Air lubrication regimes were studied using simultaneous drag force measurements and multi-plane imaging to characterise the regimes and identify the governing mechanisms of drag reduction. Bubbly, transitional and air layer regimes are identified over a large range of free-stream velocities ($U_{\infty }$), air flow rates ($Q_{\textit{air}}$) and Froude-depth numbers ($\textit{Fr}_d$). For the lowest $U_{\infty }$, drag reduction lags significantly behind the non-wetted area coverage in all cases and no simple correlation exists. Within the bubbly regime, a drag increase is found for low $U_{\infty }$ with large, slow-moving bubbles forming a single layer over the plate height. For higher velocities, bubbles become smaller and disperse vertically, while the drag starts decreasing. For higher $Q_{\textit{air}}$, irrespective of $U_{\infty }$, air patches start to form (transitional regime) and drag monotonically decreases, with the onset of the air layer regime at 60 % drag reduction. A new scaling of the associated critical $Q_{\textit{air}}$ is proposed, combining the air exit velocity, the liquid velocity close to the air layer and $\textit{Fr}_d$. For a further increase of $Q_{\textit{air}}$ and a low $U_{\infty }$, a thicker and smoother air layer is formed with even lower drag; for higher $U_{\infty }$, marginal differences are observed. The air layer morphology is significantly altered, however, depending on $\textit{Fr}_d$: for $\textit{Fr}_d\gt 0.7$, it is unbounded, extending beyond the current test section length, and for subcritical conditions (deep water regime, $\textit{Fr}_d\lt 0.61$) a closure is formed and the air layer transitions to a cavity of a specific length.

The interaction between turbulent flows and bubbles is a complex phenomenon ubiquitous in natural and industrial settings. In this work, we experimentally investigate, from a fundamental perspective, the interaction between a rising bubble and a vortex ring in counterflow. Using time-resolved three-dimensional Lagrangian particle tracking (3D-LPT) coupled with shadowgraphy, we obtain simultaneous measurements of the bubble motion and the surrounding liquid flow. This approach enables detailed observation of bubble dynamics, deformation and eventual breakup, as well as the fluid motion. We examine several flow configurations by varying the vortex circulation and the Weber number while maintaining a comparable vortex-to-bubble size ratio. Based on these measurements, we classify the interaction events into three categories according to their impact on bubble dynamics and vortex stability over time. Through experiments, we address, for the first time, the three-dimensional effects of these interactions, which had not been considered in previous studies. The analysed experiments comprise the following: Case I, corresponding to a weak interaction in which neither the bubble nor the vortex is significantly affected; Case II, where the bubble is captured and advected by the vortex, leading to a strong distortion of the vortex due to the presence of the bubble within its core; and Case III, involving a stronger vortex capable of capturing the bubble and breaking it into two fragments without a severe loss of energy in the vortex core. The analysis of these results provides insight into the bubble breakup process and the mechanisms responsible for the destabilisation of the vortex ring.

Bubble breakup in turbulence is driven by velocity increments acting on the bubble interface. Traditionally, these instantaneous increments are replaced by the inertial-range second-order moment scaling, but whether this averaged description captures the kinematics leading to breakup remains unclear. Here, we experimentally investigate how bubble deformation preceding breakup relates to carrier-phase statistics. The experiments are conducted in nearly homogeneous isotropic turbulence with $\textit{Re}_\lambda =635$. Five high-speed cameras are used to reconstruct both the three-dimensional bubble topology and the trajectories of flow tracers in the carrier phase. A two-point description of bubble deformation is used to enable a direct comparison with particle pair dispersion theory and velocity increments. We find that the pre-breakup deformation stage can be described as a ballistic-dispersion problem, mirroring the short-time behaviour of particle pairs. For bubbles with $\textit{We} = \mathcal{O}(1)$, corresponding here to sizes close to the Hinze scale, the deformation is biased towards extensional events in which positive longitudinal velocity increments separate the daughter-associated subvolumes. Using a multifractal representation of the carrier-phase longitudinal-increment probability density function, conditioned by a capillary threshold, our results suggest that the measured deformation increments are consistent with stronger-than-average extensional increments, rather than with the inertial-range estimate.

The shear flow induced by a jetting cavitation bubble within grooved structures is systematically investigated using a three-dimensional compressible volume-of-fluid (VoF) solver combined with ultra-high-speed photography of one million frames per second (fps). The structured surface comprises twenty parallel micro-channels, and local mesh refinement down to $0.1\ {\unicode[Arial]{x03BC}}\text{m}$ near the groove bottom resolves the linear tangential velocity profile within the boundary layer. The simulations accurately reproduce experimental observations for two representative configurations, namely bubbles initiated above the groove and above the protrusion. In general, a microjet formed from the distal bubble surface impacts the lower bubble interface and subsequently spreads both along and across the groove channel, generating strong shear flow. Spatio-temporal wall-stress distributions indicate that the maximum shear stress occurs near the instant of jet impact, while the subsequent evolution is further modulated by daughter-bubble fragmentation and re-expansion. For a bubble initiated above the groove, the microjet produces a single impact, whereas for a bubble initiated above the protrusion, the jet becomes oblique: it first strikes the protrusion, spreads into the trapped bubble inside the groove and finally pierces the lower bubble surface at an angle. The influences of three geometric parameters, namely the horizontal offset $d^*$, vertical stand-off distance $h^*$ and groove width $w^*$, are systematically examined, revealing their coupled effects on bubble deformation, jet orientation, fragmentation and the vortex dynamics. A peak wall-shear stress of approximately $150\,\text{kPa}$ is obtained under specific geometric conditions due to rapid jet spreading and flow refocusing within the groove. These results provide fundamental insight into the three-dimensional, unsteady wall-shear generation produced by jetting cavitation bubbles interacting with micro-structured surfaces.

Cavitation bubbles collapsing near capillary exits can generate fast microjets that penetrate into the channel and promote fluid exchange. Here, we combine high-speed imaging and axisymmetric compressible volume-of-fluid simulations to study laser-induced cavitation bubbles near the exit of a long capillary. By varying the stand-off distance $\gamma$, the normalised inner radius $R_i^*$ and the normalised outer radius $R_o^*$, we identify two distinct jetting mechanisms. Regular jets are driven primarily by the vertical collapse of the bubble surface distal to the capillary, whereas wave-driven jets arise from the propagation and convergence of an interfacial wave initiated at the proximal bubble surface, causing distal-surface splitting and strong local pressure amplification. Wave-driven jets occur for sufficiently small stand-off distances and outer radii, with formation velocities typically above $500\,\mathrm{m\,s}^{-1}$ and reaching up to $2000\,\mathrm{m\,s}^{-1}$ in the simulations. Regular jets dominate at larger stand-off distances or larger outer radii, where interfacial-wave effects weaken. The outer radius $R_o^*$ governs the jetting regime by controlling interfacial-wave formation, propagation and convergence, while the inner radius $R_i^*$ mainly affects the later jet dynamics, including the impact location and vapour-jet penetration into the capillary. Compared with the needle jet generated by a bubble collapsing near a smooth rigid wall at nearly zero stand-off distance, the wave-driven jet here occurs over a much wider parameter range and its velocity and size can be tuned geometrically. These results establish a physical framework for cavitation-driven jetting near capillary boundaries and suggest strategies for controlling confined microjets in microfluidics and biomedical applications.

This paper introduces the solubility of heat, a new parameter useful in the modelling of the thermo-mechanical behaviour of two-phase vapour–liquid processes. Unlike other parameters in current use, the solubility of heat is dimensionless and is sensitive to both thermal and mechanical aspects of the process of interest. Large values of the parameter correspond to situations in which the latent heat associated with the generation and condensation of vapour is small so that the system’s behaviour is dominated by mechanical factors. Conversely, smaller values of the parameter indicate a strong effect of the energy cost of phase-change phenomena on the mechanics of the system. These statements are illustrated with a number of examples featuring the thermo-mechanics of vapour cavities in one, two and three spatial dimensions including growth, forced oscillations, condensation and other problems. These examples are based on a generalised formulation of the pertinent equations valid in any number of space dimensions, with the vapour cavity surrounded by a finite or infinite mass of liquid. The general case of a three-dimensional cavity of unspecified shape is also briefly considered.

We investigate the reconnection of two vortex bubble rings using direct numerical simulations of the incompressible two-phase Navier–Stokes equations with a volume-of-fluid method and a continuum surface force model. At fixed Reynolds number and varying Weber numbers ($\textit{We}$) spanning surface-tension-dominated to inertia-dominated regimes, the reconnection dynamics are divided into four stages, including approach, interfacial reconnection, helicity transport and pinch-off. Low $\textit{We}$ produces a larger reduction in interfacial area, leading to efficient reconnection and the formation of daughter bubbles. High $\textit{We}$ stretches the interface into slender filaments, producing residual fragments and secondary vortical structures. Simulations show that vorticity begins to rearrange towards the contact region before reconnection occurs, with surface tension modulating vorticity redistribution and interfacial contraction as $\textit{We}$ varies. These results relate $\textit{We}$ to interfacial morphology and the resulting reconnection topology, connecting vortex dynamics and interfacial physics in two-phase flows.

A widely cited experimental dataset (Cleve et al., J. Fluid Mech., 2019, vol. 875, pp. 597–621) on non-spherical acoustic cavitation dynamics provides a valuable benchmark for model validation, yet its use is hindered by large uncertainties in the two key parameters: the equilibrium bubble radius and the acoustic pressure amplitude. This study introduces a robust parameter-identification framework to resolve these discrepancies and enable meaningful comparison with models. Using an in-house graphics processing unit-accelerated solver for solving the second-order perturbation model developed by Shaw (Phys. Fluids, 2006, vol. 18, issue 7, p. 072104), the dataset is systematically re-examined. A Fourier coefficient-based error metric is developed to quantify the pronounced mismatch between simulations and measurements. The proposed method reliably corrects the vast majority of the experimental parameters, yielding excellent agreement between numerical predictions and observations. The outcome is a validated dataset with accurately identified parameters that can serve as a reliable benchmark for validating advanced computational fluid dynamics simulations and theoretical models. In addition, the approach offers a general tool for future experiments where direct measurements of local acoustic pressure remain difficult.

In this paper, the coupled volume-of-fluid and level set method, immersed boundary method and discrete element method is extended to an axisymmetric configuration to investigate bubble detachment from solid surfaces induced by particle impact. The post-impact dynamics is systematically investigated over a range of Weber numbers (We), particle wettabilities ($\theta _{p}$), density ratios ($k_{\rho }$) and size ratios ($k_{r}$). The results reveal three distinct detachment modes: capillary-wave detachment (CWD), bubble-rebound detachment (BRD) and particle-rebound detachment (PRD). At low We, early spreading over the particle releases surface energy and excites capillary waves that drive contact-line motion and rapid detachment. The spreading follows a power law, with the exponent increasing with We, reflecting the increasing contribution of impact inertia to the spreading process. As We increases, inertial compression suppresses capillary-wave-induced momentum reversal and the detachment mode shifts to BRD, where momentum reversal is achieved through the release of stored deformation energy. At sufficiently high We, particle rebound from the substrate injects a strong upward momentum into the flow, leading to PRD. Kelvin impulse analysis is employed to quantify the evolution of vertical momentum and establish a unified interpretation of the detachment process. A detachment capability factor is further proposed to characterise the competition between interfacial energy release and inertial suppression. Regime maps in the (We, $\theta _{p}$), (We, $k_{\rho }$) and (We, $k_{r}$) parameter spaces are constructed, demonstrating that mode transitions are governed by the balance between capillary-wave-driven momentum generation and inertia-induced suppression.

This paper presents a model for the full-range formation and propagation process of near- and far-field underwater explosion shock waves. The model combines coordinate mapping with the discontinuous Galerkin method so that fast-moving discontinuities, including the shock front and the bubble interface, remain on subdomain boundaries and do not require conventional shock-capturing treatment. In the near field, the computational domain is divided into interior and exterior regions, and the boundary conditions are supplied analytically through a two-medium Riemann solver and the Hugoniot jump conditions. In the far field, a new equation for the evolution of a finite-strength shock is derived by simplifying the inward characteristic with theoretical analysis. The resulting far-field equation is much less stiff than the full Euler or wave equation system and has a substantially smaller characteristic speed, allowing larger time steps and efficient propagation to long distances. Validation against experimental data shows that the model reproduces both the primary and secondary shocks with good accuracy, and that the far-field model predicts the decay of the shock peak in close agreement with the fully nonlinear near-field solution. Finally, we examine how internal waves repeatedly reflect inside the bubble and generate multiple pressure fluctuations in the emitted pressure history. Through scaling analysis and numerical validation, we identify when internal-wave effects become dynamically important and show that ambient pressure is the dominant controlling parameter.

Boundary slip can strongly influence the wall shear stress generated by a collapsing cavitation bubble near a solid surface. Here, we investigate this effect by systematically varying slip length $l$ and bubble stand-off distance $\gamma$. We show that boundary slip has negligible influence on bubble dynamics and jet formation prior to jet impact, but markedly alters the near-wall flow during jet spreading. Increasing $l$ substantially reduces both outward and inward peak shear stresses, suppresses flow separation during fast jet spreading and reorganises the spatio-temporal stress distribution. We derive a scaling for the maximum outward stress $\tau _m$ with $\tau _m\approx {\mu {U}_{0}{Re}^{0.5}(U_e/{U}_{0})^{1.5}}/ ({0.3R_{\textit{max}}+l(U_e {Re}/{U}_{0})^{0.5}})$, which captures the coupled effects of slip length, maximum bubble radius $R_{\textit{max}}$ and the outer-edge velocity $U_e$ of the spreading wall jet. Combined with a scaling for $U_e$ in terms of $\gamma$ and $l$, this yields a semi-empirical predictive framework for the maximum wall shear stress. These results clarify how interfacial slip regulates extreme cavitation-driven shear and offer a basis for its prediction and control.

Direct numerical simulations have been employed to study coalescence of two bubbles on a flat solid substrate at a range of Ohnesorge number ($ \textit{Oh}$) between 0.019 and 0.858 aiming at a detailed understanding of the process as the viscous effects become increasingly significant. Bubble diameter ratio is varied between 1 and 1.5 and the substrate is assumed perfectly hydrophilic. Results show the onset of transition away from an inertio-capillary velocity scaling to be at an $ \textit{Oh}$ of between $0.05$ and 0.1. It is also observed that the merged bubbles stop jumping off the substrate in this range. When the inertio-capillary scaling holds, we report a maximum bubble velocity of 0.19–0.25$u_{ic}$ depending on the value of diameter ratio, where $u_{ic}$ is the inertio-capillary velocity scale. Above $ \textit{Oh}$ = 0.5, a perfect scaling with visco-capillary velocity and overdamping of bubble oscillations are observed. Furthermore, we observe that the total viscous dissipation rate peaks around the moment where the merged bubble assumes a `lemon-like shape’, and a slow down in the propagation of surface deformation after this moment. Spatially, the viscous dissipation rate is highly local and assumes its largest values around the apexes of the bubble interface at the moment of lemon-like shape. Different contributions to the total energy of the system until after the merged bubble jumps off the substrate are furthermore discussed in detail.

The stability of two bubbles rising initially in line through a viscous liquid is revisited using a global linear stability analysis formulated within an arbitrary Lagrangian–Eulerian framework, complemented by fully resolved embedded boundary method simulations. Whereas previous studies attributed the promoted in-line stability of oblate bubbles to a deformation-enhanced wake entrainment, the present analysis demonstrates that the dominant stabilizing mechanism arises instead from an inclination-induced rotational feedback generated as the trailing bubble (TB) experiences the asymmetric shear of the leading bubble’s wake. This inclination–shear coupling, rather than deformation itself, governs the recovery of stability with increasing aspect ratio. Furthermore, the results reveal that the unstable drafting–kissing–tumbling mode originates from short-range, two-way coupling between the bubbles, whereas the asymmetric side-escape mode corresponds to a long-range, one-way interaction dominated by the TB response. In addition, a previously unreported oscillatory global mode emerges from the unsteady recirculation linking the two bubbles, acting as a hydrodynamic spring whose effective stiffness and damping govern the oscillation frequency and growth rate. Together, these findings identify inclination-induced lift as the primary mechanism controlling the stability of rising bubble pairs and provide a unified framework for interpreting their stationary and oscillatory transitions across a broad range of inertial and deformable regimes.

Cavitation bubble collapse near a wall is investigated by employing a recently developed laser–fluid computational framework to simulate the complete lifecycle of a wall-detached laser-induced bubble, including the water breakdown phase. The model couples compressible multiphase Euler equations, a radiative transport equation and a latent heat reservoir formulation for phase transition. A wide range of nine stand-off ratios $\gamma \in [0.79,\ 2.14]$ is investigated and directly compared with recent experimental measurements. The simulations reproduce the interfacial dynamics of bubbles with excellent accuracy. Moreover, the computations are capable of reidentifying the three experimentally observed collapse regimes, i.e. purely torus, mixed tip-and-torus and purely tip collapse, and correctly identify the collapse as the dominant source of the peak wall pressure rather than jet impact. A sensitivity analysis shows that only the mixed tip-and-torus regime exhibits strong dependence on the laser absorption coefficient. The simulations give access to the details on pressure, density, temperature and velocity fields inside the bubble and demonstrate that the vapour remains in average thermodynamic equilibrium during most of lifetime. The results reveal significantly different time scales between thermodynamic fields where the gas pressure becomes quasi-uniform inside the bubble during expansion and collapse, whereas the temperature remains strongly non-uniform with persistent spatial gradients. This study provides the most complete numerical reproduction to date of experimental laser-induced bubble collapse near a wall, and offers new physical insight into the coupling between bubble–wall interaction, laser-induced thermodynamics and collapse regimes.

This paper presents a model for non-spherical oscillations of a lipid-encapsulated bubble infused with magnetic particles, developed using membrane theory for thin, weakly magnetic membranes. The model assumes that only the applied magnetic field contributes significantly to the Maxwell stress, with the membrane under generalised plane stress. Axisymmetric deformations are analysed under two external magnetic field configurations: symmetrically arranged current-carrying coils and symmetrically placed magnetic dipoles. The non-spherical oscillations are restricted to the linear regime, with the second mode dominating within the stable pressure range. The pressure–frequency stability region is computed, and its dependence on material properties and magnetic forcing is examined, and natural frequencies are estimated using a boundary-layer approximation. In the coil-field configuration, time-series analysis shows that the second mode attains significant amplitude relative to the bubble radius, increasing with both interfacial magnetic susceptibility and initial radius. Order-of-magnitude estimates indicate that pressure forcing dominates over magnetic forcing, implying a negligible effect of applied current on radial oscillations and stability. In contrast, for the dipole field, increasing dipole strength and reducing its distance from the bubble centre significantly reduces the stability region. Simulations with time-varying current further show that its amplitude and frequency have minimal influence on the stability diagram but strongly affect the periodicity of mode shapes.

Bubbles rising in yield-stress fluids leave behind pathways in the memory of the fluid. These in turn influence the trajectories of subsequent bubbles released. Qualitatively, the effect manifests as a damaged pathway, modelled here as a low-viscosity Newtonian fluid within the surrounding viscoplastic fluid. Secondary bubbles are attracted towards these pathways, as is observed computationally and experimentally. Here we explore the effect of a damaged path on the release of a trapped bubble, captured by the critical yield number $Y_c$. We show that proximity to a damaged path increases $Y_c$, but eventually beyond a critical distance there is no influence on $Y_c$. We explore the effects of shape and surface tension on the aforementioned proximity results.

This work investigates, based on laboratory experiments, the influence of particles on the drainage of a bottle filled with an isodense suspension. Similarly to the drainage of a pure liquid, the flow rate remains constant during the whole emptying process and is primarily controlled by the size of the exit hole. Despite a hole-to-particle size ratio that would normally promote clogging, no such events are observed due to the periodic entrainment of air bubbles. The presence of particles causes a slight decrease in flow rate when increasing the particle initial packing fraction. Even for initial packing fractions of up to 60 %, it only decreases by at most 20 %. Revisiting the model of Clanet & Searby (2004) J. Fluid Mech. 510, 145–168, the flow rate is found to be linked to the rise velocity of the bubbles, which is surprisingly nearly independent of the packing fraction, even for values as high as 60 %. This counterintuitive result suggests that the suspension becomes heterogeneous, with a particle-depleted region in the pathway of the bubbles. Moreover, during drainage, the suspension exiting the bottle has a smaller packing fraction than the initial suspension, leading to an accumulation of particles inside the bottle and therefore an increase in the global packing fraction inside the vessel. When this latter reaches a critical value close to random loose packing, particles start to emerge above the liquid free surface. Based on accurate measurements that enable the computation of the mean packing fraction at all times, a model is proposed to describe this transition.

Deciphering the incipient stages of phase change in superheated fluids – and their subsequent evolution – remains a major challenge, as it requires bridging microscopic nucleation with macroscopic bubble dynamics and heat transfer. This gap has long hindered predictive boiling models and limited progress in emerging thermal technologies. Here, we leverage large-scale simulations of fluctuating hydrodynamics, combined with a rare-event technique, to rationalise liquid–vapour transformation from nucleation to bubble growth. We quantify the statistics of nucleated bubbles and hydrodynamic fields, onset temperatures, and non-trivial wettability effects on the nucleation pathways. Despite operating at the mesoscale, the simulations recover microscopic nucleation signatures observed in atomistic studies, including the dependence of both the boiling onset temperature and the crossover between homogeneous and heterogeneous nucleation pathways on surface wettability. At larger scales, they reproduce the experimentally observed transition from an early exponential regime of bubble-contact areas to a post-critical power-law scaling. These findings establish a quantitative bridge between fluctuation-driven nucleation and emergent boiling dynamics across scales.

Bubble pairs are effective modulators of liquid jets. We investigate the jetting of an air bubble driven by a laser-induced cavitation bubble using high-speed imaging, compressible volume-of-fluid (VoF) simulations and theoretical analysis. Three distinct jet types emerge, depending on the stand-off distance $\gamma$ and size ratio $\eta$ between the bubbles. Jet formation proceeds through two stages: an initial shock-induced acceleration followed by flow focusing on the concave liquid–air interface. We derive scaling relations, $V_0=1.1 p_0R_0/(\rho cR_l)((\gamma (1+\eta )-1)/\eta )^{-1.6}$ for the shock-driven stage and $V_m={}(1+(0.8-0.5\gamma )\eta ^{0.75})V_0$ for the flow focusing stage in the strong jet regime, both of which agree closely with experimental and numerical measurements. Here, $V_0$ and $V_m$ denote the velocity increments associated with shock-wave-induced acceleration and flow focusing stages, respectively. The variables $p_0$, $R_0$, $\rho$, $c$ and $R_l$ represent the initial pressure and radius of the cavitation bubble, the fluid density, the speed of sound in the liquid and the maximum volume-equivalent radius of the cavitation bubble, respectively. A $(\eta ,\gamma )$ phase diagram delineates the weak, strong and explosive jets, with regime boundaries accurately captured by the theoretically derived transitions.

Drop tower experiments have been performed to study the capillary collapse of large high-aspect-ratio cavities. Cavities are formed by momentarily impinging the free surface of a liquid bath with a jet of air in the microgravity environment of a drop tower. The collapse may give rise to a jet and three distinct jetting regimes are identified. Simulations are performed to further investigate the phenomena. The abrupt emergence of a thin high velocity jet is observed experimentally and numerically at a specific initial cavity aspect ratio. Different power laws are identified in different regions of the cavity during the collapse providing further understanding of cavity collapse phenomena. In particular, it shows that the spherical and cylindrical self-similar collapses can compete simultaneously, that is, during the same collapse, for determining the final thin jet formation.