Bubble Translation Research Articles

Investigation of Taylor bubble behavior in upward and downward vertical and inclined pipe flows

The Taylor bubble behavior in two-phase flow is critical for various engineering applications, including momentum, heat, and mass transfer efficiencies. Therefore, understanding the dynamics of Taylor bubbles is crucial for the optimal design, operation, and safety of reactors and pipelines. In slug flow in pipes, the successive translation of liquid slugs and Taylor bubbles is characterized by the Taylor bubble velocity, which is a function of the flow distribution coefficient (C0). This study aims to compile a large database of Taylor bubble velocity and flow distribution coefficient in upward, horizontal, and downward flows, evaluate existing models, and propose a unified C0 model. As a result, it is found that the physics governing the flow distribution coefficient in downward flow is drastically different from that in upward flow, and it goes through two flow transitions, which are governed by the pipe inclination angle. This behavior is modeled by the proposed model, which predicts the Taylor bubble flow distribution coefficient through both transitions and captures its physical behavior in the downward flow. A validation study of the proposed model revealed that the proposed model outperforms the existing models as it has an average absolute percent error and standard deviation of 4.2% and 6.2%, respectively.

Experimental study of a leakage location method based on plug flow mass transfer characteristics

Leaks in water supply pipes pose a threat to water security. In order to save labor investment in pipeline leak location and to find a method to obtain the leak location by calculating upstream and downstream related data, an experimental study was conducted to investigate the plug flow mass transfer characteristics in horizontal pipelines. The results show that the addition of carbon dioxide gas can better detect the occurrence of small area ruptures in the pipeline. The translational velocity equation for elongated bubbles has better accuracy for both the insoluble gas air and the slightly soluble gas carbon dioxide. The local volumetric mass transfer coefficient shows a better linear relationship with the residual gas volume. The iterative equation derived from such a law can effectively predict the distribution of carbon dioxide concentrations in the pipeline. The study shows that the iterative equation, combined with the carbon dioxide concentration at a point downstream and the bubble translation velocity, can make a good localization judgment of the pipeline rupture point.

Self-propulsion of a periodically forced shape-deforming submillimeter gas bubble.

The self-propulsion (translational instability) of a gas bubble in a liquid undergoing parametrically induced axisymmetric shape distortion due to being forced by a temporally sinusoidal, spatially constant acoustic field is investigated. Employing a model which accounts for the nonlinear coupling between the spherical oscillations, the axial translation and shape deformation of the bubble, the parametric excitement of two neighboring shape modes by the fundamental resonance, at the same driving frequency is studied. It is shown that provided pertinent driving pressure threshold values are exceeded, the respective shape modes are excited on different timescales. The growth of the shape mode on the faster timescale saturates giving rise to sustained constant amplitude oscillations, while the growth of the shape mode on the slower timescale is both modulated and unbounded. During the growth of the second shape mode, growing, oscillatory bubble translation is also observed.

Translation of interacting cavitation bubble in a plane acoustic field

In a plane acoustic field, a model involving the radial and translational motions of bubble is derived, which is used to numerically investigate the translation of two interacting spherical cavitation bubbles. For the smaller initial distance between bubble centers, we investigate the dynamics of two bubbles, and find that they could come into contact but the velocities of closing to each other are different when the equilibrium radius is different. The results show that when the wavelength of plane acoustic field is much larger than the initial distance, the bubbles are approximately pulsating in phase. Moreover, the velocity of contact process of two bubbles can be changed by adjusting the parameters of plane acoustic field. For increasing in the initial distance, the bubbles would present two translation motions: close to each other for the pulsating in phase and away from each other for the pulsating out of phase, which could be verified by calculating the secondary Bjerknes force. Meanwhile, the larger the initial distance, the smaller the secondary Bjerknes force value is. Understanding the translation of bubble is of great significance for helpful explaining formation of streamer structures in ultrasonic cavitation.

Isothermal and non-isothermal growth of a vapor bubble in pool boiling – Effect of translational velocity of bubble

In the present work, we have numerically simulated the effect of bubble translation on the growth of a vapor bubble in a pool of superheated liquid based on the isothermal and non-isothermal model. The isothermal growth uses the ODE solver and the non-isothermal growth the PDE-ODE solver. The overall model at present considers the forces acting on the bubble to compute the bubble motion and the energy balance at the bubble surface to include the effect of bubble size on its motion. Thus, it computes equivalent bubble radius and bubble velocity simultaneously. The numerical simulation shows a remarkable improvement by our method over the previous numerical model while validating with the experimental and numerical results on bubble growth with the phase motion. The improved model has significantly reduced the deviation from the experiments reported in literature on the growth of a moving bubble. The aspect ratio of the bubble is computed to see the shape change of the bubble and is used to model the drag force accurately. It has been shown that the model of the isothermal growth can better explain the bubble growth at the initial stage, and the model of the non-isothermal growth at the final stage. The non-isothermal growth of bubble is accompanied by the slowdown of the bubble translation in the superheated liquid.

Ultrasonic Traveling Waves for Near-Wall Positioning of Single Microbubbles in a Flowing Channel.

Although microbubbles are used primarily in the medical industry as ultrasonic contrast agents, they can also be manipulated by acoustic waves for targeted drug delivery, sonothrombolysis and sonoporation. Acoustic waves can also potentially remove microbubbles from tubing systems (e.g., in hemodialysis) to prevent the negative effects associated with circulating microbubbles. A deeper understanding of the interactions between the acoustic radiation force, the microbubble and the channel wall could greatly benefit these applications. In this study, single air-filled microbubbles were injected into a flowing (polydimethylsiloxane) channel and monitored by a high-speed camera while passing through a pulsed ultrasonic wave zone (0.5 MHz). This study compared various bubble sizes, flow rates and acoustic pressure amplitudes to better understand the three physical regimes observed: free bubble translation (away from the wall); on-wall translation; and bubble-wall attachment. Comparison with a theoretical model revealed that the acoustic radiation force needs to exceed the combined repulsive forces (shear lift, wall lubrication and repulsive Van der Waal forces) for the dead state of bubble-wall attachment. The bubble dynamics revealed through this investigation provide an opportunity for efficient positioning of microbubbles in a channel flow, for either in vivo manipulation or removal in biological applications.

Translation of cavitation bubble near the different walls

The interaction between spherical cavitation bubble and flat wall is transformed into that between the real bubble and imaging bubble by the method of images. Firstly, we investigate the dynamics of real bubble and matched, inversed or mis-matched imaging bubble driven by a small amplitude ultrasound, revealing the characteristics of the interaction between cavitation bubble and rigid, soft and impedance walls. Then, we emphatically study the dynamics of real bubble and mis-matched imaging bubble driven by a finite amplitude ultrasound, and the interaction characteristics between cavitation bubble and real impedance wall are revealed. The results show that the cavitation bubble is always close to the rigid wall and far away from the soft wall; For the impedance wall, whether the cavitation bubble is far away or close depends on the specific wall parameters. Moreover, the direction and magnitude of bubble's translation velocity can be changed by adjusting the driving parameters. Understanding the interaction between cavitation bubble and impedance wall is of great significance for efficient application of ultrasonic cavitation.

Acoustically driven translation of a single bubble in pulsed traveling ultrasonic waves

The acoustic radiation force has been proven as an effective mechanism for displacing particles and bubbles, but it has been mainly applied in a standing wave mode in microfluidics. Alternatively, the use of pulsed traveling acoustic waves could enable new options, but its transient dynamic, which entails the additional complexities of pulse timing, reflections, and the type of waveform, has not yet been fully investigated. To better understand these transient effects, a transient numerical solution and an experimental testbed were developed to gain insights into the displacement of microbubbles when exposed to on- and off-periods of pulsed traveling waves. In this study, a practical sinusoid tone burst excitation at a driving frequency of 0.5 MHz is investigated. Our numerical and experimental results were found to be in good agreement, with only a 13% deviation in the acoustically driven velocity. With greater detail from the numerical solution at a sampling rate of 1 GHz, the fundamental mechanism for the bubble translation was revealed. It was found that the added mass force, gained through the on-period of the pulse, continued to drive the bubble throughout the off-period, enabling a large total displacement, even in the case of low duty-cycle (2%) pulsing. In addition, the results showed greater translational velocity is possible with a lower number of cycles for the same input acoustic energy (constant duty cycle and acoustic pressure amplitude). Overall, this study proposes a new, practical, and scalable approach for the acoustic manipulation of microbubbles for scientific, biomedical, and industrial applications.

Nonlinear acoustic theory on flowing liquid containing multiple microbubbles coated by a compressible visco-elastic shell: Low and high frequency cases

Microbubbles coated by visco-elastic shells are important for ultrasound diagnosis using contrast agents, and the dynamics of single coated bubbles has been investigated in the literature. However, although a high number of contrast agents are used in practical situations, there has long been an absence of a nonlinear acoustic theory for multiple coated bubbles, except for our recent work by Kikuchi and Kanagawa [“Weakly nonlinear theory on ultrasound propagation in liquids containing many microbubbles encapsulated by visco-elastic shell,” Jpn. J. Appl. Phys. 60, SDDD14 (2021)], under several assumptions to be excluded. Aiming for generalization, in this study, we theoretically investigate weakly nonlinear propagation of ultrasound in liquid containing multiple bubbles coated by a visco-elastic shell with compressibility. Leveraging the method of multiple scales, both the Korteweg–de Vries–Burgers (KdVB) equation for a low-frequency long wave and nonlinear Schrödinger (NLS) equation for a high-frequency short wave are derived from the volumetric averaged equations for bubbly liquids based on a two-fluid model and the up-to-date model for single coated bubbles with shell compressibility. Neglected factors in our previous paper, i.e., compressibility of the shell and liquid, drag force acting on bubbles, bubble translation, and thermal conduction, are incorporated in the present KdVB and NLS equations; the proposed model will be regarded as a generic physico-mathematical model. The results show that shell compressibility attenuated ultrasound strongly and decreased nonlinearity of ultrasound. Finally, we compared the magnitudes of six dissipation factors (shell compressibility, shell viscosity, liquid compressibility, liquid viscosity, thermal effect, and drag force) for five typical ultrasound contrast agents, and a similar tendency between KdVB and NLS equations was revealed.

Numerical simulations of interfacial and elastic instabilities

<h2>Abstract</h2> The interplay of elasticity and capillarity in free-surface flows of viscoelastic fluids gives rise to intriguing flow instabilities. We present novel numerical simulations and analyse the physics related to the appearance of surface distortions on polymer melt extrudates, often referred to as "sharkskin" instability, and the abrupt increase in the rise velocity of a bubble in a viscoelastic solution. Regarding the extrusion process, the transition from smooth to wavy extrudate with increasing flow rate is attributed to a Hopf bifurcation, followed by a sequence of period-doubling bifurcations, which eventually lead to elastic turbulence under creeping flow. We suggest that the inception of these waves is related with intense stretch of polymer chains and subsequent recoil at the region where the melt detaches from the solid wall of the die. The ‘velocity discontinuity' of the rising bubble is attributed to a hysteresis loop, triggered by the change of shape of the rear pole into a tip that favors the formation of intense stress gradients, which reduce the fluid viscosity and facilitate the bubble translation. Finally, we discuss the numerical methodology that has allowed us to obtain stable numerical solutions in highly deformed meshes and for high values of the Weissenberg number.

Nonlinear and dissipation effects of pressure waves in water flows containing translational bubbles with a drag force

Abstract Weakly nonlinear (i.e., finite but small amplitude) propagation of plane progressive pressure waves in compressible water flows uniformly containing many spherical bubbles is theoretically studied. Drag force acting bubbles and translation of bubbles are newly considered by introducing in momentum conservation equations in a two fluid model and the bubble dynamics equation for volumetric oscillations, respectively. Although these assumptions are the same as our previous paper, in this study, the energy conservation equation for each bubble describing a thermal conduction inside bubble is introduced. By using the method of multiple scales, the Korteweg–de Vries–Burgers equation for low-frequency long wave was derived from the set of basic equations in the two-fluid model. As a result, the dissipation effect was described by two types of terms, i.e., one was the second-order partial derivative owing to the liquid compressibility and the other was the term without differentiation owing to the drag force and the thermal conduction. Finally, we clarified that the dissipation owing to the drag force was smaller than that owing to the thermal conduction.

Size-dependent translational velocity of phospholipid-coated bubbles driven by acoustic radiation force

This study investigates how the translational velocity of phospholipid-coated bubbles caused by acoustic radiation force depends on their size. The translations of bubbles with mean radii of 0.9–5 μm were experimentally evaluated at five ultrasound frequency conditions (3.5, 5, 7.5, 10, and 15 MHz). We compared experimental data with theoretical prediction using a viscoelastic interfacial rheological model and a model suitable for high amplitude oscillation. The results suggested that the translation of bubbles could be enhanced for a mean radius of 1–3 μm but echo intensity could not.

Dynamics of double bubbles under the driving of burst ultrasound

This paper investigates the pulsations and translation of bubbles in a double-bubble system driven by burst ultrasound. Results illustrate that for two identical bubbles, decreasing the frequency of burst or increasing its amplitude can enhance the pulsations and improve the translation velocities of bubbles. In a certain scope, large bubble brings about fast translation velocity, but the velocity will fall down for too large bubble, such as the bubble with ambient radius over about its resonance radius. When the ambient radii of two bubbles are different, translation of the large bubble is smaller than that of the small bubble. In addition, the effect of initial distance between bubbles is described as well. If burst serials are used, shortening the time interval between each burst and improving the acoustic amplitude of bursts are beneficial for the translations of bubbles.

Experimental study of hydrodynamic parameters regarding on geyser boiling phenomenon in glass thermosyphon using wire-mesh sensor

The thermosyphon is a type of heat exchanger that has been widely used in many applications. The use of thermosyphons has been intensified in recent years, mainly in the manufacture of solar collectors and various industrial activities. A thermosyphon is a vertical sealed tube filled with a working fluid, consisting of, from bottom to top, by an evaporator, an adiabatic section, and a condenser. The study of geyser-boiling phenomena, which occurs inside the thermosyphon is of extreme importance, therefore the experimental analysis of the parameters related to the two-phase flow (liquid-steam), such as void fraction, bubble frequency, bubble velocity, and bubble length are necessary, since these parameters have a significant influence on heat transfer. In this work, a pair of wire mesh sensors was used, a relative innovative technology to obtain experimental values of the reported quantities for measuring these parameters of slug flow in thermosyphons. An experimental set-up is assembled and the sensors are coupled to the thermosyphon enabling the development of the experimental procedure. Here is presented an experimental study of a glass thermosyphon instrumented with two wire-mesh sensors, in which the aforementioned slug flow hydrodynamic parameters inherent to the geyser type boiling process are measured. It was measured successfully, as a function of the heat load (110, 120, 130, 140, and 150 W), the void fraction (instantly and average), liquid film thickness, translation velocity of the elongated bubbles, lengths of the bubbles, and the liquid slug (displaced by the bubble rise up). It was observed that the higher the heat load, the lower is the bubble translation velocity. For all heat loads, based on the measured length of liquid slug (consequent displacement of liquid volume), caused by bubbles rise from evaporator to condenser, it could be affirmed to some extent that both boiling regime (pool and film) exist in the evaporator. The measured average void fraction (80%) and liquid film thickness (around 2.5 mm) during the elongated bubble passages were approximately constant and independent of the heat load.

Erratum: “Effect of drag force and translation of bubbles on nonlinear pressure waves with a short wavelength in bubbly flows” [Phys. Fluids 33, 053314 (2021)

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Dynamics of twin bubbles formed by ultrasonic cavitation in a liquid

Based on potential flow and perturbation theory, a theoretical model is derived to describe the pulsation, translation, and deformation of twin bubbles in an ultrasound field. The amplitudes of radial oscillation, translation, and deformation of twin bubbles are found to depend on initial translation velocities. The radii, translation, and deformation of twin bubbles also exhibit periodic behavior. As the initial translation velocities increase, the periods of two bubbles’ oscillations reduce, and the instable area in the phase space of R01-R02 enlarges because of the interaction between bubbles.

Numerical Study on Weakly Nonlinear Evolution of Pressure Waves in Water Flows Containing Many Translational Bubbles Acting a Drag Force

Weakly nonlinear (i.e., finite but small amplitude) propagation of plane progressive pressure waves in compressible water flow uniformly containing many spherical gas bubbles is numerically investigated with a special attention to a drag force acting bubbles and translation of bubbles. The gas and liquid phases are flowing with initially independent velocities. Drag force and virtual mass force are introduced as interfacial momentum transports. Translation and spherically symmetric oscillations are considered as bubble dynamics. In this paper, under these assumptions, we numerically solve the KdVB (Korteweg-de Vries-Burgers) equation previously derived by ourselves (Yatabe et al., Phys. Fluids, 33 (2021), 033315) from basic equations based on a two-fluid model. The main results are summarized as follows: (i) The drag force acting on bubbles increases a dissipation effect of waves and drastically changes the phase and amplitude of waves. (ii) Although the translation of bubbles increases the nonlinear effect of waves, its contribution to waveform is quantitatively small. (iii) The effect of the drag force decreases with decreasing the initial void fraction and with increasing the initial bubble radius. That of the translation decreases with decreasing the initial void fraction, and is almost independent of the initial bubble radius. (iv) The spatiotemporal evolution of two type of dissipation effects (i.e., dissipation terms) due to the acoustic radiation and to the drag force is different tendency.

Effect of drag force and translation of bubbles on nonlinear pressure waves with a short wavelength in bubbly flows

To clarify the effect of the drag force acting on bubbles and translation of bubbles on pressure waves, the weakly nonlinear (i.e., finite but small-amplitude) propagation of plane pressure waves with a thermal conduction in compressible water flows containing many spherical bubbles is theoretically investigated for moderately high-frequency and short-wavelength case. This work is an extension of our previous report [Yatabe et al., Phys. Fluids, 33, 033315 (2021)], wherein we elucidated the same for low-frequency and long-wavelength case. Based on our assumptions, the main results of this study are as follows: (i) using the method of multiple scales, the nonlinear Schrödinger type equation was derived; (ii) as in the previous long wave case, the translation of bubbles increased the nonlinear effect of waves, and the drag force acting on the bubbles resulted in the dissipation effect of waves; (iii) the increase in the nonlinear effect of the waves owing to the translation in the present short wavelength case is larger than that in the previous long wavelength case; (iv) the dissipation effect caused by the drag force was smaller than that caused by the liquid viscosity, acoustic radiation (i.e., liquid compressibility), and thermal conduction; (v) we then succeeded the comparison of the four dissipation factors (i.e., liquid viscous damping, thermal conduction, acoustic radiation, and drag force) on pressure waves.

Theoretical elucidation of effect of drag force and translation of bubble on weakly nonlinear pressure waves in bubbly flows

Theoretical investigation of the effects of a translation of bubbles and a drag force acting on bubbles on the wave propagation in bubbly flows has long been lacking. In this study, we theoretically and numerically investigate the weakly nonlinear (i.e., finite but small amplitude) propagation of plane progressive pressure waves in compressible water flows that contain uniformly distributed spherical gas bubbles with translation and drag forces. First, we assume that the gas and liquid phases flow at independent velocities. Then, the drag force and virtual mass force are introduced in an interfacial transport across the bubble–liquid interface in the momentum conservation equations. Furthermore, we consider the translation and spherically symmetric oscillations as bubble dynamics and deploy a two-fluid model to introduce the translation and drag forces. Bubbles do not coalesce, break up, extinct, or appear. For simplicity, the gas viscosity, thermal conductivities of the gas and liquid, and phase change and mass transport across the bubble–liquid interface are ignored. The following results are then obtained: (i) Using the method of multiple scales, two types of Korteweg–de Vries–Burgers equations with a correction term due to the drag force are derived. (ii) The translation of bubbles enhances the nonlinear effect of waves, and the drag force acting on bubbles contributes the nonlinear and dissipation effects of waves. (iii) The results of long-period numerical analysis verify that the temporal evolution of the wave (not flow) dissipation due to the drag force differs from that caused by the acoustic radiation.

Interaction between Free-Surface Oscillation and Bubble Translation in a Megasonic Cleaning Bath

Visualization experiments were performed to study the relation between free-surface motion and bubble translation in a 1-MHz ultrasonic cleaning bath. From the visualization with a video camera, the characteristic frequencies of the free-surface oscillation (under the acoustic radiation force) and the translational velocity of cavitation bubbles (trapped via the primary Bjerknes force) were extracted, showing that there is a strong correlation between the free-surface oscillation and bubble translation. From the context of megasonic cleaning, such free-surface oscillation is expected to contribute to uniform cleaning performance with cavitation bubbles.