Rebounds of deformed cavitation bubbles

Presented here are experiments clarifying how the deformation of cavitation bubbles affects their rebound. Rebound bubbles carry the remaining energy of a bubble following its initial collapse, which dissipates energy mainly through shock waves, jets, and heat. The rebound bubble undergoes its own collapse, generating such violent events anew, which can be even more damaging or effective than at first bubble collapse. However, modeling rebound bubbles is an ongoing challenge because of the lack of knowledge on the exact factors affecting their formation. Here we use single-laser-induced cavitation bubbles and deform them by variable gravity or by a neighboring free surface to quantify the effect of bubble deformation on the rebound bubbles. Within a wide range of deformations, the energy of the rebound bubble follows a logarithmic increase with the bubble's initial dipole deformation, regardless of the origin of this deformation

Collapse phenomena of deformed cavitation bubbles

Cavitation bubbles are a topic of long-standing interest owing to the powerful phenomena associated with their collapse. Their unique ability to focus energy typically causes damage in hydraulic machinery (turbines, pumps, propellers, ...) but, if managed correctly, can also be beneficial in numerous applications such as cleaning practices and biomedical sciences. Here the complex problem of cavitation, often multi-scale both in time and space, is reduced to a simplified case study of the collapse of a single, initially spherical bubble. We study the bubble's energy distribution into its distinct collapse phenomena, namely the micro-jets, shock waves and luminescence, and aim to quantify and predict how such a distribution is affected by the bubble's deformation. Combining experiments with statistical analysis, numerical simulations and theoretical models, we seek to quantify and predict the key properties characterising each of the collapse phenomena. The deformation of bubbles is characterised by the liquid micro-jets formed during their non-spherical collapse. A unified framework is proposed to describe the dynamics of such jets, driven by different external sources, through an anisotropy parameter $\zeta$, which represents a dimensionless quantity of the liquid momentum at the bubble collapse (Kelvin impulse). The bubbles are carefully deformed in variable gravity aboard European Space Agency parabolic flights or by introducing surfaces nearby. Through high-speed visualisation, we measure key quantities associated with the micro-jet dynamics (e.g. jet speed, impact timing), which, upon normalisation, reduce to straightforward functions of $\zeta$. This is verified by numerical simulations based on potential flow theory. Below a certain threshold, all of these functions can be approximated by useful power laws of $\zeta$ that are independent of the micro-jet driver. For bubbles collapsing near a free surface, we identify and measure the shock waves generated through distinct mechanisms, such as the jet impact onto the opposite bubble wall and the individual collapses of the remaining bubble segments. The energy carried by each of these shocks is found to vary with $\zeta$. We find that for bubbles that produce jets, the shock wave peak pressure may be approximated by the jet-induced water hammer pressure as a function of $\zeta$. Following such an approximation, we also develop a semi-empirical model to explain the shock energy variation with $\zeta$. Finally, an innovative luminescence detection system is built to overcome the challenge of measuring the spectra (300-900nm) of the weak, small, rapid and migrating flash light from individual bubble collapses. We find an approximately exponential quenching of the luminescence energy as a function of $\zeta$. Surprisingly, the blackbody temperature of luminescence does not vary with $\zeta$. Multiple peaks are measured within a time frame of approximately 200ns, implying non-uniform gas compression during the collapse. Overall, these results help in predicting bubble collapse characteristics in known pressure fields and can be useful for numerical benchmarking

Cavitation cloud formation and surface damage of a model stone in a high-intensity focused ultrasound field

This work investigates the fundamental role of cavitation bubble clouds in stone comminution by focused ultrasound. The fragmentation of stones by ultrasound has applications in medical lithotripsy for the comminution of kidney stones or gall stones, where their fragmentation is widely assumed to result from the high acoustic wave energy. However, high-intensity ultrasound can generate cavitation which is known to contribute to erosion as well and to cause damage away from the target, although the exact contribution of cavitation remains currently unclear. Based on in-situ experimental observations, post-mortem microtomography and acoustic simulations, the present work sheds light on the fundamental role of cavitation bubbles in the stone surface fragmentation by correlating the detected damages to the observed bubble activity. Our results show that not all clouds erode the stone, but only those located in preferential nucleation sites whose locations are herein examined. Furthermore, quantitative characterizations of the bubble clouds and their trajectories within the ultrasonic field are discussed. These include experiments with and without the presence of a model stone in the acoustic path length. Finally, the optimal stone-to-source distance maximizing the cavitation-induced surface damage area has been determined. Assuming the pressure magnitude within the focal region to exceed the cavitation pressure threshold, this location does not correspond to the acoustic focus, where the pressure is maximal, but rather to the region where the acoustic beam and thereby the acoustic cavitation activity near the stone surface is the widest

Scaling laws for jets of single cavitation bubbles

Fast liquid jets, called micro-jets, are produced within cavitation bubbles experiencing an aspherical collapse. Here we review micro-jets of different origins, scales and appearances, and propose a unified framework to describe their dynamics by using an anisotropy parameter $\zeta$, representing a dimensionless measure of the liquid momentum at the collapse point (Kelvin impulse). This parameter is rigorously defined for various jet drivers, including gravity and nearby boundaries. Combining theoretical considerations with hundreds of high-speed visualisations of bubbles collapsing near a rigid surface, near a free surface or in variable gravity, we classify the jets into three distinct regimes: weak, intermediate and strong. Weak jets ($\zeta<10^{-3}$) hardly pierce the bubble, but remain within it throughout the collapse and rebound. Intermediate jets ($10^{-3}<\zeta<0.1$) pierce the opposite bubble wall close to the last collapse phase and clearly emerge during the rebound. Strong jets ($\zeta>0.1$) pierce the bubble early during the collapse. The dynamics of the jets is analysed through key observables, such as the jet impact time, jet speed, bubble displacement, bubble volume at jet impact and vapour-jet volume. We find that, upon normalising these observables to dimensionless jet parameters, they all reduce to straightforward functions of $\zeta$, which we can reproduce numerically using potential flow theory. An interesting consequence of this result is that a measurement of a single observable, such as the bubble displacement, suffices to estimate any other parameter, such as the jet speed. Remarkably, the dimensionless parameters of intermediate and weak jets only depend on $\zeta$, not on the jet driver. In the same regime, the jet parameters are found to be well approximated by power-laws of $\zeta$, which we explain through analytical arguments

Shock waves from non-spherical cavitation bubbles

We present detailed observations of the shock waves emitted at the collapse of single cavitation bubbles using simultaneous time-resolved shadowgraphy and hydrophone pressure measurements. The geometry of the bubbles is systematically varied from spherical to very non-spherical by decreasing their distance to a free or rigid surface or by modulating the gravity-induced pressure gradient aboard parabolic flights. The non-spherical collapse produces multiple shocks that are clearly associated with different processes, such as the jet impact and the individual collapses of the distinct bubble segments. For bubbles collapsing near a free surface, the energy and timing of each shock are measured separately as a function of the anisotropy parameter $\zeta$, which represents the dimensionless equivalent of the Kelvin impulse. For a given source of bubble deformation (free surface, rigid surface or gravity), the normalized shock energy depends only on $\zeta$, irrespective of the bubble radius $R_{0}$ and driving pressure $\Delta p$. Based on this finding, we develop a predictive framework for the peak pressure and energy of shock waves from non-spherical bubble collapses. Combining statistical analysis of the experimental data with theoretical derivations, we find that the shock peak pressures can be estimated as jet impact-induced hammer pressures, expressed as $p_{h} = 0.45\left(\rho c^{2}\Delta p\right)^{1/2} \zeta^{-1}$ at $\zeta > 10^{-3}$. The same approach is found to explain the shock energy quenching as a function of $\zeta^{-2/3}$.Comment: Accepted for publication in Physical Review Fluid

Detailed Jet Dynamics in a Collapsing Bubble

We present detailed visualizations of the micro-jet forming inside an aspherically collapsing cavitation bubble near a free surface. The high-quality visualizations of large and strongly deformed bubbles disclose so far unseen features of the dynamics inside the bubble, such as a mushroom-like flattened jet-tip, crown formation and micro-droplets. We also find that jetting near a free surface reduces the collapse time relative to the Rayleigh time

Synchrotron X-ray phase-contrast imaging of ultrasonic drop atomization

Ultrasonic atomization is employed to generate size-controllable droplets for a variety of applications. Here, we minimize the number of parameters dictating the process by studying the atomization of a single drop pending from an ultrasonic horn. Spatiotemporally resolved X-ray phase-contrast imaging measurements show that the number-median sizes of the ejected droplets can be predicted by the linear Navier-Stokes equations, signifying that the size distribution is controlled by the fluid properties and the driving frequency. Experiments with larger pendant water drops indicate that the fluid-structure interaction plays a pivotal role in determining the ejection onset of the pendant drop. The atomization of viscoelastic drops is dictated by extended ligament formation, entrainment of air, and ejection of drop-encapsulated bubbles. Existing scaling laws are used to explain the required higher input amplitudes for the complete atomization of viscoelastic drops as compared to inviscid drops. Finally, we elucidate the differences between capillary wave-based and cavitation-based atomization and show that inducing cavitation and strong bubble oscillations quickens the onset of daughter drop ejection but impedes their size control.Comment: 36 pages, 11 figure

Shell viscosity estimation of lipid-coated microbubbles

Understanding the shell rheology of ultrasound contrast agent microbubbles is vital for anticipating their bioeffects in clinical practice. Past studies using sophisticated acoustic and optical techniques have made enormous progress in this direction, enabling the development of shell models that adequately reproduce the nonlinear behaviour of the coated microbubble under acoustic excitation. However, there have also been puzzling discrepancies and missing physical explanations for the dependency of shell viscosity on the equilibrium bubble radius, which demands further experimental investigations. In this study, we aim to unravel the cause of such behaviour by performing a refined characterisation of the shell viscosity. We use ultra-high-speed microscopy imaging, optical trapping and wide-field fluorescence to accurately record the individual microbubble response upon ultrasound driving across a range of bubble sizes. An advanced model of bubble dynamics is validated and employed to infer the shell viscosity of single bubbles from their radial time evolution. The resulting values reveal a prominent variability of the shell viscosity of about an order of magnitude and no dependency on the bubble size, which is contrary to previous studies. We find that the method called bubble spectroscopy, which has been used extensively in the past to determine the shell viscosity, is highly sensitive to methodology inaccuracies, and we demonstrate through analytical arguments that the previously reported unphysical trends are an artifact of these biases. We also show the importance of correct bubble sizing, as errors in this aspect can also lead to unphysical trends in shell viscosity, when estimated through a nonlinear fitting from the time response of the bubble.ISSN:1744-683XISSN:1744-684

Cavitation cloud formation and surface damage of a model stone in a high-intensity focused ultrasound field

This work investigates the fundamental role of cavitation bubble clouds in stone comminution by focused ultrasound. The fragmentation of stones by ultrasound has applications in medical lithotripsy for the comminution of kidney stones or gall stones, where their fragmentation is believed to result from the high acoustic wave energy as well as the formation of cavitation. Cavitation is known to contribute to erosion and to cause damage away from the target, yet the exact contribution and mechanisms of cavitation remain currently unclear. Based on in situ experimental observations, post-exposure microtomography and acoustic simulations, the present work sheds light on the fundamental role of cavitation bubbles in the stone surface fragmentation by correlating the detected damage to the observed bubble activity. Our results show that not all clouds erode the stone, but only those located in preferential nucleation sites whose locations are herein examined. Furthermore, quantitative characterizations of the bubble clouds and their trajectories within the ultrasonic field are discussed. These include experiments with and without the presence of a model stone in the acoustic path length. Finally, the optimal stone-to-source distance maximizing the cavitation-induced surface damage area has been determined. Assuming the pressure magnitude within the focal region to exceed the cavitation pressure threshold, this location does not correspond to the acoustic focus, where the pressure is maximal, but rather to the region where the acoustic beam and thereby the acoustic cavitation activity near the stone surface is the widest

Detailed Jet Dynamics in a Collapsing Bubble

We present detailed visualizations of the micro-jet forming inside an aspherically collapsing cavitation bubble near a free surface. The high-quality visualizations of large and strongly deformed bubbles disclose so far unseen features of the dynamics inside the bubble, such as a mushroom-like flattened jet-tip, crown formation and micro-droplets. We also find that jetting near a free surface reduces the collapse time relative to the Rayleigh time.ISSN:1742-6588ISSN:1742-659