Non-spherical Bubble Research Articles

Effect of helium and its synergism with displacement damage on microstructure of CLAM steel investigated by single, sequential and simultaneous Fe and He ion irradiations

The reduced-activation ferritic/martensitic steel, China Low-Activation Martensitic (CLAM) steel, was irradiated with single Fe, sequential He/Fe, sequential Fe/He, and simultaneous Fe+He ion beam irradiations at 350 ℃–550 ℃ to a peak displacement damage dose of 15 dpa with 0 - 110 appm/dpa He to explore the effect of He and its synergism with displacement damage on microstructure evolution. The microstructures of all the irradiated specimens were investigated by transmission electron microscope (TEM). For Fe/He sequential irradiation, He inhibited the growth of dislocation loop induced by high-temperature He post-irradiation and reduced the number density of loops. Non-spherical He bubbles were observed only at post-injection He at 550 °C. The size of non-spherical He bubbles produced at 110 appm/dpa was about twice as large as 11 appm/dpa, and the number density increased about 6.4 times. The number density of dislocation loops induced by sequential He/Fe irradiation is the highest, and the average size of loops is comparable to that caused by simultaneous Fe+He irradiation. Moreover, the sequential Fe/He irradiation induced the lowest number density of loops of approximately 64% of the simultaneous Fe+He irradiation. The spherical bubble was observed in all irradiation with He injection above 350 ℃. The average size of spherical He bubbles induced by simultaneous Fe+He irradiation is the largest, and the number density is about 2.6 times that of the sequential Fe/He irradiation. The synergisms of He in different irradiation sequences were analyzed systematically, which helps to better understand the evolutionary processes of the synergistic effect of He and displacement damage.

Refined Model of Dynamics of Weakly Non-Spherical Bubbles with the Centers in a Straight Line

Refined Model of Dynamics of Weakly Non-Spherical Bubbles with the Centers in a Straight Line

Modeling of the bubble collapse with water jets and pressure loads using a geometrical volume of fluid based simulation method

The dynamic behavior of bubble collapses, water jets, and pressure loads during the collapse of the bubble near walls and a free surface were numerically investigated via a geometrical volume of fluid (VOF)-based simulation method. The numerical method is based on the compressible Navier–Stokes equations in a conservative form that describe the flow of compressible viscous fluids. The equations are discretized on a general curvilinear grid using an associated Godunov-type numerical scheme, and a reconstruction of a computational finite-volume Riemann solver is introduced for suppression of oscillation near the interface between fluids. The interface was tracked using the VOF reconstruction method. The VOF method is based on a geometrical tool and Lagrangian propagation of the interface reconstructed by a piecewise linear interface calculation (PLIC), resulting in strictly mass-conserving and sharp interface solutions. The numerical procedure was validated for capturing sharp interface and strong shock waves. For the simulation of bubble collapse, grid dependence studies of a spark-generated bubble were studies of both spherical and non-spherical bubbles were conducted. The results showed good agreement between the simulation and experiment of the bubble dynamics during the collapse process. Subsequently, an investigation of a single bubble near a wall with different standoff distances was performed. The pressure loads induced by the jets impacting the walls were calculated and analyzed. Furthermore, a more complex case of bubble collapse near an oblique wall and free surface was simulated. The resulting bubble dynamics with the jets and free surface shape were compared via photographs of the experiments.

Time-domain simulation of acoustic scattering and internal propagation from multiple gas bubbles

Acoustic scattering and resonance responses from multiple gas bubbles are computed using a time-domain simulation based on the numerical solutions of the conservation laws. The time histories of scattered pressure and velocity, both outside and inside the bubbles, are obtained simultaneously from an immersed-boundary method facilitating the investigation of both exterior and interior acoustic fields for non-spherical bubbles. Agreement is found with both analytical scattering solutions and those from empirical shape factors in limiting cases. In addition, the time-domain method allows for the study of the transient acoustic scattering from pulse forcing (Gaussian). In this case, the interior gas oscillates in an off-center, non-uniform manner compared to the steady state forcing cases. The time history and the interior gas behavior are presented in detail for combinations of two bubbles of different sizes and shapes (spherical, prolate, oblate). A comparison and analysis of this immersed-boundary method to the finite element method and boundary element methods is provided. Also, the increasingly important role of computational acoustics in the study scattering of multiple targets of diverse sizes and shapes is highlighted.

Pulsating bubbles dynamics near a concave surface

Bubble dynamics near different boundaries have always been a hot topic in ocean engineering and many other fields. In the present study, we investigate the dynamics of high-pressure pulsating bubbles near a concave surface via experimental and numerical methods. Pulsating cavitation bubbles are generated by the electric discharge technique, and the violent expansion, contraction, and jet formation are observed through high-speed photography. Additionally, a multi-vortex ring model implemented in the boundary integral method is established to simulate the bubble motion near a curved surface. The precise non-spherical bubble shapes during bubble pulsation and detailed information on the jet velocity and wall pressure are obtained. The numerical results are found to be in good agreement with the experimental results, indicating the validity of the numerical model. Finally, a quantitative study is provided on the influence of two parameters: the distance parameter γ=L/Rm (L is the distance between the initial bubble center and the lowest point of the concave surface and Rm is the maximum bubble radius) and the concave curvature ξ=Rm/Rs (Rs is the radius of concave boundary).

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.

Size quantification of non-spherical bubbles by ultrasound

Ultrasonic detection is an effective method to quantify bubbles in opaque liquid, and acoustic scattering model is the key in ultrasonic inversion technique. Classical scattering models are usually based on the spherical assumption and <em>ka</em> is much less than 1. However, these conditions are not always satisfied in practical applications. In this study, a quantitative strategy of ultrasonic inversion is proposed for non-spherical bubbles and <em>ka</em> deviation assumption. A series solution model for a spherical gas bubble is established without considering the <em>ka</em> constraint, and it was compared with the classical Medwin (<em>ka</em><<1) and Anderson (<em>ka</em>≈1) models. The difference in their scattering cross sections <em>σ<sub>bs</sub></em> is only at the higher order formants of scattering and so the fitted line can be used to solve the multi-valued problem between <em>σ<sub>bs</sub></em> and <em>ka</em>. For a non-spherical bubble, <em>σ<sub>bs</sub></em> is determined by the frequency domain backscattering signal and size is characterized by the equivalent radius<em> a</em><sup>*</sup>and the inversion is performed by fitted curve from series solution model. Ultrasonic quantitative results were examined by high-speed photography. Results show that bubble rises in a zigzag pattern and non-spherical bubbles, their scattering cross sections are measured by the frequency domain scattering signal obtained at a position of ultrasonic measurement and the equivalent radius is inverted by the series solution fitting curve. The deviation between the results and the actual results <em>r</em><sub>0</sub> is about 1mm(relative error less than 45%) when 9≤<em>kr</em><sub>0</sub>≤35. This method can be used for acoustic inversion of non-spherical bubbles in a certain range of measurement accuracy.

Interaction between double nonspherical bubbles in compressible liquid under the coupling effect of ultrasound and electrostatic field

A dynamic model for a double-bubble system in compressible liquid under the coupling effect of ultrasound and electrostatic field was developed here. In this study, we mainly discussed the effect of the interaction on the investigated bubble using the numerical solutions to the theoretic model. The variable parameters are the distance between bubble centers and the initial radius of the adjacent bubble. In addition, we applied approximate equations to analyse variations of the internal gas pressure and temperature of a bubble. We found that, the oscillation amplitude of a bubble with an adjacent bubble significantly reduces, compared to that of an isolated bubble.

Dynamics characteristics of a laser-induced non-spherical bubble collapsing micro-jet and its enhancement on hard tissue ablation

Liquid-assisted laser ablation has been investigated in osteotomy and dentistry with the aim of removing tissue while minimizing thermal injury. In this paper, the dynamics of a laser-induced non-spherical bubble collapsing micro-jet vector as well as its scaling relationship with the output tissue ablation are described. The velocities of the micro-jets with normalized stand-off distances (γ) from 0.1 to 0.7 are determined in the range of 24–35 m/s, while the corresponding crater depths are in the range of 260–1020 µm with a diameter-to-depth ratio of 0.7 to 1.9. The results show that the geometrical characteristics of the incubation crater ablated in the bone are closely related to the micro-jet vector. The crater depth and diameter are positively dependent on the micro-jet velocity and micro-jet diameter, while crater's diameter-to-depth ratio is negatively correlated with the micro-jet velocity. The corresponding micro-jet impact strength on the bone tissue is about 85.2–123.5 MPa, with the micro-jet velocity ranging from 24 m/s to 35 m/s, and the impact pressure decreases rapidly along the central axis outward, resulting in the U-shaped ablation crater. The results show that adjusting γ is an effective method for controlling the micro-jet vector and the resultant bone ablation.

Pressure reconstruction of a planar turbulent flow field within a multiply connected domain with arbitrary boundary shapes

This paper reports for the first time the implementation procedures and validation results for pressure reconstruction of a planar turbulent flow field within a multiply connected domain that has arbitrary inner and outer boundary shapes. The pressure reconstruction algorithm used in this study is the rotating parallel-ray omni-directional integration algorithm that offers high-level of accuracy in the reconstructed pressure. While preserving the nature and advantage of the parallel ray omni-directional pressure reconstruction at places with flow data, the new implementation of the algorithm is capable of processing an arbitrary number of inner void areas with arbitrary boundary shapes. Validation of the multiply connected domain pressure reconstruction code is conducted using the Johns Hopkins DNS (Direct Numerical Simulation) isotropic turbulence databases [J. Graham et al., J. Turbul. 17(2), 181 (2016)], with 1000 statistically independent pressure gradient field realizations embedded with random noise used to gauge the code performance. For further validation, the code is also applied for pressure reconstruction from the DNS data [E. Johnsen and T. Colonius, J. Fluid Mech., 629, 231 (2009)] about a shock-induced non-spherical bubble collapse in water. It is demonstrated that the parallel-ray omni-directional integration algorithm outperforms the Poisson equation approach in terms of the accuracy for the pressure reconstruction from error embedded pressure gradients in both simply connected and multiply connected domains.

Comparison of Boundary Integral and Volume-of-Fluid methods for compressible bubble dynamics

The Boundary Integral Method (BIM) has been widely applied to simulate oscillating bubbles, for its high efficiency and accuracy. A conventional BIM assumes the fluid surrounding the bubble to be inviscid and incompressible. Wang & Blake (J. Fluid Mech., 659, 2010, 191–224) proposed an improved model for bubbles in a weakly compressible flow, which is referred to as CBIM. In this study, an all-Mach method (AMM) implemented in the free software program Basilisk for the simulation of compressible multiphase flows, and using a geometric Volume-of-Fluid (VoF), is employed to study and estimate the accuracy of BIM and CBIM at different Mach numbers. First, for a spherical bubble, an extended Rayleigh-Plesset equation, CBIM and AMM give very close results when Ma≲0.3. However, a deviation between these three schemes gradually becomes evident as Ma increases from 0.3 to 0.6. Second, for the nonspherical deformation of a bubble close to a wall, the results obtained from CBIM and AMM show many similarities, including the evolution of the nonspherical bubble morphology, jet impact velocity, and impact pressure on the wall. Apart from the liquid compressibility, the gas inertia/density is found to be another factor that may affect the applicability of CBIM. In addition, we compare the CBIM and BIM results against an experiment of a spark-generated cavitation bubble, in which the liquid compressibility is found to play a vital role. From the perspective of engineering applications, BIM can reproduce the main features of the bubble dynamics in the first cycle if the initial conditions are set properly. The new findings provide a reference for research of bubble dynamics in both fundamental and applied problems.

Bubble entrapment condition in Bingham materials

We investigate the entrapment condition of initially spherical and ellipsoidal Newtonian bubbles in viscoplastic materials using direct numerical simulations. For a spherical bubble, the entrapment condition depends on the balance between the buoyancy force and the force exerted by the yield stress of the viscoplastic material. For non-spherical bubbles, surface tension may yield the surrounding material to minimize the surface energy of the bubble. The yielding of the surrounding material by surface tension force facilitates the rising motion of bubbles. Although surface tension may yield the surrounding material and start the rising motion, the bubble may get entrapped later if the stress exerted by buoyancy force is less than the yield stress of the material. We evaluate the yield-stress parameter for different bubble shapes over a range of non-dimensional parameters to predict the critical yield-stress parameter for the entrapment of a bubble. • The critical yield stress parameter decreases at very high viscosity ratios. • The yield stress parameter is a constant at low viscosity ratios. • Yield stress resistive force depends on the maximum cross-sectional area normal to the buoyancy. • The critical yield stress parameter is independent of the initial shape of the bubble. • Non-spherical bubbles may be momentarily mobile due to surface tension effects.

Pressure reconstruction of a planar turbulent flow field within a multiply-connected domain with arbitrary boundary shapes

Over the past two decades, it has been demonstrated that the instantaneous spatial pressure distribution in a turbulent flow field can be reconstructed from the pressure gradient field non-intrusively measured by Particle Image Velocimetry (PIV). Representative pressure reconstruction methods include the omnidirectional integration (Liu and Katz, 2006; Liu et al., 2016; Liu and Moreto, 2020), the Poisson equation approach (Violato et al., 2011; De Kat and Van Oudheusden, 2012), the least-square method (Jeon et al., 2015), and most recently, the adjoint-based sequential data assimilation method, which also essentially utilizes the Poisson equation to reconstruct the pressure(He et al., 2020). Most of these previous pressure reconstruction examples, however, were applied to simply-connected domains (Gluzman et al., 2017) only. None of these previous studies have discussed how to apply the pressure reconstruction procedures to a multiply-connected domain (Gluzman et al., 2017). To fill in this gap, this paper presents a detailed report for the first time documenting the implementation procedures and validation results for pressure reconstruction of a planar turbulent flow field within a multiply-connected domain that has arbitrary inner and outer boundary shapes. The pressure reconstruction algorithm used in the current study is the rotating parallelray omni-directional integration algorithm, which, as demonstrated in reference (Liu and Moreto, 2020) based on simply-connected flow domains, offers high-level of accuracy in the reconstructed pressure. While preserving the nature and advantage of the parallel ray omni-directional pressure reconstruction at places with flow data, the new implementation of the algorithm is capable of processing an arbitrary number of inner void areas with arbitrary boundary shapes. Validation of the multiply-connected domain pressure reconstruction code is conducted using the DNS (Direct Numerical Simulation) isotropic turbulence field available at the Johns Hopkins Turbulence Databases, with 1000 statistically independent pressure gradient field realizations embedded with random noise used to gauge the code performance. For further validation, the code is also applied for pressure reconstruction from the DNS pressure gradient in the ambient flow field of a shock-induced non-spherical bubble collapse in water (Johnsen and Colonius, 2009). The successful implementation of the parallel ray pressure reconstruction method to multiply-connected domains paves the way for a variety of important applications including, for example, experimental characterization of pressure field changes during the process of cavitation bubble inception, growth and collapse, non-intrusive unsteady aerodynamic force assessment for an arbitrary body shape immersed in flows, and multi-phase flow investigations, etc. In particular, as an immediate follow-up effort, the parallel ray pressure code will be used for the instantaneous pressure distribution reconstruction of the turbulent flow surrounding cavitation inception bubbles occurring on top of a cavity trailing corner based on high-speed PIV measurements.

Numerical model of bubble shape and departure in nucleate pool boiling

• For a spherical bubble, the direct numerical integration of Young-Laplace equation works very well in computing the bubble shape. • The approximate analytical solution computes a non-spherical shape of a bubble at a high superheat much better than the direct numerical integration of Young-Laplace equation non-spherical bubbles. • The shape of a bubble has been found to be influenced by superheat and Bond number Bo. • The Young-Laplace equation seems to include the growth force to produce the hemispherical shape of non-spherical bubbles. • A very low Bo results in a train of small bubbles that coalesce to a big bubble with increase in Bo. In this work, we have developed an improved numerical model to simulate the dynamics of bubble shape and departure in nucleate pool boiling at a heated surface at low and high superheats. The numerical model computes the bubble shape solving Young-Laplace equation directly and considering the effect of radial variation of film pressure in our numerical model of microlayer evaporation. The numerical results of bubble shape and departure have also been compared with the CFD-results in literature and with the results of our experiments. For a spherical bubble, the direct numerical integration of Young-Laplace works very well in computing the bubble shape. For a non-spherical bubble, an approximate analytical solution for bubble shape proposed in literature works better than the numerical solution of Young-Laplace equation. The shape of a bubble has been found to be influenced by superheat and Bond number Bo. We have also analyzed the forces acting on the bubble surface while departing the heated surface. The Young-Laplace equation seems to include the growth force to produce the hemispherical shape of non-spherical bubbles. A very low Bo results in a train of small bubbles that coalesce to a big bubble with increase in Bo.

Numerical study on simultaneous thermodynamic and hydrodynamic mechanisms of underwater explosion

In this study, we numerically investigate the simultaneous thermodynamic and hydrodynamic mechanisms of underwater explosion (UNDEX). Bubble explosion in water at the collapsing stage is extremely violent and becomes extraordinarily hot, exceeding 1,000 K. The evolution of the bubbles and temperature fields are simulated using a fully compressible mixture model. The deformable bubble and the heat transfer of the internal explosive gas are captured with higher accuracy compared with published data. First, a spherical bubble that collapses and rebounds without the effects of gravity is computed to verify the accuracy of the model. The numerical results in terms of the bubble radius and temperature fields are consistent with analytical solutions based on the Rayleigh–Plesset equation. Next, a real 5.2 g trinitrotoluene UNDEX experimental case is simulated, in which the formation of a non-spherical bubble with a non-symmetric thermal boundary layer is analyzed. An excellent agreement between bubble motions and experimental data is obtained. The temperature inside the collapsing bubble increased significantly, reached a maximum value of approximately 2,000 K at its final stage, and then decreased rapidly. In addition, a spatially non-uniform temperature field and a thicker thermal boundary layer along the jet direction at the collapse stage are observed. Furthermore, a case study is conducted to estimate the bubble dynamics of non-isothermal and isothermal cases. Finally, the effects of the initial equilibrium gas temperature and water temperature on the thermodynamic and hydrodynamic mechanisms of UNDEX are investigated in detail. An approximate non-linear relation is proposed to describe the relationship among the important parameters.

Dynamics of a bubble in a liquid fully confined by an elastic boundary

In order to investigate the dynamics of a bubble in a liquid fully confined by an elastic boundary, which are used for applications and research of cavitation bubbles in botanical and biomedical sciences, we establish a related numerical model by the boundary element method. The boundary is defined as an interface between two liquids with different densities to simulate the environment of biological tissue efficiently. Our numerical model is validated thanks to the results of an available related experiment and the calculations of a confined corrective Rayleigh–Plesset equation. Then, we focus on the dynamics of a non-spherical bubble caused by relative position of the bubble and confinement. The results show that the confinement can lead to a rapid oscillation of a bubble, and a jet will be generated along the eccentric direction because of the accumulation of high pressure and disturbance on one side of the spherical confinement. Furthermore, elastic modulus of the boundary, size of the confinement, and eccentric position of the bubble in the confinement are considered in this paper. The amplitude and cycle of a bubble oscillation will decrease with the increase of the elastic modulus and decrease of the size of the confinement. What's more, eccentricity leads to a strong restriction on the bubble surface near the boundary and obvious non-spherical deformation of the elastic boundary. The study can contribute to understandings and applications of cavitation bubbles in expulsion of spores, plant cell wall broken, thrombolysis, and other related botanical and biomedical fields.

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System.

When located near biological barriers, oscillating microbubbles may increase cell membrane permeability, allowing for drug and gene internalization. Experimental observations suggest that the temporary permeabilization of these barriers may be due to shear stress that is exerted on cell tissues by cavitation microstreaming. Cavitation microstreaming is the generation of vortex flows which arise around oscillating ultrasound microbubbles. To produce such liquid flows, bubble oscillations must deviate from purely spherical oscillations and include either a translational instability or shape modes. Experimental studies of bubble-induced flows and shear stress on nearby surfaces are often restricted in their scope due to the difficulty of capturing shape deformations of microbubbles in a stable and controllable manner. We describe the design of an acoustic levitation chamber for the study of symmetry-controlled nonspherical oscillations. Such control is performed by using a coalescence technique between two approaching bubbles in a sufficiently intense ultrasound field. The control of nonspherical oscillations opens the way to a controlled cavitation microstreaming of a free surface-oscillating microbubble. High-frame rate cameras allow investigating quasi-simultaneously the nonspherical bubble dynamics at the acoustic timescale and the liquid flow at a lower timescale. It is shown that a large variety of fluid patterns may be obtained and that they are correlated to the modal content of the bubble interface. We demonstrate that even the high-order shape modes can create large-distance fluid patterns if the interface dynamics contain several modes, highlighting the potential of nonspherical oscillations for targeted and localized drug delivery.

Acoustic backscattering observations from non-spherical gas bubbles with ka between 0.03 and 4.4.

The study of gas bubbles in liquid media is of importance in many areas of research. Gas bubbles are often studied using in situ measurement techniques; however, acoustic inversion techniques have also been used to extract physical properties of gas bubbles. These inversion techniques rely on existing analytical scattering models; however, these models often assume that the gas bubbles are spherical in shape and have an equivalent bubble radius, a, that is small compared to the incident acoustic wavelength (ka ≪ 1), which is not always valid. This study aims to understand how the departure from these assumptions affects the acoustic backscattering cross section, σbs, of non-spherical gas bubbles. Experimental estimates of σbs of non-spherical gas bubbles of different sizes, with ka values ranging between 0.03 and 4.4, were compared to four commonly known analytical σbs models. All models performed equally at predicting σbs for ka smaller than 0.5; however, there was no model that better predicted the experimental estimates of σbs for ka larger than 0.5, regardless of bubble shape. Large variabilities in the experimental estimates of σbs are observed for ka larger than 0.5, which are caused by the variability in bubble shape and size, as well as the bubble's orientation.

Spatiotemporal evolutions of forces and vortices of flow past ellipsoidal bubbles: Direct numerical simulation based on a Cartesian grid scheme

An in-depth investigation of two fixed non-spherical bubbles is an indispensable step toward revealing fundamental mechanisms in complex bubbly flows, where direct numerical simulation (DNS) is one of the most promising approaches to conduct such a task. However, accurately modeling force distribution and efficiently generating satisfactory mesh around a non-spherical bubble pair are challenging to current DNS methods. In this study, an effective non-body-fitted gas–liquid interface tracking scheme based on the Cartesian grid was developed to conduct three-dimensional DNS of two fixed ellipsoidal bubbles with frozen shape in an incompressible Newtonian fluid. The grid-independent analysis and analytical validation prove that our developed non-body-fitted gas–liquid interface tracking scheme is able to accurately retrieve all force components exerted on a bubble with less mesh generation and computational efforts than body-fitted counterparts. Using this non-body-fitted gas–liquid interface tracking scheme, spatiotemporal evolutions of forces and vortices around the two fixed ellipsoidal bubbles were directly simulated under various values of Reynolds numbers, separation distances, and the bubble’s ellipsoidicity. The analysis of drag force shows that the overall drag behaviors of ellipsoidal bubbles are quite similar to those of spherical bubbles though larger ellipsoidicity produces a higher drag coefficient. However, the sign of lift forces, i.e., either the two bubbles attract or repel each other, is highly dependent on ellipsoidicity. For the bubble pair with moderate ellipsoidicity, attractive force dominates at moderate-to-high Reynold numbers, while the two bubbles tend to repel at low Reynolds numbers. For the bubble pair with high ellipsoidicity, the two bubbles repel each other at all values of Reynolds numbers and separation distances. Characteristics of vortex developments, which are the reason behind these ellipsoidicity-dependent force behaviors, are presented and discussed. This study highlights the importance of the bubble’s shape in the interactions and associated vortex between two adjacent fixed ellipsoidal bubbles.

Numerical analysis of fluid-material coupled method on propagation of pressure and stress waves during non-spherical bubble collapse

Numerical analysis of fluid-material coupled method on propagation of pressure and stress waves during non-spherical bubble collapse