Gas-encapsulated drops, much like antibubbles, are drops enclosed in a bubble within a liquid. They show potential as payload carriers in fluid transport and mixing techniques where sound waves can be leveraged to induce the collapse of the gas core and the subsequent release of the drop. Here, the interaction of millimetre-sized gas-encapsulated drops with impulsive laser-induced shock waves is investigated to gain fundamental insights into the release process. Experimental synchrotron X-ray phase contrast imaging, which allows the drop dynamics to be visualised inside the encapsulating bubble, is complemented by numerical simulations to study the intricate physics at play. Three drop dynamical release regimes are discovered, namely the drop impact, partial deposition and jet impact regimes. The regime type is mainly dependent on the shape of the bubble interface impacting the drop and the associated Weber and Reynolds numbers. The drop dynamics of the drop impact and partial deposition regimes show similarities with the canonical configuration of drops impacting flat liquid surfaces, whereas the jet impact regime resembles binary drop collisions, which allows existing scaling laws to be applied to describe the underlying processes. The release of the drop is investigated numerically. The time evolution of the drop dissemination within the surrounding liquid discloses enhanced mixing for dynamics involving high Weber and Reynolds numbers such as the drop impact and jet impact regimes.

We experimentally investigate the effect of Reynolds number ($Re$) on the turbulence induced by the motion of bubbles in a quiescent Newtonian fluid at small $Re$. The energy spectra, $E(k)$, are determined from the decaying turbulence behind the bubble swarm obtained using particle image velocimetry. We show that when $Re \sim O(100)$, the slope of the normalized energy spectra is no longer independent of the gas volume fraction and the $k^{-3}$ subrange is significantly narrower, where $k$ is the wavenumber. This is further corroborated using second-order longitudinal velocity structure function and spatial correlation of the velocity behind the bubble swarm. On further decreasing the bubble Reynolds number ($O(1) < Re < O(10)$), the signature $k^{-3}$ of the energy spectra for the bubble-induced turbulence is replaced by $k^{-5/3}$ scaling. Thus, we provide experimental evidence to the claim by Mazzitelli et al. (Phys. Fluids, vol. 15, 2003, pp. L5–L8) that at low Reynolds numbers the normalized energy spectra of the bubble-induced turbulence will no longer show the $k^{-3}$ scaling because of the absence of bubble wake and that the energy spectra will depend on the number of bubbles, thus being non-universal.

We study single bubble deformation statistics in an homogeneous and isotropic turbulent flow by means of direct numerical simulations. We consider bubbles at low Weber number ($We <3$) that have not been broken. We show that we can reproduce bubble deformations with a linear dynamics for each spherical harmonic mode. Inferring the coefficients of the linear model from the DNS data, we find that the natural frequency corresponds to the Rayleigh frequency, derived in a quiescent flow. However, the effective damping increases by a factor 7 compared with the quiescent case, at Taylor Reynolds number $\textit {Re}_\lambda = 55$. Looking at the flow structure around the bubble, we argue that the enhanced damping originates from a thick boundary layer surrounding the bubble. We demonstrate that the effective forcing, originating from the turbulent flow forcing on the bubble surface, is independent of bubble deformability. Therefore, the interface deformations are only one-way coupled to the flow. From this model we conclude that bubbles break rather from turbulent fluctuations than from a resonant mechanism. Eventually, we investigate the pressure modes’ statistics in the absence of bubbles and compare them with the effective forcing statistics. We show that both fields share the same probability distribution function, characterized by exponential tails, and a characteristic time scale corresponding to the eddy turnover time at the mode scale.

A gas bubble sitting at a liquid–gas interface can burst following the rupture of the thin liquid film separating it from the ambient, owing to the large surface energy of the resultant cavity. This bursting bubble forms capillary waves, a Worthington jet and subsequent droplets for a Newtonian liquid medium. However, rheological properties of the liquid medium like elastoviscoplasticity can greatly affect these dynamics. Using direct numerical simulations, this study exemplifies how the complex interplay between elasticity (in terms of elastic stress relaxation) and yield stress influences the transient interfacial phenomenon of bursting bubbles. We investigate how bursting dynamics depends on capillary, elastic and yield stresses by exploring the parameter space of the Deborah number ${{\textit {De}}}$ (dimensionless relaxation time of elastic stresses) and the plastocapillary number $\mathcal {J}$ (dimensionless yield-stress of the medium), delineating four distinct characteristic behaviours. Overall, we observe a non-monotonic effect of elastic stress relaxation on the jet development while plasticity of the elastoviscoplastic (EVP) medium is shown to affect primarily the jet evolution only at faster relaxation times (low ${{\textit {De}}}$). The role of elastic stresses on jet development is elucidated with the support of energy budgets identifying different modes of energy transfer within the EVP medium. The effects of elasticity on the initial progression of capillary waves and droplet formation are also studied. In passing, we study the effects of solvent–polymer viscosity ratio on bursting dynamics and show that polymer viscosity can increase the jet thickness apart from reducing the maximum height of the jet.

The motion of a bubble of negligible viscosity, such as air, forced down a tube filled with a viscous fluid which wets the walls of the tube has become a classic of the fluid dynamical literature. The differential motion of the bubble and the fluid are determined by the thin film which surrounds the bubble, whose shape and thickness are set by the interplay between gradients in surface tension and viscous shear stresses. Bretherton (J. Fluid Mech., vol. 10, issue 2, 1961, p. 166) provided a first, clear mathematical analysis in the lubrication limit coupled with carefully constructed experimental confirmation of the thin films deposited by a bubble moving in the confining geometry of the capillary tube. Its lasting impact has been not only in the migration of bubbles, but in a host of related fluid dynamical, industrial, biological and environmental processes for which thin lubricating films on the sometimes convoluted geometries of complex microstructures, such as porous media, determine the large-scale behaviour.

Vapour bubbles produced by long-pulsed laser often have complex non-spherical shapes that reflect some characteristics of the laser beam. The transition between two commonly observed shapes, namely, a rounded pear-like shape and an elongated conical shape, is studied using a new computational model that combines compressible multiphase fluid dynamics with laser radiation and phase transition. Two laboratory experiments are simulated, in which a holmium:YAG or thulium fibre laser is used to generate bubbles of different shapes. In both cases, the predicted bubble nucleation and morphology agree reasonably well with the experimental observation. The full-field results of laser irradiance, temperature, velocity and pressure are analysed to explain bubble dynamics and energy transmission. It is found that due to the lasting energy input, the vapour bubble's dynamics is driven not only by advection, but also by the continued vaporisation at its surface. Vaporisation lasts less than $1~{\rm \mu}$s in the case of the pear-shaped bubble, compared with over $50~{\rm \mu}$s for the elongated bubble. It is thus hypothesised that the bubble's morphology is determined by competition. When the speed of advection is higher than that of vaporisation, the bubble tends to grow spherically. Otherwise, it elongates along the laser beam direction. To test this hypothesis, the two speeds are defined analytically using a model problem, then estimated for the experiments using simulation results. The results support the hypothesis. They also suggest that when the laser's power is fixed, a higher laser absorption coefficient and a narrower beam facilitate bubble elongation.

The collapse of a vapour bubble over a material surface has been widely studied over the past few decades, but a comprehensive and quantitative analysis of the cavitation dynamics and its effects on solid materials at the mesoscale (nanometre up to micrometre), which would be of particular interest in applications exploiting cavitation power, is still lacking. In this work, we adopt a diffuse interface model to describe the microbubble dynamics, and a dynamic plasticity model for the solid. The former is particularly suited to studying the rich phenomenology characterising bubble collapse at the mesoscale, which comprises transitions to supercritical conditions, emission and propagation of shock waves, generation of liquid microjets and topological transitions, whereas the latter is used to characterise the permanent plastic deformation caused by the bubble collapse, and has been augmented to consider inertial effects, to assess whether or not an interaction between elastic and plastic waves may influence the resulting deformation. Results concerning the collapse of a microbubble at different liquid overpressures and initial standoff ratios are discussed, and the elastoplastic wave propagation in the solid, together with plastic deformation, is studied for different cases, depending on elastic and plastic material parameters.

A novel theoretical model for bubble dynamics is established that simultaneously accounts for the liquid compressibility, phase transition, oscillation, migration, ambient flow field, etc. The bubble dynamics equations are presented in a unified and concise mathematical form, with clear physical meanings and extensibility. The bubble oscillation equation can be simplified to the Keller–Miksis equation by neglecting the effects of phase transition and bubble migration. The present theoretical model effectively captures the experimental results for bubbles generated in free fields, near free surfaces, adjacent to rigid walls, and in the vicinity of other bubbles. Based on the present theory, we explore the effect of the bubble content by changing the vapour proportion inside the cavitation bubble for an initial high-pressure bubble. It is found that the energy loss of the bubble shows a consistent increase with increasing Mach number and initial vapour proportion. However, the radiated pressure peak by the bubble at the collapse stage increases with decreasing Mach number and increasing vapour proportion. The energy analyses of the bubble reveal that the presence of vapour inside the bubble not only directly contributes to the energy loss of the bubble through phase transition but also intensifies the bubble collapse, which leads to greater radiation of energy into the surrounding flow field due to the fluid compressibility.

This study investigates the interaction between a freely rising, deformable bubble and a freely settling particle of the same size due to gravity. Initially, an in-line configuration is considered while varying the Bond, Galilei and Archimedes numbers. The study shows that as the bubble and particle approach each other, a liquid film forms between them that undergoes drainage. The formation of the liquid film leads to dissipation of kinetic energy, and for sufficiently large bubble velocities, particle flotation takes place. Increasing the Bond number causes the bubble to deform more severely, which may allow the particle to pass through the bubble as it ruptures. This work also considers an offset configuration, which shows that the bubble slides away from the particle, affecting its settling trajectory.

In confined systems, the entrapment of a gas volume with an equivalent spherical diameter greater than the dimension of the channel can form extended bubbles that obstruct fluid circuits and compromise performance. Notably, in sealed vertical tubes, buoyant long bubbles cannot rise if the inner tube radius is below a critical value near the capillary length. This critical threshold for steady ascent is determined by geometric constraints related to the matching of the upper cap shape with the lubricating film surrounding the elongated part of the bubble. Developing strategies to overcome this threshold and release stuck bubbles is essential for applications involving narrow liquid channels. Effective strategies involve modifying the matching conditions with an external force field to facilitate bubble ascent. However, it is unclear how changes in acceleration conditions affect the motion onset of buoyancy-driven long bubbles. This study investigates the mobility of elongated bubbles in sealed tubes with an inner radius near the critical value inhibiting bubble motion in a vertical setting. Two strategies are explored to tune bubble motion, leveraging variations in axial and transversal accelerations: tube rotation around its axis and tube inclination relative to gravity. By revising the geometrical constraints of the simple vertical setting, the study predicts new thresholds based on rotational speed and tilt angle, respectively, providing forecasts for the bubble rising velocity under modified apparent gravity. Experimental measurements of motion threshold and rising velocity compare well with theoretical developments, thus suggesting practical approaches to control and tune bubble motion in confined environments.

We describe the rising trajectory of bubbles in isotropic turbulence and quantify the slowdown of the mean rise velocity of bubbles with sizes within the inertial subrange. We perform direct numerical simulations of bubbles, for a wide range of turbulence intensity, bubble inertia and deformability, with systematic comparison with the corresponding quiescent case, with Reynolds number at the Taylor microscale from 38 to 77. Turbulent fluctuations randomise the rising trajectory and cause a reduction of the mean rise velocity $\tilde {w}_b$ compared with the rise velocity in quiescent flow $w_b$. The decrease in mean rise velocity of bubbles $\tilde {w}_b/w_b$ is shown to be primarily a function of the ratio of the turbulence intensity and the buoyancy forces, described by the Froude number $Fr=u'/\sqrt {gd}$, where $u'$ is the root-mean-square velocity fluctuations, $g$ is gravity and $d$ is the bubble diameter. The bubble inertia, characterised by the ratio of inertial to viscous forces (Galileo number), and the bubble deformability, characterised by the ratio of buoyancy forces to surface tension (Bond number), modulate the rise trajectory and velocity in quiescent fluid. The slowdown of these bubbles in the inertial subrange is not due to preferential sampling, as is the case with sub-Kolmogorov bubbles. Instead, it is caused by the nonlinear drag–velocity relationship, where velocity fluctuations lead to an increased average drag. For $Fr > 0.5$, we confirm the scaling $\tilde {w}_b / w_b \propto 1 / Fr$, as proposed previously by Ruth et al. (J. Fluid Mech., vol. 924, 2021, p. A2), over a wide range of bubble inertia and deformability.

Toroidal bubbles (TBs) represent cases of vortex rings with a gas–liquid interface where a gas vortex ring is encased within a liquid vortex ring, and can serve as effective media for mass conveyance, process mixing, noise reduction and reaction regulation. In this study, we carry out a systematic study on the interaction between a TB and a free surface. According to the high-speed photographic images from the experiments, we identify strong and weak interactions in terms of the normalized maximum free surface deformation $h_{max}^*$. Then, we perform numerical simulations based on the volume of fluid (VOF) method in the OpenFOAM platform. Based on both the experimental and the numerical results, we conclude that the Froude number, $Fr$, determines the main characteristics during the interaction process. The TB–free surface interaction is essentially the interaction between the liquid vortex ring enveloping the TB and the free surface, supplemented by the TB's complex behaviour. Next, we establish the scaling law of $h_{max}^*$ based on the energy balance condition. Based on this, we provide the critical $Fr$ and the slenderness of the TB, $\eta$, for identifying the strong and weak interactions, and a parametric plot of the interactions in terms of $Fr$ and $\eta$.

The buoyancy-driven motion of a deformable bubble rising near a vertical hydrophilic wall is studied numerically. We focus on moderately inertial regimes in which the bubble undergoes low-to-moderate deformations and would rise in a straight line in the absence of the wall. Three different types of near-wall motion are observed, depending on the buoyancy-to-viscous and buoyancy-to-capillary force ratios defining the Galilei ($Ga$) and Bond ($Bo$) numbers of the system, respectively. For low enough $Ga$ or large enough $Bo$, bubbles consistently migrate away from the wall. Conversely, for large enough $Ga$ and low enough $Bo$, they perform periodic near-wall bounces. At intermediate $Ga$ and $Bo$, they are first attracted to the wall down to a certain critical distance, and then perform bounces with a decreasing amplitude before stabilising at this critical separation. Periodic bounces are accompanied by the shedding of a pair of streamwise vortices in the wake, the formation of which is governed by the near-wall shear resulting from the no-slip condition. These vortices provide a repulsive force that overcomes the viscous resistance of the fluid to the departing motion, making the bubble capable of returning to the region where it is attracted again to the wall. Although periodic, the shedding/regeneration cycle of these vortices is highly asymmetric with respect to the lateral bubble displacements, vortices being shed when the gap left between the bubble and the wall reaches its maximum, and reborn only when this gap comes back to its minimum.

Frozen water might appear opaque since gas bubbles can get trapped in the ice during the freezing process. They nucleate and then grow near the advancing solidification front, due to the formation of a gas supersaturation region in its vicinity. A delicate interplay between the rate of mass transfer and the rate of freezing dictates the final shapes and sizes of the entrapped gas bubbles. In this work, we experimentally and numerically investigate the initial growth of such gas bubbles that nucleate and grow near the advancing ice front. We show that the initial growth of these bubbles is governed by diffusion and is enhanced due to a combination of the presence of the background gas concentration gradient and the motion of the approaching front. Additionally, we recast the problem into that of mass transfer to a moving spherical object in a homogeneous concentration field, finding good agreement between our experimental data and the existing scaling relations for that latter problem. Lastly, we address how fluid flow around the bubble might further affect this growth and qualitatively explore this through numerical simulations.

Cross-stream migration of a deformable fluid particle is investigated computationally in a pressure-driven channel flow of a viscoelastic fluid via interface-resolved simulations. Flow equations are solved fully coupled with the Giesekus model equations using an Eulerian–Lagrangian method and extensive simulations are performed for a wide range of flow parameters to reveal the effects of particle deformability, fluid elasticity, shear thinning and fluid inertia on the particle migration dynamics. Migration rate of a deformable particle is found to be much higher than that of a solid particle under similar flow conditions mainly due to the free-slip condition on its surface. It is observed that the direction of particle migration can be altered by varying shear thinning of the ambient fluid. With a strong shear thinning, the particle migrates towards the wall while it migrates towards the channel centre in a purely elastic fluid without shear thinning. An onset of elastic flow instability is observed beyond a critical Weissenberg number, which in turn causes a path instability even for a nearly spherical particle. An inertial path instability is also observed once particle deformation exceeds a critical value. Shear thinning is found to be suppressing the path instability in a viscoelastic fluid with a high polymer concentration whereas it reverses its role and promotes path instability in a dilute polymer solution. It is found that migration of a deformable particle towards the wall induces a secondary flow with a velocity that is approximately an order of magnitude higher than the one induced by a solid particle under similar flow conditions.

Cavity evolution in granular media is crucial in explosion-driven gas–particle flows, particularly in many engineering applications. In this study, a theoretical model was first proposed to describe the cavity evolution in granular media by extending the classical Rayleigh–Plesset model. A closed equation set comprising the radius, pressure and gas leak-off velocity equations was built by considering the gas expansion and non-Darcy gas-penetration effects. Both centrally symmetric and non-centrally symmetric cases of gas injection into granular media were investigated. Especially for modelling the non-symmetric scenario, the radius and gas leak-off velocity equations were proposed in each radial direction with angle $\theta$, and then the pressure equation was built up based on the integral gas leak-off along the cavity outline. Through non-dimensionalizing the theoretical equations, four key dimensionless numbers $\varPi_1,\ \varPi_4$ were obtained to characterize the response time of cavity expansion and the intensity of non-Darcy effects for both cases. This allowed us to determine a scaling law of effective cavity radius $R_{eff}^*=\sqrt {2\varPi _2/(7{\rm \pi} )}t^{*1/2}$ and the critical time $t_{cr}^*=\sqrt {12.5/\varPi _1}$ for two-dimensional cavity evolution. Additionally, the necessity of incorporating non-Darcy effects was ascertained under conditions of $\varPi _4>400$. The findings demonstrate that the proposed theoretical equations effectively predict the cavity evolution results under various operational conditions ($0.7<\varPi _1<7\times 10^2, 3<\varPi _4<1.1\times 10^3$), as validated by refined Euler–Lagrange numerical simulations.

Buoyancy-driven bubbly flows play pivotal roles in various scenarios, such as the oxygenation and mixing in the upper ocean and the reaction kinetics in chemical and bio-reactors. This work focuses on the convective flow induced by the localised release of large air bubbles ($D_b=3.7$ mm, ${Re}_b=950$) in a water tank, exploring the resulting flow and the transition from laminar to disturbed states as a function of the Rayleigh number ranging from $3\times 10^3$ to $2\times 10^5$. At low ${Ra}$ the flow is smooth and laminar with weak temporal oscillations, while a highly disturbed state appears above a critical value ${Ra}_c$. A theoretical analysis is presented that links the mean flow circulation to the Rayleigh number. Through an experimental investigation, utilising three-dimensional particle tracking velocimetry and flow visualisation, we confirm the theory presented, and characterise the laminar to disturbed transition in the system. These findings not only enhance our fundamental understanding of buoyancy-driven convective flows but also hold significant implications for practical applications, particularly in the optimisation of bio-reactor design and other industrial processes reliant on controlled convective dynamics.

We investigate air-entraining flows where degassing, rather than fragmentation, plays a significant role. Of interest is the power-law slope $\beta$ of the bulk bubble size distribution $N(a)$ during the air-generating period, when the total volume of bubbles is increasing. We study a canonical air-entraining flow created by strong underlying free-surface turbulence. We perform analysis using the population balance equation (PBE) and computations using direct numerical simulations (DNS) with bubble tracking. We quantify the importance of degassing by the ratio of degassing flux ($Q_D$) to entrainment flux ($Q_I$), $\mathcal {D}=Q_D/Q_I$, and the ratio of degassing rate ($\varLambda (a)$) to fragmentation rate ($\varOmega (a)$) for a bubble of radius $a$, $\varLambda (a)/\varOmega (a)$. For a broad range of large Froude numbers ${{Fr}}=U/\sqrt {L g}$, DNS give $\mathcal {D}=\operatorname {O}(1)$ (independent of ${{Fr}}$), showing that degassing is relevant, and $\varLambda (a) \gg \varOmega (a)$, showing that the bubble population is degassing-dominated. In contrast to fragmentation-dominated populations, such as those due to wave breaking, where $\beta =-10/3$, degassing-dominated populations have qualitatively different $N(a)$ during air entrainment. Analysis using the PBE shows that degassing-dominated $\beta$ is a function of $\varLambda (a)$, which has a turbulence-driven regime ($a< a_\varLambda$) and a buoyancy-driven regime ($a>a_\varLambda$). Here, $a_\varLambda$ is the bubble radius where terminal buoyant rise velocity equals $u_{rms}$. Consequently, $N(a)$ exhibits a split power with $\beta (a< a_\varLambda )=-4.\bar {3}$ and $\beta (a>a_\varLambda )=-5.8\bar {3}$ for moderate bubble Reynolds numbers ${{Re}}_b$. For large ${{Re}}_b$, $\beta (a>a_\varLambda )=-4.8\bar {3}$. The DNS strongly confirm these findings for moderate ${{Re}}_b$. By identifying and describing degassing-dominated bubble populations, this work contributes to the understanding and interpretation of broad types of air-entraining problems where degassing plays a relevant role.

We investigate the phenomena of crater formation and gas release caused by projectile impact on underwater beds, which occurs in many natural, geophysical and industrial applications. The bed in our experiment is constructed of hydrophobic particles, which trap a substantial amount of air in the pores of the bed. In contrast to dry beds, the air–water interface in a submerged bed generates a granular skin that provides rigidity to the medium by producing skin over the bulk. The projectile's energy is used to reorganize the grains, which causes the skin to crack, allowing the trapped air to escape. The morphology of the craters as a function of impact energy in submerged beds exhibits different scaling laws than what is known for dry beds. This phenomenon is attributed to the contact line motion on the hydrophobic fractal-like surface of submerged grains. The volume of the gas released is a function of multiple factors, chiefly the velocity of the projectile, depth of the bed and depth of the water column.

An ultrasonic phased array system is introduced to study the three-dimensional (3-D) movement of a single bubble in a GaInSn alloy under a transverse magnetic field (MF), which is verified by bubble experiments in water. The 3-D motion trajectories of individual bubbles in the GaInSn are obtained under a horizontal MF. As the MF becomes stronger, the bubble successively oscillates in random directions (R mode), a direction perpendicular to the MF (V mode), a direction parallel to the MF (P mode) and finally it rises straight (S mode). The significant anisotropy of the oscillation directions at a moderate MF intensity may be due to the anisotropy of the vortex structure around the bubble. Furthermore, the oscillation amplitude gradually declines with increasing MF intensity until the bubble trajectory finally becomes a straight line. Our measurements allow us to specify the characteristic regions for the observed bubble modes in the $N-Eo-Re$ parameter space (N is the magnetic interaction parameter, Eo is the Eötvös number and Re is the Reynolds number). In addition, more detailed characteristics of bubble terminal velocity are revealed, showing that the bubble velocities are closely related to the motion modes. The increase in bubble velocity at a moderate MF intensity is caused by the weakening oscillation. At a high strength, the MF monotonically suppresses the rise velocity of the bubble with a fixed scaling law.