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Physics of fluids 35(1), 016126 (2023). doi:10.1063/5.0131457, We explore the pressure evolution and structural dynamics of transient phase transitions in a microfluidic water jet after laser-induced dielectric breakdown. To this end, we use a combined approach of near-field holography with single femtosecond x-ray free-electron laser pulses and x-ray diffraction. During cavitation and jet breakup, we observe shock wave emission along the jet. The formation of the shockwave is accompanied by pronounced changes in the structure factor of water as an evidence by a shift in the water diffraction peak. This indicates a transition to a high density liquid structure induced by the transient pressure increase., Published by American Institute of Physics, [Erscheinungsort nicht ermittelbar]

The dynamics of a laser-induced bubble on top of a solid cylinder is studied both experimentally and numerically. When the bubble is generated close to the flat top along the axis of the cylinder and its maximum radius exceeds the one of the flat top surface, it collapses in the form of a mushroom with a footing on the cylinder, a long stem and a hat-like cap typical for a mushroom head. The head may collapse forming a thin, fast liquid jet into the stem, depending on bubble size and bubble distance to the top of the cylinder. Several experimental and numerical examples are given. The results represent a contribution to understand the behavior of bubbles collapsing close to structured surfaces and in particular, how thin, fast jets are generated.

The main aim of this paper is to demonstrate the benefit of the application of high-performance computing techniques in the field of non-linear science through two kinds of dynamical systems as test models. It is shown that high-resolution, multi-dimensional parameter scans (in the order of millions of parameter combinations) via an initial value problem solver are an efficient tool to discover new features of dynamical systems that are hard to find by other means. The employed initial value problem solver is an in-house code written in C++ and CUDA C software environments, which can exploit the high processing power of professional graphics cards (GPUs). The first test model is the Keller–Miksis equation, a non-linear oscillator describing the dynamics of a driven single spherical gas bubble placed in an infinite domain of liquid. This equation is important in the field of cavitation and sonochemistry. Here, the high-resolution parameter scans gave us the opportunity to lay down the basis of a non-feedback technique to control multi-stability in which direct selection of the desired attractor is possible. The second test model is related to a pressure relief valve that can exhibit a special kind of impact dynamics called grazing impact. A fine scan of the initial conditions revealed a second focal point of the grazing lines in the initial-condition space that was hidden in previous studies.

A parameter identification technique of an underlying bubble model of an experimentally observed single bubble in a cluster under dual-frequency external forcing is presented. The measurements are carried out via high-speed camera recordings at a rate of 162750 frames per second. The used frequencies during the experiment are 25 kHz and 50 kHz. With a digital image processing technique, the measured bubble radius as a function of time is determined. The employed governing equation for the parameter fitting is the Keller–Miksis equation being a second order ordinary differential equation. The unknown four-dimensional parameter space is composed by the two pressure amplitudes, the phase shift of the dual-frequency driving and the equilibrium size of the bubble. In order to obtain an optimal parameter set within reasonable time, an in-house initial value problem solver is used running on a graphics processing unit (GPU). The error function measuring the distance between the numerical simulations and the measurement is based on the identification of the maximum bubble radii during each subsequent period of the external forcing. The results show a consistent estimation of both pressure amplitudes. The optima of phase shift and equilibrium bubble size are less significant due to a valley-like shape of the error function. Nevertheless, reasonable values are found that lead to estimations of pressure and temperature peaks during bubble collapse.

Experimental analysis of cavitation bubble dynamics typically uses optical imaging and photographic recording. However, the images are often severely affected by distortions and shadows due to refraction and total reflection of the illuminating light at the liquid–gas interface of the bubble. Optical ray tracing may become a powerful tool for the analysis process by assisting in the comparison of experiments to numerical two-phase flow simulations. The novelty of the present approach consists in digitizing almost the complete experimental arrangement with all its optically relevant elements and objects—including a numerical model of the yet unknown bubble—and numerically photographing the scene via ray tracing. The method is applied to the jetting dynamics of single bubbles collapsing at a solid wall. Here, ray tracing can help in the interpretation of raw experimental data concerning the complex bubble interface deformations and internal structures during the collapse. The precise shape of the highly dynamical bubbles can be inferred, thus ray tracing provides a correction method for velocity values of the liquid jets. Strong evidence is found for the existence of an ultra-short-time, fast jet, exceeding velocities known to date in the field. Graphic abstract

XFEL radiation based on the stochastic SASE principle can be described by a low-dimensional configuration space. This space of pulse shapes can be sufficiently sampled before an imaging experiment. This approach is used to implement near-field holography of dynamic processes, demonstrated for the example of a micro-fluidic jet illuminated by the divergent wavefront emanating from a compound refractive lens nano-focus. Droplet formation in the break-up regime of the jet, as well as the hydrodynamic phenomena following plasma generation by an intense infrared laser pulse, can be imaged, based on flat-field corrected holograms and subsequent phase retrieval., X-ray free-electron lasers (XFELs) have opened up unprecedented opportunities for time-resolved nano-scale imaging with X-rays. Near-field propagation-based imaging, and in particular near-field holography (NFH) in its high-resolution implementation in cone-beam geometry, can offer full-field views of a specimen’s dynamics captured by single XFEL pulses. To exploit this capability, for example in optical-pump/X-ray-probe imaging schemes, the stochastic nature of the self-amplified spontaneous emission pulses, i.e. the dynamics of the beam itself, presents a major challenge. In this work, a concept is presented to address the fluctuating illumination wavefronts by sampling the configuration space of SASE pulses before an actual recording, followed by a principal component analysis. This scheme is implemented at the MID (Materials Imaging and Dynamics) instrument of the European XFEL and time-resolved NFH is performed using aberration-corrected nano-focusing compound refractive lenses. Specifically, the dynamics of a micro-fluidic water-jet, which is commonly used as sample delivery system at XFELs, is imaged. The jet exhibits rich dynamics of droplet formation in the break-up regime. Moreover, pump–probe imaging is demonstrated using an infrared pulsed laser to induce cavitation and explosion of the jet.

Ultrasonic microreactors are increasingly applied to particle synthesis, crystallization processes, or organic synthesis involving solids because of the clogging prevention offered by ultrasound ir...

Journal of synchrotron radiation 28(3), 987 - 994 (2021). doi:10.1107/S1600577521003052, Single-pulse holographic imaging at XFEL sources with 1012 photons delivered in pulses shorter than 100 fs reveal new quantitative insights into fast phenomena. Here, a timing and synchronization scheme for stroboscopic imaging and quantitative analysis of fast phenomena on time scales (sub-ns) and length-scales (���100 nm) inaccessible by visible light is reported. A fully electronic delay-and-trigger system has been implemented at the MID station at the European XFEL, and applied to the study of emerging laser-driven cavitation bubbles in water. Synchronization and timing precision have been characterized to be better than 1 ns., Published by Wiley-Blackwell, [S.l.]

A feedforward control technique is presented to steer a harmonically driven, non-linear system between attractors in the frequency-amplitude parameter plane of the excitation. The basis of the technique is the temporary addition of a second harmonic component to the driving. To illustrate this approach, it is applied to the Keller-Miksis equation describing the radial dynamics of a single spherical gas bubble placed in an infinite domain of liquid. This model is a second-order, non-linear ordinary differential equation, a non-linear oscillator. With a proper selection of the frequency ratio of the temporary dual-frequency driving and with the appropriate tuning of the excitation amplitudes, the trajectory of the system can be smoothly transformed between specific attractors; for instance, between period-3 and period-5 orbits. The transformation possibilities are discussed and summarized for attractors originating from the subharmonic resonances and the equilibrium state (absence of external driving) of the system.

A small, spherical bubble of high internal pressure is inserted into water at constant ambient pressure as a model of a laser-induced bubble. Its subsequent dynamics near a flat solid boundary is studied in dependence on the distance of the bubble to the boundary by numerically solving the Navier-Stokes equations with the help of the open source software environment OpenFOAM. Implemented is the finite volume method for discretization of the equations of motion and the volume of fluid method for capturing the interface between the bubble interior and exterior. The bubble contains a small amount of non-condensable gas that is treated as an ideal gas. The liquid is water obeying the Tait-equation. Surface tension is included where necessary. The evolution of the bubble shape and a selection of pressure and velocity fields are given for normalized distances $D^* = D/R_{\rm max}$ between 0 and 3 ($D$ = initial distance of the bubble centre to the boundary, $R_{\rm max}$ = maximum radius the bubble would attain without any boundary). $R_{\rm max} = 500 ��$m is chosen for the study. Normal axial jet formation ($\sim 100$ m s$^{-1}$) by axial flow focusing is found for $0.24 \le D^* \le 3$ and the change to a different type of axial jet formation ($\sim 1000$ m s$^{-1}$) by annular-liquid-flow collision for bubbles very near to the solid boundary ($0 \le D^* \le 0.2$). The transition region ($0.2 < D^* < 0.24$) is characterized by additional inbound and outbound annular jets. Remarkably, the inclusion of the viscosity of the water is decisive to get the fast jets., 32 pages, 26 figures

A novel method to control multistability of nonlinear oscillators by applying dual-frequency driving is presented. The test model is the Keller–Miksis equation describing the oscillation of a bubble in a liquid. It is solved by an in-house initial-value problem solver capable to exploit the high computational resources of professional graphics cards. During the simulations, the control parameters are the two amplitudes of the acoustic driving at fixed, commensurate frequency pairs. The high-resolution bi-parametric scans in the control parameter plane show that a period-2 attractor can be continuously transformed into a period-3 one (and vice versa) by proper selection of the frequency combination and by proper tuning of the driving amplitudes. This phenomenon has opened a new way to drive the system to a desired, pre-selected attractor directly via a non-feedback control technique without the need of the annihilation of other attractors. Moreover, the residence in transient chaotic regimes can also be avoided. The results are supplemented with simulations obtained by the boundary-value problem solver AUTO, which is capable to compute periodic orbits directly regardless of their stability, and trace them as a function of a control parameter with the pseudo-arclength continuation technique.

The acoustic waves being generated during the motion of a bubble in water near a solid boundary are calculated numerically. The open source package OpenFOAM is used for solving the Navier-Stokes equation and extended to include nonlinear acoustic wave effects via the Tait equation for water. A bubble model with a small amount of gas is chosen, the gas obeying an adiabatic law. A bubble starting from a small size with high internal pressure near a flat, solid boundary is studied. The sequence of events from bubble growth via axial microjet formation, jet impact, annular nanojet formation, torus-bubble collapse, and bubble rebound to second collapse is described. The different pressure and tension waves with their propagation properties are demonstrated.

Bubble dynamics and luminol emissions of cavitation in sub-millimeter-sized PFA flow tubes, submerged in an ultrasonic bath reactor, are studied at 27 kHz driving frequency. Nucleation of cavitation inside the tubes only takes place via a free interface, realized here in form of an alternating water-air slug flow. High-speed recordings show that cavitation bubbles in the water slugs often develop localized structures in form of clusters or bubble plugs, and that such structures can be seeded via a single pinch-off from the free interface. Within the structures, bubbles strongly interact and frequently undergo merging or splitting events. Due to the mutual interaction and resulting motion, bubbles often collapse with a fast displacement, suggesting jetting dynamics. Bubble compression ratios are estimated on basis of observed individual bubble dynamics and numerical fitting by a single bubble model. The resulting peak temperatures around 3000 K allow for dissociation of water vapor. This is in accordance with observed sonochemiluminescence from luminol, originating from active bubble zones in the tubes., Comment: 23 pages, 7 figures

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 (Rmax-RE)/RE, where RE is the equilibrium size of the bubble and Rmax 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 (Rmax-RE)/RE=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 (Rmax-RE)/RE=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.

The detailed link of liquid phase sonochemical reactions and bubble dynamics is still not sufficiently known. To further clarify this issue, we image sonoluminescence and bubble oscillations, translations, and shapes in an acoustic cavitation setup at 23kHz in sulfuric acid with dissolved sodium sulfate and xenon gas saturation. The colour of sonoluminescence varies in a way that emissions from excited non-volatile sodium atoms are prominently observed far from the acoustic horn emitter ("red region"), while such emissions are nearly absent close to the horn tip ("blue region"). High-speed images reveal the dynamics of distinct bubble populations that can partly be linked to the different emission regions. In particular, we see smaller strongly collapsing spherical bubbles within the blue region, while larger bubbles with a liquid jet during collapse dominate the red region. The jetting is induced by the fast bubble translation, which is a consequence of acoustic (Bjerknes) forces in the ultrasonic field. Numerical simulations with a spherical single bubble model reproduce quantitatively the volume oscillations and fast translation of the sodium emitting bubbles. Additionally, their intermittent stopping is explained by multistability in a hysteretic parameter range. The findings confirm the assumption that bubble deformations are responsible for pronounced sodium sonoluminescence. Notably the observed translation induced jetting appears to serve as efficient mixing mechanism of liquid into the heated gas phase of collapsing bubbles, thus potentially promoting liquid phase sonochemistry in general.

Cavitation bubbles collapsing in the vicinity to a solid substrate induce intense micro-convection at the solid. Here we study the transient near-wall flows generated by single collapsing bubbles by chronoamperometric measurements synchronously coupled with high-speed imaging. The individual bubbles are created at confined positions by a focused laser pulse. They reach a maximum expansion radius of approximately 425μm. Several stand-off distances to the flat solid boundary are investigated and all distances are chosen sufficiently large that no gas phase of the expanding and collapsing bubble touches the solid directly. With a microelectrode embedded into the substrate, the time-resolved perturbations in the liquid shear layer are probed by means of a chronoamperometric technique. The measurements of electric current are synchronized with high-speed imaging of the bubble dynamics. The perturbations of the near-wall layer are found to result mainly from ring vortices created by the jetting bubble. Other bubble induced flows, such as the jet and flows following the radial bubble oscillations are perceptible with this technique, but show a minor influence at the stand-off distances investigated.

Laser generated cavitation bubbles are numerically modeled with the finite volume method using the open source software package OpenFOAM. The alterations applied to the native code are described and validated by solving the spherical bubble collapse problem and comparing the solution with the Gilmore model and experiments. Problems of spherical stability and their connection with the mesh are discussed. Shock wave emission upon laser bubble generation and bubble collapse is modeled by inserting the Tait equation for the liquid (water) into the code. The results are compared with calculations by Hickling and Plesset and experiments. The calculations are extended to the problem of cavitation bubble collapse in front of a solid boundary.

Ultrasonic horn transducers are frequently used in applications of acoustic cavitation in liquids. It has been observed that if the horn tip is sufficiently small and driven at high amplitude, cavitation is very strong, and the tip can be covered entirely by the gas/vapor phase for longer time intervals. A peculiar dynamics of the attached cavity can emerge with expansion and collapse at a self-generated frequency in the subharmonic range, i.e. below the acoustic driving frequency. The term "acoustic supercavitation" was proposed for this type of cavitation Žnidarčič et al. (2014) [1]. We tested several established hydrodynamic cavitation models on this problem, but none of them was able to correctly predict the flow features. As a specific characteristic of such acoustic cavitation problems lies in the rapidly changing driving pressures, we present an improved approach to cavitation modeling, which does not neglect the second derivatives in the Rayleigh-Plesset equation. Comparison with measurements of acoustic supercavitation at an ultrasonic horn of 20kHz frequency revealed a good agreement in terms of cavity dynamics, cavity volume and emitted pressure pulsations. The newly developed cavitation model is particularly suited for simulation of cavitating flow in highly fluctuating driving pressure fields.

The aim of this study is to investigate acoustic streaming in water at very high ultrasonic frequencies, namely beyond 100 MHz. At such high frequencies, the dissipation length of acoustic waves shrinks considerably, and the acoustic streaming transforms from the well-known Eckart type into a Stuart-Lighthill type: While Eckart streaming is driven by a small momentum transfer along the path of a weakly damped travelling sound wave, Stuart-Lighthill streaming is generated by rather local and strong momentum transfer of a highly damped and therefore rapidly decaying wave. Then the inertia of the induced flow cannot be neglected anymore, and a potentially turbulent jet flow emerges. Here we report on streaming velocity measurements for the case where the sound is completely absorbed within a region much smaller than the generated jet. In contrast to previous work in this frequency range, where mainly surface acoustic wave transducers have been employed, we use piston-type transducers that emit vertically to the transducer surface. The acoustic streaming effects are characterized by ink front tracking and particle tracking velocimetry, and by numerical studies. The results show narrow high-speed jet flows that extend much farther into the liquid than the acoustic field. Velocities of several m/s are observed.

Intense microscale convection is produced by single cavitation bubbles. Ring vortices can be formed by bubbles collapsing near solid surfaces. Such unsteady flow fields are measured with a high-speed particle imaging velocimetry (\textmu{}PIV) setup. Net liquid displacement is tracked and visualized by synthesized Lagrangian ink maps.

The interest in application of ultrasonic cavitation for cleaning and surface treatment processes has increased greatly in the last decades. However, not much is known about the behavior of cavitation bubbles inside the microstructural features of the solid substrates. Here we report on an experimental study on dynamics of acoustically driven (38.5 kHz) cavitation bubbles inside the blind and through holes of PMMA plates by using high-speed imaging. Various diameters of blind (150, 200, 250 and 1000 µm) and through holes (200 and 1000 µm) were investigated. Gas bubbles are usually trapped in the holes during substrate immersion in the liquid thus preventing their complete wetting. We demonstrate that trapped gas can be successfully removed from the holes under ultrasound agitation. Besides the primary Bjerknes force and acoustic streaming, the shape oscillations of the trapped gas bubble seem to be a driving force for bubble removal out of the holes. We further discuss the bubble dynamics inside microholes for water and Cu2+ salt solution. It is found that the hole diameter and partly the type of liquid media influences the number, size and dynamics of the cavitation bubbles. The experiments also showed that a large amount of the liquid volume inside the holes can be displaced within one acoustic cycle by the expansion of the cavitation bubbles. This confirmed that ultrasound is a very effective tool to intensify liquid exchange processes, and it might significantly improve micro mixing in small structures. The investigation of the effect of ultrasound power on the bubble density distribution revealed the possibility to control the cavitation bubble distribution inside the microholes. At a high ultrasound power (31.5 W) we observed the highest bubble density at the hole entrances, while reducing the ultrasound power by a factor of ten shifted the bubble locations to the inner end of the blind holes or to the middle of the through holes.

A laboratory filtration plant for drinking water treatment is constructed to study the conditions for purely mechanical in situ cleaning of fouled polymeric membranes by the application of ultrasound. The filtration is done by suction of water with defined constant contamination through a membrane module, a stack of five pairs of flat-sheet ultrafiltration membranes. The short cleaning cycle to remove the cake layer from the membranes includes backwashing, the application of ultrasound and air flushing. A special geometry for sound irradiation of the membranes parallel to their surfaces is chosen. Two frequencies, 35kHz and 130kHz, and different driving powers are tested for their cleaning effectiveness. No cleaning is found for 35kHz, whereas good cleaning results are obtained for 130kHz, with an optimum cleaning effectiveness at moderate driving powers. Acoustic and optic measurements in space and time as well as analytical considerations and numerical calculations reveal the reasons and confirm the experimental results. The sound field is measured in high resolution and bubble structures are high-speed imaged on their nucleation sites as well as during their cleaning work at the membrane surface. The microscopic inspection of the membrane surface after cleaning shows distinct cleaning types in the cake layer that are related to specific bubble behaviour on the membrane. The membrane integrity and permeate quality are checked on-line by particle counting and turbidity measurement of the permeate. No signs of membrane damage or irreversible membrane degradation in permeability are detected and an excellent water permeate quality is retained.

Despite the increasing use of high frequency ultrasound in heterogeneous reactions, knowledge about the spatial distribution of cavitation bubbles at the irradiated solid surface is still lacking. This gap hinders controllable surface sonoreactions. Here we present an optimization study of the cavitation bubble distribution at a solid sample using sonoluminescence and sonochemiluminescence imaging. The experiments were performed at three ultrasound frequencies, namely 580, 860 and 1142 kHz. We found that position and orientation of the sample to the transducer, as well as its material properties influence the distribution of active cavitation bubbles at the sample surface in the reactor. The reason is a significant modification of the acoustic field due to reflections and absorption of the ultrasonic wave by the solid. This is retraced by numerical simulations employing the Finite Element Method, yielding reasonable agreement of luminescent zones and high acoustic pressure amplitudes in 2D simulations. A homogeneous coverage of the test sample surface with cavitation is finally reached at nearly vertical inclination with respect to the incident wave.

The impact of a droplet onto a dry or wet surface leads to a rapid formation of a shear flow at the boundary. We present a novel method to experimentally resolve this flow in time at different heights above the solid. The radial flow field close to the substrate is reconstructed by evaluation of streak images of fluorescent tracer particles in the liquid. By using a microscope objective with a narrow depth of field, it is possible to scan through the flow in thin horizontal layers of 5 μm thickness. We focus on the flow close (≤40 μm) to the boundary during the impact of elongated drops with diameters of 0.3–0.4 mm and speeds in the range of 2–3 m s−1. The spatial resolution is obtained from several individual events of the repeatable impact process and varying the focal plane. Fluorescent streaks formed by the suspended particles are recorded with high-speed photography at up to 20,000 frames per second. The impact of water and of ethanol is investigated both on dry glass and on glass covered with a thin film of the same liquid. Results are given as spatio-temporal maps of radial flow velocity at different heights, and the maximum shear stress at the substrate is evaluated. The implications of the results are discussed with respect to cleaning applications.

A microbubble in a sound wave oscillates in volume and translates unsteadily. The two motions are coupled. In large-scale simulations of the structure of bubble clouds driven by acoustic fields, it has been of significant convenience to decouple volume oscillations and translation, as an approximation. The errors of this decoupling approximation were considered in an earlier presentation [A. J. Reddy and A. J. Szeri, J. Acoust. Soc. Am. 112, 1346–1352 (2002)], in the parameter range of interest in medical ultrasound. In this work, the approximation is reexamined for a much broader range of driving frequencies and bubble sizes. Solving the equation of motion for linearly oscillating bubbles, it is found that even for weak acoustic forcing, the translation speed obtained with the decoupling approximation can be in error as much as 30% relative to the translation speed in the full equations. The error depends on the bubble size, the driving frequency, and the liquid properties. The results are presented in a...

Filamentary formations of acoustic cavitation bubbles in an ultrasonic resonator are recorded by high-speed stereoscopic means. The bubble locations and motions are reconstructed in three dimensions, and a velocity distribution of bubbles is obtained. Experimental bubble trajectories are compared to a one-to-one simulation by a particle modeling approach which shows reasonable agreement. Such investigations are important for a better understanding of the mechanisms taking place in applications of intense ultrasound in liquids, and for verification and improvement of particle modeling of cavitation bubbles.

Technologies including (3D-) (bio-)printing, diesel engines, laser-induced forward transfer, and spray cleaning require optimization and therefore understanding of micrometer-sized droplets impacting at velocities beyond 10 m s−1. However, as yet, this regime has hardly been addressed. Here we present the first time-resolved experimental investigation of microdroplet impact at velocities up to V0 = 50 m s−1, on hydrophilic and -phobic surfaces at frame rates exceeding 107 frames per second. A novel method to determine the 3D-droplet profile at sub-micron resolution at the same frame rates is presented, using the fringe pattern observed from a bottom view. A numerical model, which is validated by the side- and bottom-view measurements, is employed to study the viscous boundary layer inside the droplet and the development of the rim. The spreading dynamics, the maximal spreading diameter, the boundary layer thickness, the rim formation, and the air bubble entrainment are compared to theory and previous experiments. In general, the impact dynamics are equal to millimeter-sized droplet impact for equal Reynolds-, Weber- and Stokes numbers (Re, We, and St, respectively). Using our numerical model, effective scaling laws for the progression of the boundary layer thickness and the rim diameter are provided. The dimensionless boundary layer thickness develops in time (t) according to Image ID:c4sm02474e-t1.gif, and the diameter of the rim develops as Image ID:c4sm02474e-t2.gif, with drop diameter D0 and inertial time scale τ = D0/V0. These scalings differ from previously assumed, but never validated, values. Finally, no splash is observed, at variance with many predictions but in agreement with models including the influence of the surrounding gas. This confirms that the ambient gas properties are key ingredients for splash threshold predictions

Sonoluminescing single bubbles driven simultaneously by two harmonic frequencies were recently reported to increase the maximum light output up to a factor of 3 with respect to single mode excitation. In this paper, experimental and numerical results on single-bubble sonoluminescence (SBSL) in an air/water system using the fundamental mode of 25 kHz and the second harmonic at 50 kHz are presented. The region of light emission is mapped in the three-dimensional parameter space spanned by the two driving pressure amplitudes and their relative phase. Good agreement was seen between measured light output, maximum bubble radius, and stability boundaries and the numerical model which is based on spherical bubble oscillations regarding diffusive and shape stability. The maximum brightness was enhanced by a factor up to 2.5 with respect to single mode SBSL. However, long-term measurements reveal great variation of the emission at fundamental mode driven SBSL and of the boost factor reached with two frequencies. The overall brightness maxima of both excitation methods within a period of several hours turn out to show little difference.

Single cavitation bubble luminescence induced by laser in contrast to single bubble sonoluminescence has no need in a sound field for a strong collapse and for light emission. The cavitation bubbles are produced by focused laser light and make the single strong collapse. As shown experimentally, the number of emitted photons from cavitation luminescence is much greater than it was observed in sonoluminescence due to the large bubble size during the final stage of collapse. To describe the process of laser-induced bubble collapse a mathematical model is used, which is based upon the spherically symmetric motion including compressibility, heat and mass transfer effects. The basic results of the numerical solution are presented for the bubbles with maximum radii of about 1 mm. According to the observed results the minimum bubble radius in collapse is about 15 μm, and the mass decreases up to 5% of the initial value. Calculations with a small amounts of noncondensable gas inside the bubble predict its strong influence on the dynamics. As shown numerically the theoretical model gives a good agreement with experimental measurements.

The dynamics of collapsing bubbles close to a flat solid is investigated with respect to its potential for removal of surface attached particles. Individual bubbles are created by nanosecond Nd:YAG laser pulses focused into water close to glass plates contaminated with melamine resin micro-particles. The bubble dynamics is analysed by means of synchronous high-speed recordings. Due to the close solid boundary, the bubble collapses with the well-known liquid jet phenomenon. Subsequent microscopic inspection of the substrates reveals circular areas clean of particles after a single bubble generation and collapse event. The detailed bubble dynamics, as well as the cleaned area size, is characterised by the non-dimensional bubble stand-off γ = d / R max , with d: laser focus distance to the solid boundary, and R max : maximum bubble radius before collapse. We observe a maximum of clean area at γ ≈ 0.7 , a roughly linear decay of the cleaned circle radius for increasing γ , and no cleaning for γ > 3.5 . As the main mechanism for particle removal, rapid flows at the boundary are identified. Three different cleaning regimes are discussed in relation to γ : (I) For large stand-off, 1.8 γ 3.5 , bubble collapse induced vortex flows touch down onto the substrate and remove particles without significant contact of the gas phase. (II) For small distances, γ 1.1 , the bubble is in direct contact with the solid. Fast liquid flows at the substrate are driven by the jet impact with its subsequent radial spreading, and by the liquid following the motion of the collapsing and rebounding bubble wall. Both flows remove particles. Their relative timing, which depends sensitively on the exact γ , appears to determine the extension of the area with forces large enough to cause particle detachment. (III) At intermediate stand-off, 1.1 γ 1.8 , only the second bubble collapse touches the substrate, but acts with cleaning mechanisms similar to an effective small γ collapse: particles are removed by the jet flow and the flow induced by the bubble wall oscillation. Furthermore, the observations reveal that the extent of direct bubble gas phase contact to the solid is partially smaller than the cleaned area, and it is concluded that three-phase contact line motion is not a major cause of particle removal. Finally, we find a relation of cleaning area vs. stand-off γ that deviates from literature data on surface erosion. This indicates that different effects are responsible for particle removal and for substrate damage. It is suggested that a trade-off of cleaning potential and damage risk for sensible surfaces might be achieved by optimising γ .

International audience; The sonoluminescence spectra from acoustic cavitation in aqueous NaCl solutions are systematically studied in a large range of ultrasonic frequencies under variation of electrical power and argon sparging. At the same time, bubble dynamics are analysed by high-speed imaging. Sodium line and continuum emission are evaluated for acoustic driving at 34.5, 90, 150, 365, and 945 kHz in the same reactor vessel. The results show that the ratio of sodium line to continuum emission can be shifted by the experimental parameters: an increase in the argon flow increases the ratio, while an increase in power leads to a decrease. At 945 kHz, the sodium line is drastically reduced, while the continuum stays at elevated level. Bubble observations reveal a remarkable effect of argon in terms of bubble distribution and stability: larger bubbles of non-spherical shapes form and eject small daughter bubbles which in turn populate the whole liquid. As a consequence, the bubble interactions (splitting, merging) appear enhanced which supports a link between non-spherical bubble dynamics and sodium line emission.

The details of bubble behaviour in chemically active cavitation are still not sufficiently well understood. Here we report on experimental high-speed observations of acoustically driven single-bubble and few-bubble systems with the aim of clarification of the connection of their dynamics with chemical activity. Our experiment realises the sonochemical isomerization reaction of maleic acid to fumaric acid, mediated by bromine radicals, in a bubble trap set-up. The main result is that the reaction product can only be observed in a parameter regime where a small bubble cluster occurs, while a single trapped bubble stays passive. Evaluations of individual bubble dynamics for both cases are given in form of radius-time data and numerical fits to a bubble model. A conclusion is that a sufficiently strong collapse has to be accompanied by non-spherical bubble dynamics for the reaction to occur, and that the reason appears to be an efficient mixing of liquid and gas phase. This finding corroborates previous observations and literature reports on high liquid phase sonochemical activity under distinct parameter conditions than strong sonoluminescence emissions.

A liquid jet that is ejected from a nozzle into air will disintegrate into drops via the well-known Plateau–Rayleigh instability within a certain range of Ohnesorge and Reynolds numbers. With the focus on the micrometer scale, we investigate the control of this process by superimposing a suitable ultrasonic signal, which causes the jet to break up into a very precise train of monodisperse droplets. The jet leaves a pressurized container of liquid via a small orifice of about 20 μm diameter. The break-up process and the emerging droplets are recorded via high-speed imaging. An extended parameter study of exit speed and ultrasonic frequency is carried out for deionized water to evaluate the jet’s state and the subsequent generation of monodisperse droplets. Maximum exit velocities obtained reach almost 120 m s−1, and frequencies have been applied up to 1.8 MHz. Functionality of the method is confirmed for five additional liquids for moderate jet velocities $$\lesssim$$ 38 m s−1. For the uncontrolled jet disintegration, the drop size spectra revealed broad distributions and downstream drop growth by collision, while the acoustic control generated monodisperse droplets with a standard deviation less than 0.5 %. By adjustment of the acoustic excitation frequency, drop diameters could be tuned continuously from about 30 to 50 μm for all exit speeds. Good agreement to former experiments and theoretical approaches is found for the relation of overpressure and jet exit speed, and for the observed stability regions of monodisperse droplet generation in the parameter plane of jet speed and acoustic excitation frequency. Fitting of two free parameters of the general theory to the liquids and nozzles used is found to yield an even higher precision. Furthermore, the high-velocity instability limit of regular jet breakup described by von Ohnesorge has been superseded by more than a factor of two without entering the wind-induced instability regime, and monodisperse droplet generation was always achievable. Thus, the reliable and robust realization of tunable high-speed monodisperse micro-droplet trains is demonstrated. Some implication for applications is discussed.

Acoustically induced cavitation at 20 kHz is observed by means of high speed CCD recording at a framerate of 2250 per second. Using digital image processing the bubbles' trajectories are reconstructed. The experimental data reveal that collision and coalescence of bubbles is a predominant phenomenon that limits their individual lifetime. Measurements of bubble sizes and velocities are in agreement with previous results.

Bubble clouds forming in an extended volume of liquid in acoustic cavitation show a slowly varying filamentary structure, whose origin is still not completely understood. Experimental observations are reported that provide some characteristics of the phenomenon, such as bubble distributions and sound–field measurements. A discussion of relevant physical interactions in bubbly liquids is comprised of wave dynamics, Bjerknes and drag forces, nucleation and coalescence. For describing the structure formation process, continuum and particle approaches are employed. In the framework of the continuum model it is shown that homogeneous bubble distributions are unstable, and regions with high bubble concentration emerge in the course of a self–concentration process. In the particle model, all bubbles are treated as interacting objects that move in the liquid. This approach is complementary to the continuum model. It allows the inclusion of some particular features, for instance Bjerknes forces based on nonlinear bubble oscillations. Both models are discussed and results are compared with experimentally observed patterns.

It has been established that chaotic iterated maps can be transferred to a periodic motion by application of periodic signals. As a next step, we investigate the optimization of such signals with respect to a small norm. This method employs a cost function on the space of periodic inputs. By means of a direct optimization search in this space, the approach stabilizes periodicity with small forces. The results for increasing driving periods are compared.

We introduce homotopy transformations of vector fields as an efficient way to design families of chaotic attractors or transients with specific geometrical and dynamical properties. Those properties are inherited from different progenitor attractors, which allows a morphing between the progenitors. The method can provide a simple tool for a systematic design of attractors of desired dynamical characteristics. It is based on the robustness of invariant manifolds of the homotopic vector fields with respect to parametric perturbations. We analytically construct a convex subfamily of Chua attractors which illustrates this approach. Connections to control and synchronisation schemes of chaotic systems are shown. We also discuss applications in the area of sound synthesis.

The transport of bubbles to a neighboring surface is very important in surface chemistry, bioengineering, and ultrasonic cleaning, etc. This paper proposes a multi-bubble transport method by using an acoustic standing wave field and establishes a model that explains the multi-bubble translation by expressing the balance between Bjerknes forces and hydrodynamic forces on a bubble in a liquid medium. Results indicated that the influence of primary Bjerknes force, secondary Bjerknes force, and buoyancy force on the bubble translation depends on the position of the target bubble in the acoustic field. Moreover, it was found that increasing the size of a bubble or pressure amplitude can accelerate the bubble motion and enhance the bubble-bubble interaction. The secondary Bjerknes force between two bubbles can switch from an attractive one when they oscillate in phase to a repulsive one when the bubble oscillations are out of phase. These findings provide an insight into the multi-bubble translation near a surface and can be applied to future bubble motion control studies, especially in drug delivery, sonoporation, and ultrasonic cleaning.

A mathematical model for a nonlinear oscillator, which is composed of an oscillating mass interacting with a freely sliding friction damper, is introduced and investigated. This oscillator is a strongly simplified model for a damping principle applied to turbine blades to suppress oscillations induced by inhomogeneous flow fields. It exhibits periodic, quasi-periodic, as well as chaotic dynamics occuring suddenly due to adding sliding bifurcations. Mathematically, the oscillator is given as a piecewise smooth (Filippov) system with a switching manifold corresponding to the sticking phase of the damper mass. The rich dynamics of this system is analyzed and illustrated by means of resonance curves, Lyapunov diagrams, Poincaré sections and reductions to iterated one-dimensional maps.

The bifurcation set in the three-dimensional parameter space of the periodically driven van der Pol oscillator has been investigated by continuation of local bifurcation curves. The two regions in which the driving frequency ω is greater or less than the limit cycle frequency ω0 of the nondriven oscillator are considered separately. For the case ω > ω0, the subharmonic region, the extent and location of the largest Arnol'd tongues are shown, as well as the period-doubling cascades and chaotic attractors that appear within most of them. Special attention is paid to the pattern of the bifurcation curves in the transitional region between low and large dampings that is difficult to approach analytically. In the case ω < ω0, the ultraharmonic region, a recurrent pattern of the bifurcation curves is found for small values of the damping d. At medium damping the structure of the bifurcation curves becomes involved. Period-doubling sequences and chaotic attractors occur.

A generic bubble structure in a 230 kHz ultrasonic field is observed in a partly developed standing wave field in water. It is characterized by high-speed imaging, sonoluminescence recordings, and surface cleaning tests. The structure has two distinct bubble populations. Bigger bubbles (much larger than linear resonance size) group on rings in planes parallel to the transducer surface, apparently in locations of driving pressure minima. They slowly rise in a jittering, but synchronous way, and they can have smaller satellite bubbles, thus resembling the arrays of bubbles observed by Miller [D. Miller, Stable arrays of resonant bubbles in a 1-MHz standing-wave acoustic field, J. Acoust. Soc. Am. 62 (1977) 12]. Smaller bubbles (below and near linear resonance size) show a fast “streamer” motion perpendicular to and away from the transducer surface. While the bigger bubbles do not emit light, the smaller bubbles in the streamers show sonoluminescence when they pass the planes of high driving pressure. Both bubble populations exhibit cleaning potential with respect to micro-particles attached to a glass substrate. The respective mechanisms of particle removal, though, might be different.