single bubble sonoluminescence were centered on radially bifurcated collapses. The present experiments show unequivocally that the observations are primarily a result of breaking the spherical symmetry in the bubble collapse. Period doubling will at most show up as secondary effects in the total light output, if at all.

Period-doubling bifurcations from breaking the spherical symmetry in sonoluminescence: experimental verification

Using a fiber-based four-channel correlation scheme to investigate spatial and temporal correlations, we show that observations of period-doubling phenomena in single bubble sonoluminescence are primarily a result of spontaneously breaking the spherical symmetry in the bubble collapse and, at most, may show up as secondary effects in the flash-to-flash spatially integrated light output.

Characterisation of the acoustic cavitation cloud by two laser techniques

An experimental investigation of the size and volumetric concentration of acoustic cavitation bubbles is presented. The cavitation bubble cloud is generated at 20 kHz by an immersed horn in a rectangular glass vessel containing bi-distilled water. Two laser techniques, laser diffraction and phase Doppler interferometry, are implemented and compared. These two techniques are based on different measuring principles. The laser diffraction technique analyses the light pattern scattered by the bubbles along a line-of-sight of the experimental vessel (spatial average). The phase Doppler technique is based on the analysis of the light scattered from single bubbles passing through a set of interference fringes formed by the intersection of two laser beams: bubble size and velocity distributions are extracted from a great number of single-bubble events (local and temporal average) but only size distributions are discussed here. Difficulties arising in the application of the laser diffraction technique are discussed: in particular, the fact that the acoustic wave disturbs the light scattering patterns even when there are no cavitation bubbles along the measurement volume. As a consequence, a procedure has been developed to correct the raw data in order to get a significant bubble size distribution. After this data treatment has been applied the results from the two measurement techniques show good agreement. Under the emitter surface, the Sauter mean diameter D(3, 2) is approximately 10 microm by phase Doppler measurement and 7.5 microm by laser diffraction measurement at 179 W. Note that the mean measured diameter is much smaller than the resonance diameter predicted by the linear theory (about 280 microm). The influence of the acoustic power is investigated. Axial and radial profiles of mean bubble diameters and void fraction are also presented.

High-speed off-axis holographic cinematography with a copper-vapor-pumped dye laser

A series of coherent light pulses is generated by pumping a dye laser with the pulsed output of a copper-vapor laser at rates of as much as 20 kHz. Holograms are recorded at this pulse rate on a rotating holographic plate. This technique of high-speed holographic cinematography is demonstrated by viewing the bubble filaments that appear in water under the action of a sound field of high intensity.

Mie scattering used to determine spherical bubble oscillations

Linearly polarized laser light is scattered from an oscillating, acoustically levitated bubble, and the scattered intensity is measured with a suitable photodetector. The output photodetector current is converted into a voltage and digitized. For spherical bubbles, the scattered intensity I(rel)(R,theta,t) as a function of radius R and angle theta is calculated theoretically by solving the boundary value problem (Mie theory) for the water-bubble interface. The inverse transfer function R(I) is obtained by integrating over the photodetector solid angle centered at some constant theta. Using R(I) as a look-up table, the radius vs time [R(t)] response is calculated from the measured intensity vs time [I(exp)(R,t)].

In-line holography with a frequency doubled Nd:YAG laser for particle size analysis

An arrangement for determining the size distribution of small particles (e.g., droplets or bubbles) is presented. It consists of taking high speed holograms with a frequency doubled Nd:YAG laser, reconstructing the real image with an argon-ion laser, and a digital image processing system with a random access image dissector camera and two cascaded computers for filtering, segmentation, and higher recognition tasks. Results are presented for cavitation bubbles as test objects. It is shown that the quality of the holograms is sufficient for detecting bubbles with a diameter of <20 mum by digital image processing with the present configuration.