Bubble Rebound Research Articles

Non-Spherical Cavitation Bubbles: A Review

Cavitation is a phase-change phenomenon from the liquid to the gas phase due to an increased flow velocity. As it causes severe erosion and noise, it is harmful to hydraulic machinery such as pumps, valves, and screw propellers. However, it can be utilized for water treatment, in chemical reactors, and as a mechanical surface treatment, as radicals and impacts at the point of cavitation bubble collapse can be utilized. Mechanical surface treatment using cavitation impacts is called “cavitation peening”. Cavitation peening causes less pollution because it uses water to treat the mechanical surface. In addition, cavitation peening improves on traditional methods in terms of fatigue strength and the working life of parts in the automobile, aerospace, and medical fields. As cavitation bubbles are utilized in cavitation peening, the study of cavitation bubbles has significant value in improving this new technique. To achieve this, many numerical analyses combined with field experiments have been carried out to measure the stress caused by bubble collapse and rebound, especially when collapse occurs near a solid boundary. Understanding the mechanics of bubble collapse can help to avoid unnecessary surface damage, enabling more accurate surface preparation, and improving the stability of cavitation peening. The present study introduces three cavitation bubble types: single, cloud, and vortex cavitation bubbles. In addition, the critical parameters, governing equations, and high-speed camera images of these three cavitation bubble types are introduced to support a broader understanding of the collapse mechanism and characteristics of cavitation bubbles. Then, the results of the numerical and experimental analyses of non-spherical cavitation bubbles are summarized.

Understanding cavitation bubble collapse and rebound near a solid wall

The collapse of cavitation bubbles is known for its intense and aggressive behavior, producing concentrated bursts of energy that can cause erosion, noise, and damage to metallic surfaces and mechanical equipment. However, this concentrated energy also offers significant potential for various applications in biomedical science, industrial engineering, and related technologies. This study presents a comprehensive numerical investigation of the collapse and rebound of cavitation bubbles near a wall using a conservative, compressible multiphase flow model. Laser-generated cavitation bubbles growing, collapsing, and rebounding in distilled water near a wall at three standoff distances were experimentally studied to validate the numerical method. The results show good agreement between the bubble shapes and radii from the numerical simulations and experiments. Additionally, velocity of microjets and thermodynamics of the bubble collapse were validated against the reference data in the literature. Subsequently, the pressure and temperature distributions and jet shapes were examined in detail, exploring the impact of standoff distances ranging from 0.2 to 1.8. A quantitative analysis of the pressure and temperature produced on the wall, as well as the jet velocity and bubble movement during the collapse, was systematically conducted. Jet velocities observed ranged from 30 m/s to 130 m/s, and numerical simulations were compared with experimental data from the literature, showing good agreement. Maximum temperature and pressure induced at the wall center can reach up to 616.2 K and 139.5 MPa, respectively. The detailed analyses in this study provide significant insights into the behavior of cavitation bubbles and the effect of standoff distance on their collapse and rebound near a wall.

Large-scale molecular dynamics simulations of bubble collapse in water: Effects of system size, water model, and nitrogen

Molecular dynamics simulations in the microcanonical ensemble are performed to study the collapse of a bubble in liquid water using the single-site mW and the four-site TIP4P/2005 water models. To study system size effects, simulations for pure water systems are performed using periodically replicated simulation boxes with linear dimensions, L, ranging from 32 to 512 nm with the largest systems containing 8.7 × 106 and 4.5 × 109 molecules for the TIP4P/2005 and mW water models, respectively. The computationally more efficient mW water model allows us to reach converging behavior when the bubble dynamics results are plotted in reduced units, and the limiting behavior can be obtained through linear extrapolation in L−1. Qualitative differences are observed between simulations with the mW and TIP4P/2005 water models, but they can be explained by the models’ differences in predicted viscosity and surface tension. Although bubble collapse occurs on time scales of only hundreds of picoseconds, the system sizes used here are sufficiently large to obtain bubble dynamics consistent with the Rayleigh–Plesset equation when using the models’ thermophysical properties as input. For the conditions explored here, extreme heating of the interfacial water molecules near the time of collapse is observed for the larger mW water systems (but the model underpredicts the viscosity), whereas heating is less pronounced for the TIP4P/2005 water systems because its larger viscosity contribution slows the collapse dynamics. The presence of nitrogen within the bubble only starts to affect bubble dynamics near the very end of the initial collapse, leading to an incomplete collapse and strong rebound for the mW water model. Although nitrogen is non-condensable at 300 K, it becomes highly compressed and reaches a liquid-like density near the collapse point. We find that the dissolution of nitrogen is much slower than the movement of the collapsing water front, and the re-expansion of the dense nitrogen droplet gives rise to bubble rebound. The incompatibility of the collapse and dissolution time scales should be considered for continuum-scale modeling of bubble dynamics. We also confirm that the diffusion coefficient for dissolved nitrogen is insensitive to pressure as the liquid transitions from a compressed to a stretched state.

Damping effect of surfactants on induced bubble shape deformations

The addition of surfactants suppresses interfacial deformations, and surface elasticity is expected to play a critical role. High-speed imaging is used to study the influence of surfactants on the shape oscillations of air bubbles attached to a capillary and on the rebound of bubbles from a horizontal glass plate. The experiments are conducted in pure water and in aqueous solutions containing five different surfactants: terpineol, sodium dodecyl sulfate, hexadecyltrimethylammonium bromide, Triton X-100, and Triton X-45. The frequencies and damping times of the decaying oscillations and the restitution coefficients of the decaying rebounds are evaluated. The damping time and the restitution coefficient both decrease sharply with an increasing surfactant concentration and then reach a minimum before finally stabilizing. The oscillation frequency initially increases due to enhanced surface elasticity but then drops suddenly when the surfactant concentration corresponding to the maximum damping is reached. The suppression of bubble rebounds by surfactants bears a strong resemblance to the damping of quadrupole bubble oscillations. In both cases studied, a surface elasticity of about 4 mN/m is required to achieve the maximum damping of interfacial deformations, regardless of the surfactant used. Moreover, the bubble rebounds are found to be more susceptible to the presence of trace concentrations of surfactants.

Modeling of shock wave produced by collapse of cavitation bubble using a fully conservative multiphase model

In this study, we extensively validated the applicability of the fully conservative compressible multiphase flow model to simulate the collapse of cavitation bubbles. The mathematical model is fully conservative, which is crucial for accurately modeling the strong shock phenomena induced via bubble collapse. The numerical method accounts for compressibility and mass transfer with phase-change transitions. A high-resolution shock-capturing finite-volume method and an accurate Riemann solver were employed to capture the strong shocks produced by bubble collapse. A grid-resolution study and validation were performed to ensure the convergence and consistency of the numerical method. This study focused on analyzing the shock waves generated during the collapse as well as the dynamics of bubble collapse and rebound. Quantitative comparisons between the simulation results and experimental data as well as the reference results revealed a high level of agreement. The investigation focused on the impact of various factors, including the bubble radius, phase change, and liquid pressure, on the collapse and rebound of the cavitation bubble, as well as the resulting shock waves. These analyses yielded valuable insight into the complex behavior of cavitation bubbles that collapse in a free field.

Behaviors of cavitation bubbles driven by high-intensity ultrasound

In a multi-bubble system, the bubble behavior is modulated by the primary acoustic field and the secondary acoustic field. To explore the translational motion of bubbles in cavitation liquids containing high-concentration cavitation nuclei, evolutions of bubbles are recorded by a high-speed camera, and translational trajectories of several representative bubbles are traced. It is found that translational motion of bubbles is always accompanied by the fragmentation and coalescence of bubbles, and for bubbles smaller than 10 μm, the possibility of bubble coalescence is enhanced when the spacing of bubbles is less than 30 μm. The measured signals and their spectra show the presence of strong negative pressure, broadband noise, and various harmonics, which implies that multiple interactions of bubbles appear in the region of high-intensity cavitation. Due to the strong coupling effect, the interaction between bubbles is random. A simplified triple-bubble model is developed to explore the interaction patterns of bubbles affected by the surrounding bubbles. Patterns of bubble interaction, such as attraction, repulsion, stable spacing, and rebound of bubbles, can be predicted by the theoretical analysis, and the obtained results are in good agreement with experimental observations. Mass exchange between the liquid and bubbles as well as absorption in the cavitation nuclei also plays an important role in multi-bubble cavitation, which may account for the weakening of the radial oscillations of bubbles.

Numerical Simulation of Collapse and Rebound of a Cavitation Bubble in Water

Numerical Simulation of Collapse and Rebound of a Cavitation Bubble in Water

Bubble collapse near porous plates

The collapse of a gas or vapour bubble near a non-porous boundary is directed at the boundary due to the asymmetry induced by the nearby boundary. High surface pressure and shear stress from this collapse can damage, or clean, the surface. A porous boundary, such as a filter, would act similarly to a non-porous boundary but with reduced asymmetry and thus reduced effect. Prior research has measured the cleaning effect of bubbles on filters using ultrasonic cleaning, but it is not known how the bubble dynamics are fundamentally affected by the porosity of the surface. We address this question experimentally by investigating how the standoff distance, porosity, pore size and pore shape affect two collapse properties: bubble displacement and bubble rebound size. We show that these properties depend primarily on the standoff distance and porosity of the boundary and extend a previously developed numerical model that approximates this behaviour. Using the numerical model in combination with experimental data, we show that bubble displacement and bubble rebound size each collapse onto respective single curves.

Interaction of a single bubble and an elastic plate: Influence of the standoff distance

The objective of this study was to investigate the coupled dynamics of a collapsing bubble and the motion of a nearby elastic plate at different initial distances. This was achieved using a combination of experimental and computational models. In the experiments, high-speed photography was used to record the temporal and spatial evolution of the collapse of a single bubble near an elastic boundary under normalized standoff distances γ ranging from 1.0 to 3.3. Digital image correlation was used to synchronously record the motion of the elastic plate. For the numerical simulations, taking the fluid compressibility and boundary motion into account, the immersed-boundary method was introduced to simulate the interaction between the elastic plate and bubble collapse. The results show that, with different initial distances, the dynamic behaviors of the bubble, including oscillation time, impact mode, and energy conversion, are different, and this is caused by the elastic rebound of the plate. In addition, the direction and amplitude of the deformation of the elastic plate are also influenced by the impact effects during bubble oscillation and rebound. The combined form of these impact behaviors changes with initial distance, and there are three typical impact patterns: the shock-wave effect, jet-effect, and hybrid shock-wave and jet-effect modes. In particular, when γ < 1.5, the jet effect and hybrid impact forms, which are dominated by the high-speed jet, can result in asymmetric deformation and cause greater local damage to the elastic plate. Finally, we summarize the combined mechanisms that govern the impact of a collapsing bubble on an elastic plate.

Relationship between a non-spherical collapse of a bubble and a stress state inside a wall

This study performed a fluid/material coupled numerical simulation of the first stage of a non-spherical collapse of a bubble near a wall and investigated the stress state inside the elastic material of the wall according to the change in the stand-off distance γ between the bubble and the wall. The relationship between the collapse behavior of the bubble and propagation of stress waves was confirmed for typical collapse modes: pancake-shaped mode at γ = −0.3, hemispherical mode at γ = 0, microjet mode at 0.3 < γ < 1.0, and detaching mode at γ > 1.2. The stress influence area, which is an index of material damage, was estimated. At 0.3 < γ < 1.0, the stress influence area caused by the microjet is narrow and shallow in the material; in contrast, that caused by the pressure waves spreads more widely and deeply, especially inside the material. This means that the pressure wave has a larger influence than the microjet on damage to a material even though the maximum value of the equivalent stress is nearly identical between the microjet and the pressure wave. Additionally, the depth of the stress influence area at 0.3 < γ < 0.5 is larger than that at γ = 0, although the volume and the maximum stress are larger at γ = 0 than at 0.3 < γ < 0.5. This indicates that the case of toroidal bubble rebound attaching to a wall has the potential to cause a deeper damage inside a material in comparison with hemispherical bubble collapse.

Numerical Study on Single-Bubble Contraction–Rebound Characteristics in Cryogenic Fluids

In cryogenic fluid storage and delivery, the rapid contraction and rebound of bubbles are prone to occur during bubble collapse due to the pressure saltation. With the contraction and rebound of bubbles, the pressure and temperature in the bubbles fluctuate greatly, which affects the service life of fluid machinery. During bubble contraction and rebound, there is an accompanied complex heat and mass transfer process. According to the thermal properties of cryogenic fluids, a single-bubble collapse model is proposed considering the temperature variations inside the bubble. In order to study the variation in temperature and pressure during bubble collapse in cryogenic fluids, the contraction and rebound of a single bubble in liquid hydrogen are investigated numerically under various operating pressures and supercooling degrees. The numerical results of the model indicate that there are periodic contraction and rebound of the bubble when the pressure rises suddenly. Furthermore, the periods and attenuation rates of bubbles in different media are studied and compared. For the most concerned pressure and temperature characteristics, the relationship between the peak pressure, the attenuation rate of the temperature and the dimensionless number is proposed.

Cavitation bubble collapse and rebound in water: Influence of phase transitions

The influence of the mass transfer across the bubble surface due to evaporation and condensation on the cavitation (vapor) bubble collapse and rebound in water under room conditions has been studied. The bubble is spherical with an initial radius of 1.92mm. The dynamics of the vapor in the bubble and the surrounding liquid is governed by the gas dynamics equations. The effects of the liquid viscosity and heat conductivity of both fluids are taken into account. The liquid and vapor states are mainly described by the known wide-range equations by Nigmatulin and Bolotnova. The mass transfer is governed by the accommodation coefficient αac in the Hertz–Knudsen–Langmuir formula. It has been found that at αac in the range 0.001−0.075 the vapor in the bubble is homobaric at collapse. As αac increases in the range αac>0.075, an isentropic compression wave convergent to the bubble center is formed in the bubble. At focusing of this wave at the bubble center, a divergent (reflected from the center) isentropic compression wave occurs. With rising αac the intensities of these convergent and divergent waves increase. The divergent wave partially penetrates to the liquid in the form of an isentropic divergent wave. With growing αac the penetrated wave becomes steeper. At αac≈0.25 the divergent isentropic wave in the bubble transforms into a shock wave during its propagation to the bubble surface. This shock wave partially penetrates to the liquid in the form of a divergent shock wave. At small αac the outgoing pulse in liquid is shockless. Starting with αac≈0.03, it becomes discontinuous. In the range 0.03≤αac≤0.12 the shock pulse results from only large pressure gradients in the liquid in the vicinity of the bubble at the beginning of rebound. In the range 0.12<αac<0.25 the discontinuous outgoing pulse is formed from the divergent isentropic compression wave arisen in liquid as a result of partial escape of the isentropic wave out of the bubble. At αac>0.25 the shock pulse is formed directly on the bubbles surface as a result of the partial penetration of the divergent shock wave from the bubble to liquid. The obtained numerical results are in good agreement with available numerical and experimental data.

Three-dimensional analysis of the rising dynamics of individual ellipsoidal bubbles in an inclined column

In this study, the dynamics of a single ellipsoidal air bubble rising in an inclined cylindrical vessel is experimentally investigated. The three-dimensional bubble trajectory reconstruction shows that the spirally rising bubble maintains two out-of-phase modes of oscillations, while the zigzagging bubble maintains a two-dimensional motion, despite the irregular rebounds with small amplitude. Assessing the bubble-wall rebounds for the helicoidal rising bubble shows that the normal restitution coefficient correlates with a modified normal Stokes number in the same manner as the normal wall collisions of liquid droplets [Legendre et al., 2005, Physics of Fluids 17, 097105]. A similar contribution of normal-to-wall and tangent-to-wall components of the kinetic energy in helicoidal bubble rise is maintained up to the highest inclination angle, i.e. 15°. However, for the zigzag rising bubble, despite the bubble rebounds on the wall, the wall-normal contribution of the kinetic energy is much less than its tangent-to-wall component.

Characteristics of the bubble-induced pressure, force, and impulse on a rigid wall

When a bubble collapses near a rigid wall, a localized area of high pressure is generated on the wall. In the present study, experiments are carried out to record the dynamics of cavitation bubbles near a rigid wall and the corresponding numerical simulations are performed using computational fluid dynamics. The bubble expansion, contraction, collapse, jet formation, and rebound observed in the numerical simulations are in good agreement with the experimental results. Thereafter, the influence of the stand-off parameter γ on the bubble-induced pressure, force, and impulse on a rigid wall is quantitatively studied. The peak value of the initial shock wave is higher than that generated by the bubble collapse. Nevertheless, the bubble pulse and jet impact are superimposed, resulting in a much longer and stronger impulse than that of the initial shock wave. The impulse increases as γ decreases in the initial shock wave stage. However, this is not the case in the bubble collapse stage. For different ranges of the pressure integration, the maximum impulse caused by the bubble collapse occurs at a moderate value of γ. The findings reported in this paper provide a reference for cavitation- or bubble-related applications.

Thermodynamic effects on single cavitation bubble dynamics under various ambient temperature conditions

Thermodynamic characteristics and their effects on single cavitation bubble dynamics are important to elucidate the physical behaviors of cavitation phenomena. In this study, experimental and numerical methods were utilized to explore the thermodynamic effects on single cavitation bubble dynamics under various ambient temperature conditions. A series of experiments was performed to generate a single cavitation bubble at ambient temperatures between 20 and 80 °C using a laser-induced method and a high-speed camera to observe the dynamic behaviors of bubbles. By increasing the ambient temperature, a nonspherical bubble shape with a jet flow at the bubble rebound stage was observed. Next, the numerical simulation results in terms of the bubble radius and bubble shape were validated with the corresponding experimental data. Generally, the results exhibited reasonable agreement, particularly at the later collapse and rebound stages. Critical hydrodynamic and thermodynamic mechanisms over multiple oscillation stages at different ambient temperatures were analyzed. The bubble behaviors and their intensities were numerically quantified with respect to the bubble radius, collapsing time, internal pressure, internal temperature, and phase transition rate parameters. The results showed that the maximum bubble radius, first minimum bubble radius, and collapsing time increased with an increase in the ambient temperature. Nevertheless, the peak values of the internal pressure and internal temperature decreased with an increase in the ambient temperature. Generally, the bubble collapsed less violently at high temperatures than at low temperatures.

Numerical study of the effect of liquid compressibility on acoustic droplet vaporization

In acoustic droplet vaporization (ADV), a cavitated bubble grows and collapses depending on the pressure amplitude of the acoustic pulse. During the bubble collapse, the surrounding liquid is compressed to high pressure, and liquid compressibility can have a significant impact on bubble behavior and ADV threshold. In this work, a one-dimensional numerical model considering liquid compressibility is presented for ADV of a volatile microdroplet, extending our previous Rayleigh-Plesset based model [Ultrason. Chem. 71 (2021) 105361]. The numerical results for bubble motion and liquid energy change in ADV show that the liquid compressibility highly inhibits bubble growth during bubble collapse and rebound, especially under high acoustic frequency conditions. The liquid compressibility effect on the ADV threshold is quantified with varying acoustic frequencies and amplitudes.

Numerical investigation of non-condensable gas effect on vapor bubble collapse

We numerically investigate the effect of non-condensable gas inside a vapor bubble on bubble dynamics, collapse pressure, and pressure impact of spherical and aspherical bubble collapses. Free gas inside a vapor bubble has a damping effect that can weaken the pressure wave and enhance the bubble rebound. To estimate this effect numerically, we derive and validate a multi-component model for vapor bubbles containing gas. For the cavitating liquid and the non-condensable gas, we employ a homogeneous mixture model with a coupled equation of state for all components. The cavitation model for the cavitating liquid is a barotropic thermodynamic equilibrium model. Compressibility of all phases is considered in order to capture the shock wave of the bubble collapse. After validating the model with an analytical energy partitioning model, simulations of collapsing wall-attached bubbles with different stand-off distances are performed. The effect of the non-condensable gas on rebound and damping of the emitted shock wave is well captured.

Liposome destruction by a collapsing cavitation microbubble: A numerical study

Hydrodynamic cavitation poses as a promising new method for wastewater treatment as it has been shown to be able to eradicate bacteria, inactivate viruses, and destroy other biological structures, such as liposomes. Although engineers are already commercializing devices that employ cavitation, we are still not able to answer the fundamental question: What exactly are the damaging mechanisms of hydrodynamic cavitation in various applications? In this light, the present paper numerically addresses the interaction between a single cavitation microbubble and a nearby lipid vesicle of a similar size. A coupled fluid–structure interaction model is employed, from which three critical modes of vesicle deformation are identified and temporally placed in relation to their corresponding driving mechanisms: (a) unilateral stretching at the waist of the liposome during the first bubble collapse and subsequent shock wave propagation, (b) local wrinkling at the tip until the bubble rebounds, and (c) bilateral stretching at the tip of the liposome during the phase of a second bubble contraction. Here, unilateral and bilateral stretching refer to the local in-plane extension of the bilayer in one and both principal directions, respectively. Results are discussed with respect to critical dimensionless distance for vesicle poration and rupture. Liposomes with initially equilibrated envelopes are not expected to be structurally compromised in cases with δ>1.0, when a nearby collapsing bubble is not in their direct contact. However, the critical dimensionless distance for the case of an envelope with pre-existing pores is identified at δ=1.9. Additionally, the influence of liposome-bubble size ratio is addressed, from which a higher potential of larger bubbles for causing stretching-induced liposome destruction can be identified.

Strong and fast rising pressure waves emitted by plasmonic vapor nanobubbles

Plasmonic vapor nanobubbles are currently considered for a wide variety of applications ranging from solar energy harvesting and photoacoustic imaging to nanoparticle-assisted cancer therapy. Yet, due to their small size and unstable nature, their generation and consequences remain difficult to characterize. Here, building on a phase-field model, we report on the existence of strong pressure waves that are emitted when vapor nanobubbles first form around a laser-heated nanoparticle immersed in water and subsequently after bubble rebound. These effects are strongest when the fluid is locally brought high in its supercritical state, which may be realized with a short laser pulse. Because of the greatly out-of-equilibrium nature of nanobubble generation, the waves combine a high-pressure peak with a fast pressure rising time and propagate in water over micron distances, opening the way to induce spatially and temporally localized damage. Discussing the consequences on biological cell membranes, we conclude that acoustic-mediated perforation is more efficient than nanobubble expansion to breach the membrane. Our findings should serve as a guide for optimizing the thermoacoustic conversion efficiency of plasmonic vapor nanobubbles.4 MoreReceived 10 December 2020Accepted 13 May 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023231Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCavitationDrops & bubblesThermoacoustic effectCondensed Matter & Materials PhysicsFluid Dynamics

Numerical simulation of spherical bubble collapse by a uniform bubble pressure approximation and detailed description of heat and mass transfer with phase transition

A mathematical model for the simulation of the dynamics of spherical vapor-air bubbles and its numerical implementation is presented. Heat and mass transfer and phase transition in terms of evaporation and condensation as well as air absorption and desorption are considered. Flow variables are discretized by a mixed finite volume / finite difference scheme and solved either by a Crank-Nicolson or Runge-Kutta scheme. Due to the assumption of homogeneous bubble pressure (homobaricity), the solution of momentum equations is restricted to the Rayleigh-Plesset equation which makes the model computationally efficient. The model is validated by measurement data for bubble growth and applied to bubble collapse and rebound. By a comparison with Navier-Stokes results from literature, the homobaricity assumption is shown to be appropriate even in the last stage of bubble collapse. The relation of the local velocity and temperature field with heat and mass transfer is discussed. Equilibrium bubble interface conditions (liquid and gaseous side have the same temperature and chemical potential) are compared to non-equilibrium conditions and are shown to yield the same local velocity and temperature field for each stage of bubble collapse and rebound.