Pair Of Bubbles Research Articles

Dynamics of two interacting acoustic bubbles at short separation distances

We investigate experimentally the attraction between two closely spaced, oscillating microbubbles. Above a certain value of the applied acoustic field, the bubbles jump to a new equilibrium location, where they are separated by a thin fluid layer whose the thickness is much smaller than the bubble radii. We demonstrate that this new equilibrium is caused by the sign reversal of the radiation interaction force acting between the two bubbles, attributed to the multiple rescattering effects of the waves emitted by the bubbles. Theoretical investigation reveals that a new stable equilibrium appears at short distances, resulting in a quasi-contacting bubble pair.

Implosion of a bubble pair near a solid surface

A compressible two-phase flow solver is developed for the simulation of a collapsing bubble pair. With the adaptive mesh and high-resolution scheme, the discontinuities and shock waves due to bubble collapse are well captured. Numerical results show that the collapse of two bubbles horizontally arranged ($\ensuremath{\phi}={0}^{\ensuremath{\circ}}$) produces the highest wall pressure peak among the oblique angles (${0}^{\ensuremath{\circ}}\ensuremath{\le}\ensuremath{\phi}\ensuremath{\le}{90}^{\ensuremath{\circ}}$) while the perpendicular arrangement ( $\ensuremath{\phi}={90}^{\ensuremath{\circ}}$) leads to the lowest wall pressure peak, even weaker than that of the single bubble collapse.

Transition mechanisms of translational motions of bubbles in an ultrasonic field.

The translation behaviors of oscillating bubbles are closely related to the polymerizations and dispersions between them, which are crucial for the ultrasonic cavitation effect. In this study, six types of translational motion of bubbles with a wide range of sizes (2-100μm) in the R01-R02 plane are investigated. Our results demonstrate that in addition (to the 2nd order harmonic), the 1/2 order subharmonic can change the bubble pairs from the three states of the attraction, stable after attraction, and repulsion to that of the repulsion, coalescence, and attraction, respectively. Furthermore, within the range of the main resonance radius and the 1/2 order subharmonic resonance radius, the chaotic bubble pairs with alternating attractive and repulsive forces appear in the region between the coalescence pairs and stable pairs after attraction. Finally, the corresponding physical mechanisms of the chaotic translational motions are also revealed.

Hydrodynamic interaction of a bubble pair in viscoelastic shear-thinning fluids

We experimentally investigate the interaction between a pair of bubbles ascending in a stagnant viscoelastic shear-thinning fluid. In particular, we focus on the effect of bubble size, across the velocity discontinuity, on the bubble-bubble interaction. Compared to the drafting–kissing–tumbling (DKT) behavior in Newtonian fluids, bubbles in the viscoelastic shear-thinning fluid exhibit a drafting–kissing–dancing (DKD) phenomenon. In the dancing phase, the bubble pair repeatedly interchange their relative leading and trailing positions as they rise to the free surface. To gain further insights, the flow fields around the bubble pair interaction are obtained using particle image velocimetry (PIV). From the experimental results, we suggest that the elasticity, deformability, and negative wake are responsible for such an interaction between the bubble pair, thus revealing the fundamental physics of bubble clustering often observed in non-Newtonian fluids. • Strikingly different two bubble interactions in viscoelastic shear-thinning fluids. • At critical bubble volume, a discontinuity in the bubble velocity occurs. • For subcritical bubble pairs, the bubbles attract to form chains and coalesce. • Whereas, in supercritical bubble pairs, a ‘dancing’ oscillating behavior is observed. • Negative wake, deformability, and elasticity determine the type of interaction.

Experimental study on dynamic response of aluminum film under two spark bubbles coupling loading

The interaction of two or more bubbles with various structures is involved in many engineering problems, a clear understanding of the dynamic response process of the target under different coupling forms of bubbles loading is helpful to give full play to the value of bubbles in engineering application and avoid relevant harm. In the paper, the dynamic response process of aluminum (Al) film under the loading of a single bubble is first studied, and the deformation modes of the Al film under different bubble sizes and loading distances were considered. Then, two spark bubbles with different phase differences and initial distances are generated by a high-voltage power supply that can delay discharge, and different coupling types of two spark bubbles with different parameter combinations are given. Furthermore, the dynamic response process of the Al film with the loading of different types of coupled jets generated by bubble pairs is studied. In addition, the influence of the bubbles’ loading direction is considered. Finally, the center deflection of Al film with the loading of spark bubble pairs with different phase differences and initial distances is statistically analyzed. It is found that the piercing jet with forward loading is the most likely to cause holes in the Al film, while the relatively moving jet has the weakest damage power. The research results of this paper have a certain reference value for some engineering problems such as ship damage and ice breaking.

Jittering Jets by Negative Angular Momentum Feedback in Cooling Flows

I apply the jittering jets in a cooling flow scenario to explain the two pairs of bubbles in the cooling flow galaxy cluster RBS 797 which are perpendicular to each other and almost coeval, and conclude that the interaction of the jets with the cold dense clumps that feed the supermassive black hole (SMBH) takes place in the zone where the gravitational influence of the SMBH and that of the cluster are about equal. According to the jittering jets in a cooling flow scenario, jets uplift and entrain cold and dense clumps, impart the clumps’ velocity perpendicular to the original jets’ direction, and ‘drop’ them closer to the jets’ axis. The angular momentum of these clumps is at a very high angle compared to the original jets’ axis. When these clumps feed the SMBH in the next outburst (jet-launching episode) the new jets’ axis might be at a high angle to the axis of the first pair of jets. I apply this scenario to recent observations that show the two perpendicular pairs of bubbles in RBS 797 have a small age difference of <10 Myr, and conclude that the jets–clumps interaction takes place at a distance of about ≈10–100 pc from the SMBH. Interestingly, in this zone, the escape velocity from the SMBH is about equal to the sound speed of the intracluster medium (ICM). I mention two other clusters of galaxies and discuss the implications of this finding.

Effects of translational motion on the Bjerknes forces of bubbles activated by strong acoustic waves

The motion of a small cavitation bubble is influenced by a neighboring large bubble, and these two bubbles can be mutually attractive or repulsive. The state of the bubble pair is strongly related to the secondary Bjerknes force in a strong acoustic field. Non-spherical oscillations are easily observed when a small cavitation bubble approaches a large bubble. The effects of translational motion and non-spherical oscillations of the small cavitation bubble on the secondary Bjerknes force are considered numerically in this paper, at large (greater than20 μm) and small (3 μm) bubble pair sizes. We show that the radial oscillation of the cavitation bubble is suppressed by the large bubble when the two are close to each other, and the magnitude and direction of the secondary Bjerknes force on the cavitation bubble are significantly different to those predicted results without considering translational motion. With the increase in size of the large bubble, the value of the secondary Bjerknes force varies from negative to positive, implying a transition between attraction and repulsion. The secondary Bjerknes force is sensitive to changes in the size of the large bubble, as there are many spikes in the curve in the range 20 μm < R10 < 100 μm. Moreover, the cavitation bubble is slightly repulsed when the large bubble is larger than 100 μm. There is a critical distance that can lead to a transition between mutual attraction and repulsion of bubbles. Cavitation bubbles can be driven toward the larger bubble by increasing acoustic pressure. The findings presented here will be helpful in understanding the complex behavior of cavitation bubbles in practical applications in which large bubbles exist and may interact with cavitation.

Jetting mechanisms in bubble-pair interactions

Jetting mechanisms in cavitation bubbles play a crucial role in the destructive forces of cavitation. Depending on the application, these forces can have desirable effects like in medical treatments or catastrophic effects like in the erosion of ship propellers. Still today, thorough understanding of all details in complex bubble collapse scenarios is lacking. Hence, in this work, we numerically investigate the jetting mechanisms for air bubble pairs in water following a recent experimental setup. We apply a finite-volume approach with fifth-order low-dissipation shock-capturing weighted essentially non-oscillatory reconstruction. The interface interaction is described by a conservative sharp-interface level-set method. For time integration, a third-order total-variation-diminishing Runge–Kutta scheme is employed. Complementing experimental observations, our simulations reveal the presence of dominating gas jets and new types of jetting mechanisms.

Coalescence of bubbles in a high Reynolds number confined swarm

We investigate experimentally the coalescence cascade process for a confined swarm of deformable bubbles immersed in a bidimensional vertical cell filled with water. For different gas volume fractions, air bubbles of size $D_0$ larger than the cell thickness are injected at the bottom of the cell. The bubbles swarms transformation is explored using high-speed visualizations. The time evolution of each bubble in the swarm is determined using a specifically developed algorithm, enabling bubble tracking and coalescence detection. We determine the evolution of the bubble size distribution downstream from the injection point, and show that the stages of the coalescence cascade are characterized by the diameter, $D_{V90}$ , representative of the largest bubbles. The collision frequency of pairs of bubbles of sizes $D_k$ and $D_{k'}$ , $h(D_k, D_{k'})$ , and their coalescence efficiency, $\lambda$ , are obtained from the experiments. The efficiency is nearly constant, independently of the bubble sizes and of the gas volume fraction. Concerning collision frequency, our results reveal the existence of two different coalescence regimes depending on the capability of the bubbles to deform. Models describing $h(D_k, D_{k'})$ for both regimes are provided. They take into account the specific response of the bubble pair, which depends on the reduced diameter $D_p = 2 D_k D_{k'} / (D_k + D_{k'})$ , to the global swarm-induced agitation governed by $D_{V90}$ and the gas volume fraction. In the first regime, occurring for smaller $D_p$ , bubbles are brought together by agitation and rapidly coalesce, while for sufficiently large $D_p$ , both bubbles are able to deform and spend more time adapting mutually their shapes before coalescing.

Three-dimensional dynamics of a pair of deformable bubbles rising initially in line. Part 2. Highly inertial regimes

The buoyancy-driven dynamics of a pair of gas bubbles released in line is investigated numerically, focusing on highly inertial conditions under which isolated bubbles follow non-straight paths. In an early stage, the second bubble always drifts out of the wake of the leading one. Then, depending on the ratios of the buoyancy, viscous and capillary forces which define the Galilei ( $Ga$ ) and Bond ( $Bo$ ) numbers of the system, five distinct regimes specific to such conditions are identified, in which the two bubbles may rise independently or continue to interact and possibly collide in the end. In the former case, they usually perform large-amplitude planar zigzags within the same plane or within two distinct planes, depending on the oblateness of the leading bubble. However, for large enough $Ga$ and low enough $Bo$ , they follow nearly vertical paths with small-amplitude erratic horizontal deviations. Increasing $Bo$ makes the wake-induced attraction toward the leading bubble stronger, forcing the two bubbles to realign vertically one or more times along their ascent. During such sequences, wake vortices may hit the trailing bubble, deflecting its path and, depending on the case, promoting or hindering further possibilities of interaction. In some regimes, varying the initial distance separating the two bubbles modifies their lateral separation beyond the initial stage. Similarly, minute initial angular deviations favour the selection of a single vertical plane of rise common to both bubbles. These changes may dramatically affect the fate of the tandem as, depending on $Bo$ , they promote or prevent future vertical realignments.

Investigation on the bouncing and coalescence behaviors of bubble pairs based on an improved APR-SPH method

Bubbles rising in fluids are widespread in many engineering fields. In this paper, the bouncing and coalescing of two bubbles rising side by side are studied based on a multi-phase smoothed particle hydrodynamics (SPH) model. An improved adaptive particle refinement (APR) scheme is applied in the SPH model to make the numerical simulation sufficiently accurate and efficient. The effect of the surface-tension model is firstly verified, then various testing cases including the rising of a single bubble and two horizontally positioned bubbles are carried out and validate the numerical model well. Furthermore, the interaction between two three-dimensional bubbles rising side by side is studied considering the effects of viscous forces (with the Reynolds number Re), surface tensions (with the Eotvos number Eo), and the initial centroid distance of the two bubbles (Γ). The motion and the deformation of the bubbles are displayed and the mechanism of the bubbles' interaction is discussed. The results reveal that for the lower Eotvos number cases indicating a larger surface tension effect, the surface tension force increases dramatically when the two bubbles collide with each other and coalesce.

Impulsive forces of two spark-generated cavity bubbles with phase differences

The characteristics of synchronous and phase difference bubble pairs in axisymmetric configuration near a boundary are investigated experimentally by the spark discharge method. Their destructive forces on nearby boundaries are measured using a polyvinylidene fluoride sensor. The bubble pair interactions and deformed features in the boundary vicinity are dissimilar to those in bulk water. Moreover, significant discrepancies between in-phase and out-of-phase pair interactions and their intensities of impulses are also witnessed. The interbubble distance (η), stand-off distance from the boundary (γ), and phase offset (τ) are crucial parameters affecting the shape evolutions and impulsive forces. From the qualitative analysis of sensor acquisition and high-speed imaging, it is observed that bubble periods are either prolonged or shorter than their corresponding isolated single cavity according to different parameters and arrangements. Additionally, the strongest impingements are produced by in-phase pairs. The impulses of phase difference bubble pairs are remarkably lower than in-phase pairs and even lower than a single bubble in some arrangements.

Leidenfrost levitation of a spherical particle above a liquid bath: Evolution of the vapour-film morphology with particle size

We consider a spherical particle levitating above a liquid bath owing to the Leidenfrost effect, where the vapour of either the bath or sphere forms an insulating film whose pressure supports the sphere’s weight. Starting from a reduced formulation based on a lubrication-type approximation, we use matched asymptotics to describe the morphology of the vapour film assuming that the sphere is small relative to the capillary length (small Bond number) and that the densities of the bath and sphere are comparable. We find that this regime is comprised of two formally infinite sequences of distinguished limits which meet at an accumulation point, the limits being defined by the smallness of an intrinsic evaporation number relative to the Bond number. These sequences of limits reveal a surprisingly intricate evolution of the film morphology with increasing sphere size. Initially, the vapour film transitions from a featureless morphology, where the thickness profile is parabolic, to a neck–bubble morphology, which consists of a uniform pressure bubble bounded by a narrow and much thinner annular neck. Gravity effects then become important in the bubble leading to sequential formation of increasingly smaller neck–bubble pairs near the symmetry axis. This process terminates when the pairs closest to the symmetry axis become indistinguishable and merge. Subsequently, the inner section of that merger transitions into a uniform-thickness film that expands radially, gradually squishing increasingly larger neck–bubble pairs into a region of localised oscillations sandwiched between the uniform film and what remains of the bubble whose radial extent is presently comparable to the uniform film; the neck–bubble pairs farther from the axis remain essentially intact. Ultimately, the uniform film gobbles up the largest outermost bubble, whereby the morphology simplifies to a uniform film bounded by localised oscillations. Overall, the asymptotic analysis describes the continuous evolution of the vapour film from a neck–bubble morphology typical of a Leidenfrost drop levitating above a flat solid substrate to a uniform-film morphology which resembles that in the case of a large liquid drop levitating above a liquid bath.

Oscillation behavior of bubble pair in magnetic fluid tube under magneto-acoustic complex field

Based on the dynamic model of a single bubble in a magnetic fluid tube, the dynamic equation of a bubble pair system in a magneto-acoustic field is established by introducing the secondary sound radiation between bubbles and considering the magnetic field effect of the viscosity of the magnetic fluid. The effects of magnetic field intensity, bubble pair’s size, bubble interaction (including secondary Bjerknes force &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;B&lt;/sub&gt; and magnetic attraction &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt;) and fluid characteristics on the vibration characteristics of double bubbles are analyzed. The results show that magnetic field increases the amplitude of bubbles, and the influence of magnetic field on the large bubble is greater than on the small bubble. When the center distance between the two bubbles is constant and the relative size of two bubbles is larger, or when the size of the two bubbles is constant and the surface distance between two bubbles is small, the interaction between two bubbles is stronger. In the magneto-acoustic composite field, magnetic field can affect &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;B&lt;/sub&gt;, &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt;, magnetic pressure &lt;i&gt;P&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt; and viscosity resistance, and the influence degrees are different. There is competition between &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;B&lt;/sub&gt; and &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt; and between &lt;i&gt;P&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt; and viscosity resistance, and the forces acting on the microbubble jointly affect the movement of the bubbles. By studying the dynamic behavior of paired bubbles, it can provide a theoretical basis for improving the therapeutic effect of targeted regulation of microbubbles on biological tissues by adjusting the magneto-acoustic field in practical application.

Hydrodynamic Interaction of a Bubble Pair in Viscoelastic Shear-Thinning Fluids

Hydrodynamic Interaction of a Bubble Pair in Viscoelastic Shear-Thinning Fluids

Dynamics of Bubble Pairs in Water Induced by Focused Nanosecond Laser Pulse

Dynamics of Bubble Pairs in Water Induced by Focused Nanosecond Laser Pulse

An accurate and robust axisymmetric SPH method based on Riemann solver with applications in ocean engineering

The present work develops an accurate and robust axisymmetric SPH method by introducing the Riemann solver into the framework of axisymmetric SPH. To reduce numerical dissipations caused by the intrinsic numerical viscosity of the Riemann solver, PVRS Riemann solver with MUSCL reconstruction is embedded into the scheme of the axisymmetric Riemann SPH. In addition, in order to maintain the uniformity of particle distributions, the volume adaptive scheme and the particle shifting technique are applied in this work. The advantage of the present axisymmetric Riemann SPH method is that it can consider the real compressibility of the air, which allows a larger stable time step in the simulation of the strongly-compressible flows. Through the three benchmark tests, including the Sod shock tube test, the Sedov point explosion test and the blast wave problem test, the accuracy of the present axisymmetric Riemann SPH method is verified. Then this method is applied to the simulations of some practical issues in ocean engineering, including the shockwave propagation of the underwater explosion, the water entry of the sphere and the coalescence of an oscillating bubble pair.

Synergistic effects of frothers, collector and salt on bubble stability

This work investigates synergistic and antagonistic effects of flotation reagents and salt on the air–liquid interface and stability of air bubbles under quasi-static conditions. Frothers of different families (aliphatic alcohol, polypropylene glycol and propylene glycol methyl ether), potassium amyl xanthate (PAX), a common collector used in the flotation of sulphide minerals, and sodium chloride (NaCl) were employed in the study. Adsorption of frother and collector molecules from individual and mixed solutions was studied through surface tension and Quartz Crystal Microbalance with Dissipation (QCM–D) measurements, while bubble stability was examined by the coalescence time of the bubble pairs in these solutions. The results show that NaCl enhanced the adsorption of frothers, while PAX's impact on the adsorption of the frother was found to be rather insignificant compared to the salt. The bubble coalescence time measurements, however, pointed to a significant synergistic effect between PAX and two frothers i.e., Methyl Iso Butyl Carbinol (MIBC) and Di Propylene Glycol (DPG) as reflected in the improvement of bubble stability. In the ternary solution systems (frother/NaCl/PAX), the concentration of salt in the MIBC mixture solution was found to have an opposite impact on the bubble lifetime in the DPG and DPM solutions. For instance, bubble lifetime increased with higher NaCl concentrations added to the DPG and DPM solutions, whereas it decreased in the MIBC solutions.

Interaction of two out-of-phase underwater explosion bubbles

This study presents an experimental investigation of the dynamic properties of underwater explosion (UNDEX) bubble pairs produced with a range of phase differences Δθ, defined as 2π(t1−t2)/Tosc, where ti (i = 1,2) represents the bubble inception moment and Tosc is the experimentally obtained first period of a single UNDEX bubble. Each bubble was generated by a spherical hexogen explosive charge detonated in a cubical tank and observed via high-speed photography. The phase difference was adjusted by setting different delays between the two detonations, with an accuracy of 1.0 ms. Experiments were conducted with both horizontally and vertically positioned bubble pairs and with single bubbles as well. UNDEX bubble pairs are subject to a larger buoyancy effect than cavitation or spark-generated bubble pairs. The resultant bubble behavior in the bubble–bubble interaction is more complex and is yet to be understood. In our experiments, various bubble parameters, including bubble pulsation periods, bubble elongation ratios, and collapse-induced shock wave pressures bubble, were measured and studied. Dependence of the bubble dynamics on Δθ was found, demonstrating the significant influence of Δθ on the morphology and shock wave pressure of bubble pairs. The findings suggest a method of strengthening or weakening the damage potential of an UNDEX bubble pair based on the proper adjustment of the delay between two detonations. It may also lead to a better understanding of the dynamics of interacting bubbles with buoyancy effects.

Microstreaming induced by two interacting acoustic bubbles

Microbubbles submitted to a sufficiently strong ultrasound field can show nonspherical oscillations called surface modes. These oscillations induce a slow mean flow named microstreaming in the vicinity of the bubble interface. We present experimental and theoretical investigations of the microstreaming induced by a bubble pair as an elementary modelling of a dense bubble cloud. Two bubbles are trapped in a dual-frequency acoustic chamber that allows studying their interface dynamics. The secondary radiation force they experience and make them attract under increasing acoustic forcing is quantified through the relative location of the bubble within the acoustic field. Each bubble can exhibit several nonspherical modes that are either axisymmetric or not. The typical flow signatures induced by these nonspherical modes are identified. When the bubble shape oscillations are axisymmetric, the extension of microstreaming pattern does not allow fluid interaction in the region between the two bubbles. In case of asymmetric oscillations, large-scale microstreaming is obtained. These experimental findings are discussed by means of a theoretical modelling of the fluid flow induced by two nonspherically-oscillating microbubbles.