This study experimentally and numerically investigates the dynamics of a high-speed liquid jet generated from the interaction of two tandem cavitation bubbles, termed bubble 1 and bubble 2, depending on their generation sequence. Although the overall collapse pattern and jet orientation are well documented, the underlying mechanisms for supersonic jet acceleration, tip fragmentation and subsequent penetration remain to be elucidated. In our experiments, two near-identical, highly energised cavitation bubbles were generated using an underwater electric discharge method, and their transient interactions were captured using a high-speed camera. We identify three distinct jet regimes that emerge from the tip of bubble 2: conical, umbrella-shaped and spraying jets, characterised by variations in the initial bubble–bubble distance (denoted as $\gamma$) and the initiation time difference (denoted as $\theta$). Our numerical simulations using both volume of fluid and boundary integral methods reproduce the experimental observations quite well and explain the mechanism of jet acceleration. We show that the transition between the regimes is governed by the spatio-temporal characteristics of the pressure wave induced by the collapse of bubble 1, which impacts the high-curvature tip of bubble 2. Specifically, a conical jet forms when the pressure wave impacts the bubble tip prior to its contraction, while an umbrella-shaped jet develops when this impact occurs after the contraction. The spraying jets result from the breakup of the bubble tip, exhibiting mist-like and needle-like morphologies with velocities ranging from 10 to over 1200 m s−1. Remarkably, we observe that the penetration distance of spraying jets exceeds ten times the maximum bubble radius, making them ideal for long-range, controlled fluid delivery. Finally, phase diagrams for jet velocity and penetration distance in the $\gamma -\theta$ parameter space are established to provide a practical reference for biomedical applications, such as needle-free injection and micro-pumping.

Interfacial interactions between gas bubbles and the free surface are a hallmark of flows involving aqueous foams. In practice, bubble foams commonly arise from processes such as breaking waves at the ocean–atmosphere interface, plunging liquid jets and the effervescence of carbonated liquids. Once generated, bubbles within foam layers remain afloat at the free surface for finite durations before finally bursting into a fine spray of droplets. While the birth and bursting of bubble foams have received considerable attention, the understanding of floating bubbles is limited mainly to a single bubble. To build on this, in this article, we undertake numerical simulations of two or more floating bubbles in various canonical settings to examine their geometry and self-organising nature, with implications for real-world phenomena such as ocean spray production. Under lateral confinement, floating bubbles are prone to form vertically stacked layers. To this end, we analyse the geometry of coaxial pairs of floating bubbles and link geometrical differences between single and coaxial bubbles to various aspects of the ensuing bursting stage. Furthermore, we extend the existing theory of isolated floating bubbles to obtain unified analytical expressions for the shape parameters of single and coaxial bubbles of small sizes. Next, we investigate a pair of side-by-side floating bubbles, which serves as a minimal configuration to understand the formation of bubble rafts through self-organisation. We discover that Bond numbers in the range $10\leqslant \textit{Bo}\leqslant 50$ are more favourable for raft formation due to pronounced capillary attraction. The time required for two floating bubbles to assemble through capillary attraction grows exponentially with their initial separation. We also develop a linear model to capture the evolution of bubble spacing during capillary migration at low Bond numbers. Lastly, we extend the two-bubble configuration and showcase the emergent dynamics of a swarm of floating bubbles in mono- and bilayer configurations.

Nucleation phenomena associated with cloud cavitation about a three-dimensional (3-D) NACA$\,$16-029 hydrofoil are explored experimentally in a cavitation tunnel where susceptible free stream nuclei are absent. Microbubble nuclei are found to be intrinsically generated by cavity collapse and become sequestered in the low-momentum separated region ahead of the cavity leading edge. Nuclei dynamics upstream of a shedding sheet cavity was investigated using high-speed photography. Measurements were performed at zero incidence for cavitation numbers in the range of $0.55 \gt \sigma \gt 0.45$, and chord-based Reynolds numbers of $ \textit{Re} = 0.75\times 10^6$ and $ \textit{Re} = 1.5\times 10^6$. Nuclei are generated each shedding cycle due to cavity breakup from condensation shock-wave phenomena. These nuclei may undergo immediate activation or transport due to pressure gradients, local re-circulation and jetting. Some nuclei remain upstream of the cavity leading edge over multiple cycles. Several phenomena influence this behaviour, including cyclical variation of the boundary layer properties with each shedding cycle. A major conclusion of the work is that these nuclei are produced in a self-sustaining manner from near surface, small scale, interfacial or viscous phenomena rather than from surface or free stream nuclei. Additionally, these experiments reveal the low-momentum region upstream of the cavity to be above vapour pressure, despite the meta-stable tension developed in the boundary layer further upstream of the cavity.

The interaction between cavitation bubbles and particles near rigid boundaries plays a crucial role in applications from surface cleaning to cavitation erosion. We present a combined experimental, numerical and theoretical investigation of how boundary layer flows affect particle motion during the growth and collapse of the cavitation bubble. Using laser-induced cavitation bubbles and particles of varying radius ratios and stand-off distances, we observe that increasing the bubble-to-particle size ratio suppresses particle displacement. Through one-way coupled simulations and theoretical modelling, we demonstrate that this suppression arises from a shift in the dominant forces acting on the particle: for small radius ratios, the pressure gradient force governs particle motion, while for large ratios, the interplay between added mass, lubrication, and pressure gradient forces becomes significant due to boundary layer growth in the bubble-induced stagnation flow. Based on a theoretical framework combining potential flow theory and axisymmetric viscous stagnation flow analysis, we identify the inviscid- and viscous-flow dominated regimes characterised by the combination of the stand-off distance, the bubble-to-particle radius ratio, and the bubble Reynolds number. Finally, we derive scaling laws for particle displacement consistent with experiments and simulations. These findings advance our understanding of unsteady boundary layer effects in cavitation bubble-particle interactions, offering new insights for applications in microparticle manipulation and flow measurements.

In this work, we study the reaction-controlled dual bubbles ripening on a heterogeneous substrate with high surface wettability hysteresis, where the bubbles evolve with constant contact radius but varied contact angle. We first theoretically derived the governing kinetic equation of bubble curvature radius $R_B$, based on which we surprisingly found three possible ripening processes under six different conditions, i.e. the classical Ostwald ripening (the bubble with the larger curvature radius $R_B$ exhibits an increase in $R_B$, while the bubble with the smaller curvature radius $R_B$ experiences a decrease in $R_B$), the reversed ripening (converse to Ostwald ripening), and the consistent ripening ($R_B$ of both bubbles increases or reduces consistently). Further analyses from the aspects of chemical potential and free energy lead to an interesting finding that the $R_B$ of two bubbles finally reach egalitarianism, independently of different ripening processes. Numerical results obtained from two-phase lattice Boltzmann modelling demonstrate excellent agreement with theoretical predictions, specifically concerning the kinetic equation, the various ripening processes, and the egalitarianism of bubble radii $R_B$ after ripening completion.

Surface bubbles in the ocean are critical in moderating several fluxes between the atmosphere and the ocean. In this paper, we experimentally investigate the drainage and lifetime of surface bubbles in solutions containing surfactants and salts, subjected to turbulence in the air surrounding them modelling the wind above the ocean. We carefully construct a set-up allowing us to repeatably measure the mean lifetime of a series of surface bubbles, while varying the solution and the wind speed or humidity of the air. To that end, we show that renewing the surface layer is critical to avoid a change of the physical properties of the interface. We show that the drainage of the bubbles is well modelled by taking into account the outwards viscous flow and convective evaporation. The mean lifetime of surface bubbles in solutions containing no salt is controlled by evaporation and independent on surfactant concentration. When salt is added, the same scaling is valid only at high surfactant concentrations. At low concentrations, the lifetime is always smaller and independent of wind speed, owing to the presence of impurities triggering a thick bursting event. When the mean lifetime is controlled by evaporation, the probability density of the lifetime is very narrow around its mean, while when impurities are present, a broad distribution is observed.

We examine how ambient temperature $T$ (23–90 $^\circ \mathrm{C}$) alters the dynamics of spark-induced cavitation bubbles across a range of discharge energies. As $T$ rises, the collapse of an isolated spherical bubble weakens monotonically, as quantified by the Rayleigh collapse factor, minimum volume and maximum collapse velocity. When the bubble is generated near a rigid wall, the same thermal attenuation is reflected in reduced jet speed and diminished migration. Most notably, at $T \gtrsim 70\,^\circ \text{C}$, we observe a previously unreported phenomenon: secondary cavitation nuclei appear adjacent to the primary bubble interface where the local pressure falls below the Blake threshold. The pressure reduction is produced by the over-expansion of the primary bubble itself, not by rarefaction waves as suggested in earlier work. Coalescence between these secondary nuclei and the parent bubble seeds pronounced surface wrinkles that intensify Rayleigh–Taylor instability and promote fission, providing an additional route for collapse strength attenuation. These findings clarify the inception mechanism of high-temperature cavitation and offer physical insight into erosion mitigation in heated liquids.

This study is devoted to the analysis of capillary oscillations of a gas bubble in a liquid with an insoluble surfactant adsorbed on the surface. The influence of the Gibbs elasticity, the viscosities of the liquid and gas, as well as the shear and dilatational surface viscosities, on the damping of free oscillations is examined. Dependences of the frequency shift and the damping rate on the parameters of the problem are determined. In the limit of small viscosities and neglecting the surfactant surface diffusion, a simplified dispersion relation is obtained, which includes finite parameters of surface viscosities and Gibbs elasticity. From this relation, conditions are identified under which the damping of capillary oscillations can occur with a small frequency. Numerical solutions of the full dispersion relation demonstrate that a non-oscillatory regime is impossible for the considered configuration. An additional mode associated with Gibbs elasticity is discovered, characterized as a rule by low natural frequency and damping rate. Approximate relations for the complex natural frequency of bubble oscillations in a low-viscosity liquid in the presence of a surfactant are derived, including an estimate of the contribution of the gas inside the bubble to viscous dissipation. An original Lagrangian–Eulerian method is proposed and used to perform direct numerical simulations based on the full nonlinear Navier–Stokes equations and natural boundary conditions at the interface, accounting for shear and dilatational viscosities. The numerical data on the damping process confirm the results of the linear theory.

Experiments have shown that ultrasound-stimulated microbubbles can translate through gel phantoms and tissues, leaving behind tunnel-like degraded regions. A computational model is used to examine the tunnelling mechanisms in a model material with well-defined properties. The high strain rates motivate the neglect of weak elasticity in favour of viscosity, which is taken to degrade above a strain threshold. The reference parameters are motivated by a 1 $\unicode{x03BC}$m diameter bubble in a polysaccharide gel tissue phantom. This is a reduced model and data are scarce, so close quantitative agreement is not expected, but tunnels matching observations do form at realistic rates, which provides validation sufficient to analyse potential mechanisms. Simulations of up to 100 acoustic cycles are used to track tunnelling over 10 bubble diameters, including a steady tunnelling phase during which tunnels extend each forcing cycle in two steps: strain degrades the tunnel front during the bubble expansion, and then the bubble is drawn further along the tunnel during its subsequent inertial collapse. Bubble collapse jetting is damaging, though it is only observed during a transient for some initial conditions. There is a threshold behaviour when the viscosity of the undamaged material changes the character of the inertial bubble oscillation. Apart from that, the tunnel growth rate is relatively insensitive to the high viscosity of the material. Higher excitation amplitudes and lower frequencies accelerate tunnelling. That acoustic radiation force, elasticity and bubble jetting are not required is a principal conclusion.

In air-entraining flows, there is often strong turbulence beneath the free surface. We consider the entrainment of bubbles at the free surface by this strong free-surface turbulence (FST). Our interest is the entrainment size distribution (per unit free surface area) $I(a)/A_{\textit{FS}}$, for bubbles with radius $a$ greater than the capillary scale ($\approx 1.3\ \mathrm{mm}$ for air–water on Earth), where gravity dominates surface tension. We develop a mechanistic model based on entrained bubble size being proportional to the minimum radius of curvature of the initial surface deformation. Using direct numerical simulation of a flow that isolates entrainment by FST, we show that, consistent with our mechanism, $I(a)/A_{\textit{FS}} = C_I \, g^{-3} \varepsilon ^{7/3} (2 a)^{-14/3}$, where $g$ is gravity, and $\varepsilon$ is the turbulence dissipation rate. In the limit of negligible surface tension, $C_I\approx 3.62$, and we describe how $C_I$ decreases with increasing surface tension. This scaling holds for sufficiently strong FST such that near-surface turbulence is nearly isotropic, which we show is true for turbulent Froude number ${\textit{Fr}}^2_T = \varepsilon /u_{\textit{rms}} g \gt 0.1$. While we study FST entrainment in isolation, our model corroborates previous numerical results from shear-driven flow, and experimental results from open-channel flow, showing that the FST entrainment mechanism that we elucidate can be important in broad classes of air-entraining flows.

In this study, we experimentally investigate the stress field around a gradually contaminated bubble as it moves straight ahead in a dilute surfactant solution with an intermediate Reynolds number ($20 \lt {{\textit{Re}}} \lt 220$) and high Péclet number. Additionally, we investigate the stress field around a falling sphere unaffected by surface contamination. A newly developed polarisation measurement technique, highly sensitive to the stress field in the vicinity of the bubble or the sphere, was employed in these experiments. We first validated this method by measuring the flow around a solid sphere sedimenting in a quiescent liquid at a terminal velocity. The measured stress field was compared with established numerical results for ${{\textit{Re}}} = 120$. A quantitative agreement with the numerical results validated this technique for our purpose. The results demonstrated the ability to determine the boundary layer. Subsequently we measured a bubble rising in a quiescent surfactant solution. The drag force on the bubble, calculated from its rise velocity, was set to transiently vary from that of a clean bubble to a solid sphere within the measurement area. With the intermediate drag force between clean bubble and solid sphere, the stress field in the vicinity of the bubble front was observed to be similar to that of a clean bubble, and the structure near the rear was similar to that of a solid sphere. Between the front and rear of the bubble, the phase retardation exhibited a discontinuity around the cap angle at which the boundary conditions transitioned from no slip to slip, indicating an abrupt change in the flow structure. A reconstruction of the axisymmetric stress field from the phase retardation and azimuth obtained from polarisation measurements experimentally revealed that stress spikes occur around the cap angle. The cap angle (stress jump position) shifted as the drag on the bubble increased owing to surfactant accumulation on its surface. Remarkably, the measured cap angle as a function of the normalised drag coefficient quantitatively agreed with the numerical results at intermediate ${{\textit{Re}}} = 100$ of Cuenot et al. (1997 J. Fluid Mech. 339, 25–53), exhibiting only a slight deviation from the curve predicted by the stagnant cap model at low ${\textit{Re}}$ (creeping flow) proposed by Sadhal & Johnson (1983 J. Fluid Mech. 126, 237–250).

Interactions between shock waves and gas bubbles in a liquid can lead to bubble collapse and high-speed liquid jet formation, relevant to biomedical applications such as shock wave lithotripsy and targeted drug delivery. This study reveals a complex interplay between acceleration-induced instabilities that drive jet formation and radial accelerations causing overall bubble collapse under shock wave pressure. Using high-speed synchrotron X-ray phase contrast imaging, the dynamics of micrometre-sized air bubbles interacting with laser-induced underwater shock waves are visualised. These images offer full optical access to phase discontinuities along the X-ray path, including jet formation, its propagation inside the bubble, and penetration through the distal side. Jet formation from laser-induced shock waves is suggested to be an acceleration-driven process. A model predicting jet speed based on the perturbation growth rate of a single-mode Richtmyer–Meshkov instability shows good agreement with experimental data, despite uncertainties in the jet-driving mechanisms. The jet initially follows a linear growth phase, transitioning into a nonlinear regime as it evolves. To capture this transition, a heuristic model bridging the linear and nonlinear growth phases is introduced, also approximating jet shape as a single-mode instability, again matching experimental observations. Upon piercing the distal bubble surface, jets can entrain gas and form a toroidal secondary bubble. Linear scaling laws are identified for the pinch-off time and volume of the ejected bubble relative to the jet’s Weber number, characterising the balance of inertia and surface tension. At low speeds, jets destabilise due to capillary effects, resulting in ligament pinch-off.

This paper explores the role of barodiffusion in the dynamics of gas bubble growth in highly viscous gas-saturated magma subjected to instant decompression. A mathematical model describing the growth of a single isolated bubble is formulated in terms of the modified Rayleigh–Plesset equation coupled with the mass transfer and material balance equations. The model simultaneously takes into account both dynamic and diffusion mechanisms, including the effect of barodiffusion caused by emergence of a large pressure gradient in the liquid, which, in turn, is associated with formation of a diffusion boundary layer around the bubble. An analytical solution of the problem is found, the construction of which is based on the existence of a quasi-stationary state of the bubble growth process. It is shown that barodiffusion manifests itself at the initial and transient stages and under certain conditions can play a paramount role.

Understanding how bubbles on a substrate respond to ultrasound is crucial for applications from industrial cleaning to biomedical treatments. Under ultrasonic excitation, bubbles can undergo shape deformations due to Faraday instability, periodically producing high-speed jets that may cause damage. While recent studies have begun to elucidate this behaviour for free bubbles, the dynamics of wall-attached bubbles is still largely unexplored. In particular, the selection and evolution of non-spherical modes in these bounded systems have not previously been resolved in three dimensions, and the resulting jetting dynamics has yet to be compared with that observed in free bubbles. In this study, we investigate individual micrometric air bubbles in contact with a rigid substrate and subjected to ultrasound. We introduce a novel dual-view imaging technique that combines top-view bright-field microscopy with side-view phase-contrast X-ray imaging, enabling visualisation of bubble shape evolution from two orthogonal perspectives. This set-up reveals the progression of bubble shape through four distinct dynamic regimes: purely spherical oscillations, onset of harmonic axisymmetric meniscus waves, emergence of half-harmonic axisymmetric Faraday waves and the superposition of half-harmonic sectoral Faraday waves. This stepwise evolution contrasts with the behaviour of free bubbles, which exhibit their ultimate Faraday wave pattern immediately upon instability onset. For the substrate chosen, the resulting shape-mode spectrum appears to be degenerate and exhibits a continuous range of shape mode degrees, in line with our theoretical predictions derived from kinematic arguments. While free bubbles also display a degenerate spectrum, their shape mode degrees remain discrete, constrained by the bubble spherical periodicity. Experimentally measured ultrasound pressure thresholds for the onset of Faraday instability agree well with classical interface stability theory, modified to incorporate the effects of a rigid boundary. Complementary three-dimensional boundary element simulations of bubble shape evolution align closely with experimental observations, validating this method’s predictive capability. Finally, we determine the acceleration threshold at which shape mode lobes initiate cyclic jetting. Unlike free bubbles, jetting in wall-attached bubbles consistently emerges from the side not restricted by the substrate.

In gas evolving electrolysis, bubbles grow at electrodes due to a diffusive influx from oversaturation generated locally in the electrolyte by the electrode reaction. When considering electrodes of micrometre size resembling catalytic islands, direct numerical simulations show that bubbles may approach dynamic equilibrium states at which they neither grow nor shrink. These are found in undersaturated and saturated bulk electrolytes during both pinning and expanding wetting regimes of the bubbles. The equilibrium is based on the balance of local influx near the bubble foot and global outflux. To identify the parameter regions of bubble growth, dissolution and dynamic equilibrium by analytical means, we extend the solution of Zhang & Lohse (2023 J. Fluid Mech. vol. 975, R3) by taking into account modified gas fluxes across the bubble interface, which result from a non-uniform distribution of dissolved gas. The Damköhler numbers at equilibrium are found to range from small to intermediate values. Unlike pinned nanobubbles studied earlier, for micrometre-sized bubbles the Laplace pressure plays only a minor role. With respect to the stability of the dynamic equilibrium states, we extend the methodology of Lohse & Zhang (2015a Phys. Rev. E vol. 91, 031003(R)) by additionally taking into account the electrode reaction. Under contact line pinning, the equilibrium states are found to be stable for flat nanobubbles and for microbubbles in general. For unpinned bubbles, the equilibrium states are always stable. Finally, we draw conclusions on how to possibly enhance the efficiency of electrolysis.

This study investigates the fluid mechanisms underlying the interaction between ventilated shoulder and tail cavities under vertical launching conditions. It is found that expansion and contraction coexist within the tail cavity. When the expansion rate exceeds the contraction rate, the volume of the tail cavity increases; conversely, it decreases. Through this process, the cavity undergoes cyclic pulsation during its vertical evolution, including expansion, over-expansion, contraction and over-contraction. Before the shoulder cavity extends to the position of the tail cavity, wall confinement restricts the tail cavity from expanding towards the vehicle’s lateral wall. After the encounter between the shoulder and tail cavities, the re-entrant flow at the end of the shoulder cavity induces the tail cavity to overcome wall confinement and expand towards the lateral wall, initiating their fusion. As a result, a supercavity forms and attaches to the surface of the vehicle. Moreover, after the fusion, the pressure driving mode at the vehicle’s bottom wall shifts from the tail cavity pulsation to the re-entrant flow. In addition, an increase in the ventilation rate induces progressive expansion of the shoulder cavity’s radial dimension, and accelerates its downstream propagation. The fusion mode between the shoulder and tail cavities transitions from progressive fusion to coverage fusion.

Underwater capillary tubes fill rapidly with the surrounding liquid. Capillary and hydrostatic pressures push the liquid into the tube, causing the air to exit as bubbles at the other end. We study the natural filling process of a vertical capillary tube immersed in water during several bubble formation events. A theoretical model is proposed that captures the dynamics of the meniscus inside the capillary tube as it fills with water. We find good agreement with the experimental data that describe this special case of spontaneous flow using a dynamic contact angle model based on molecular kinetic theory.

Bubble–particle collisions in turbulence are key to the froth flotation process that is widely employed industrially to separate hydrophobic from hydrophilic materials. In our previous study (Chan et al., 2023 J. Fluid Mech. 959, A6), we elucidated the collision mechanisms and critically reviewed the collision models in the no-gravity limit. In reality, gravity may play a role since, ultimately, separation is achieved through buoyancy-induced rising of the bubbles. This effect has been included in several collision models, which have remained without a proper validation thus far due to a scarcity of available data. We therefore conduct direct numerical simulations of bubbles and particles in homogeneous isotropic turbulence with various Stokes, Froude and Reynolds numbers, and particle density ratios using the point-particle approximation. Generally, turbulence enhances the collision rate compared with the pure relative settling case by increasing the collision velocity. Surprisingly, however, for certain parameters the collision rate is lower with turbulence compared with without, independent of the history force. This is due to turbulence-induced bubble–particle spatial segregation, which is most prevalent at weak relative gravity and decreases as gravitational effects become more dominant, and reduced bubble slip velocity in turbulence. The existing bubble–particle collision models only qualitatively capture the trends in our numerical data. To improve on this, we extend the model by Dodin & Elperin (2002 Phys. Fluids 14, 2921–2924) to the bubble–particle case and found excellent quantitative agreement for small Stokes numbers when the history force is negligible and segregation is accounted for.

Cavitation bubble pulsation and liquid jet loads are the main causes of hydraulic machinery erosion. Methods to weaken the load influences have always been hot topics of related research. In this work, a method of attaching a viscous layer to a rigid wall is investigated in order to reduce cavitation pulsations and liquid jet loads, using both numerical simulations and experiments. A multiphase flow model incorporating viscous effects has been developed using the Eulerian finite element method (EFEM), and experimental methods of a laser-induced bubble near the viscous layer attached on a rigid wall have been carefully designed. The effects of the initial bubble–wall distance, the thickness of the viscous layer, and the viscosity on bubble pulsation, migration and wall pressure load are investigated. The results show that the bubble migration distance, the normalised thickness of the oil layer and the wall load generally decrease with the initial bubble–wall distance or the oil-layer parameters. Quantitative analysis reveals that when the initial bubble–wall distance remains unchanged, there exists a demarcation line for the comparison of the bubble period and the reference period (the bubble period without viscous layer under the same initial bubble–wall distance), and a logarithmic relationship is observed that $\delta \propto \log_{10} \mu ^*$, where $\delta =h/R_{max}$ is the thickness of the viscous layer h normalised by the maximum bubble radius $R_{max}$, $\mu ^* = \mu /({R_{max }}\sqrt {{\rho }{{\mathop {P}\nolimits } _{{atm}}}})$ is the dynamic viscosity $\mu$ normalised by water density $ \rho $ and atmospheric pressure $P_{atm}$. The results of this paper can provide technical support for related studies of hydraulic cavitation erosion.

We investigate the dynamics of a cavitation bubble near rigid surfaces decorated with a single gas-entrapping hole to understand the competition between the attraction of the rigid and the repulsion of the free boundary. The dynamics of laser-induced bubbles near this gas-entrapping hole is studied as a function of the stand-off distance and diameter of the hole. Two kinds of toroidal collapses are observed that are the result of the collision of a wide microjet with the bubble wall. The bubble centroid displacement and the strength of the microjet are compared with the anisotropy parameter $\zeta$, which is derived from a Kelvin impulse analysis. We find that the non-dimensional displacement $\delta$ scales with $\zeta$.