Bubble Size Ratio Research Articles

The influence of liquid height to bubble size ratio on the boiling crisis in pool boiling

We conducted experiments to analyze water boiling under 10 K subcooling and atmospheric conditions in a horizontal pool boiling test setup, focusing on the effect of liquid height above the heating surface. Our main interest was the transition in boiling crisis mechanisms at liquid heights comparable to bubble size. For pool heights above 4.0 mm, we observed a relatively constant critical heat flux (CHF) of approximately 1.21 MW/m^2. Conversely, CHF significantly dropped to around 0.19 MW/m^2 for liquid heights below 2.5 mm. For depths between 2.5 – 4.0 mm the measured CHF values varied within these limits. Our pool boiling facility featured a stainless-steel chamber filled with deionized water heated by external circulating oil. A ceramic cartridge supported a transparent heater at the cell’s center-bottom, which utilized an indium tin oxide layer on a sapphire substrate for heat dissipation. We monitored bubbles’ footprint dynamics during boiling using infrared and high-speed video cameras. Preliminary high-speed data analysis revealed different hydrodynamic mechanisms corresponding to the obtained CHFs. For heights above 4.0 mm, the formation of an irreversible dry patch is triggered by bubble interactions. Conversely, at heights below 2.5 mm, one of the bubbles nucleating shortly after the onset of boiling failed to detach from the surface shortly. Instead, it grew in size and eventually spread over the entire surface, prematurely triggering a boiling crisis. We attributed this behavior to a lack of buoyancy forces to detach the bubble from the surface as it grew above the liquid level. Pool heights between 2.5 – 4.0 mm showed both behaviors. Further investigations will focus on exploring the transition in boiling mechanisms shifting from buoyancy- to surface-tension-dominated processes by varying bubble dimensions through the introduction of surfactants. Ultimately, we aim to analyze fundamental boiling parameters and heat flux to characterize how boiling dynamics, boiling crisis and CHF value vary with the bubble-to-liquid height ratio.

The Challenges and Prospects of Recovering Fine Copper Sulfides from Tailings Using Different Flotation Techniques: A Review

Flotation is a common mineral processing method used to upgrade copper sulfide ores; in this method, copper sulfide mineral particles are concentrated in froth, and associated gangue minerals are separated as tailings. However, a significant amount of copper is lost into tailings during the processing; therefore, tailings can be considered secondary resources or future deposits of copper. Particle–bubble collision efficiency and particle–bubble aggregate stability determines the recovery of target particles; this attachment efficiency plays a vital role in the selectivity process. The presence of fine particles in the flotation circuit is because of excessive grinding, which is to achieve a higher degree of liberation. Complex sulfide ores of markedly low grade further necessitate excessive grinding to achieve the maximum degree of liberation. In the flotation process, fine particles due to their small mass and momentum are unable to collide with rising bubbles, and their rate of flotation is very slow, further lowering the recovery of target minerals. This collision efficiency mainly depends on the particle–bubble size ratio and the concentration of particles present in the pulp. To overcome this problem and to maintain a favorable particle–bubble size ratio, different techniques have been employed by researchers to enhance particle–bubble collision efficiency either by increasing particle size or by decreasing bubble size. In this article, the mechanism of tailing loss is discussed in detail. In addition, flotation methods for fine particles recovery such as microbubble flotation, column flotation, nanobubble flotation, polymer flocculation, shear flocculation, oil agglomeration, and carrier flotation are reviewed, and their applications and limitations are discussed in detail.

2つのレーザ誘起キャビテーション気泡により生成するマイクロジェットに関する研究

Two cavitation bubbles generated by laser irradiation in water generate microjets due to their mutual interference. The characteristics of microjets vary depending on the size and distance of the bubbles, as well as on the time difference between bubble generation and microjet generation. Therefore, the purpose of this study is to clarify the effect of the bubble generation time difference, T*D in dimensionless form, on the bubble motion and microjet by numerical calculations and experiments. Numerical calculations are performed using the boundary element method and the VOF method, both of which have conflicting characteristics, and two numerical methods are used for efficient analysis. In this study, cavitation bubbles are generated at the top and bottom, and the lower bubble that is generated first is bubble A, and the upper bubble that is generated after a delay is bubble B. When the distance between the bubbles and the bubble size ratio are kept constant and the bubble generation time difference is varied, it is found that there are three types of microjets generated in bubble A due to the mutual interference between the two cavitation bubbles. Upward microjets are generated in bubble A and penetrate upward when the bubble generation time difference is small. This occurs when the expansion of bubble A is slightly disturbed, causing the underside of bubble A to become concave. A downward microjet is generated in bubble A and penetrates downward when the bubble generation time difference is large. This is caused by the upper side of bubble A being pushed in due to the strong influence of the expansion of bubble B. When the bubble generation time difference is in the range of 0.16 ≤ T*D ≤ 0.20, bubble A is separated into two parts, resulting in the creation of upward and downward microjets. This is caused by the predominant horizontal nipping of bubble A.

Dynamics of the passive pulsation of a surface-attached air bubble subjected to a nearby oscillating spark-generated bubble

The dynamics of a spark-generated bubble (a discharge short circuit) generated in proximity to a stationary air bubble attached to a plate is experimentally investigated by high-speed photography. Numerous interesting and complex interactions occur during the two bubble coupling pulsation owing to the deformation properties or “free surface” characteristics supplied to the plate by the attached air bubble. Complex bubble jetting behaviors, such as bubble splitting, jets away from the plate, variable directional jets, and multidirectional jets are observed. Passive pulsation of the air bubble is observed in response to the spark bubble. Moreover, five types of bubble behaviors are summarized: bubble coalescence, the air bubble skirt phenomenon, the “mountain”-shaped bubble, and the “cup cover”-shaped air bubble with or without splitting. To develop a better understanding of the coupling interactions between the two bubbles during their oscillations, four types of bubble volume–time curves are summarized using the image outline identification code established to obtain information regarding the bubble shape. The complex phenomena during the two-bubble interactions, such as the bubble jetting direction, air bubble shapes, and volume–time curves, are summarized as graphs and are highly dependent on the bubble size ratio, dimensionless cavitation bubble oscillation time, and initial displacement parameter.

Bubble dynamics and bubble-induced agitation in the homogeneous bubble-swarm past a circular cylinder at small to moderate void fractions

An investigation into how the presence of a circular cylinder disturbs a buoyancy-driven homogeneous bubble-swarm using a novel two-phase particle-image velocimetry is presented. Depending on the void fraction and ratio of bubble size to cylinder diameter, two regimes of bubble distribution in the cylinder wake are classified and corresponding mechanisms are explained. Also, the liquid-phase flow forms an interesting two-phase wake behind a cylinder. To analyze this, a novel model for bubble-induced agitation (Reynolds stress) that agrees well with the measurements is suggested.

Numerical study of an individual Taylor bubble rising through stagnant liquids under laminar flow regime

Slug flow is one of the main flow regimes encountered in multiphase flow systems especially in oil and gas production systems. In the present study, the rise of single Taylor bubble through vertical stagnant Newtonian liquid is investigated by performing complete dimensionless treatment followed by an order of magnitude analysis of the terms of equations of motion. Based on this analysis, it is concluded that Froude, Eötvös and Reynolds numbers are the sole physical parameters influencing the dimensionless slug flow equations. Using the guidelines of the order of magnitude analysis, computational fluid dynamics simulation is carried out to investigate the dynamics of Taylor bubbles in vertical pipe using the volume-of-fluid (VOF) method. Good agreement with previous experimental data and models available in the literature is established confirming that the density ratio, viscosity ratio and the initial ratio of bubble size to pipe diameter (LTB/D) have minimal effect on the main hydrodynamic features of slug flow. Based on the developed results, correlations for the terminal velocity of the Taylor bubble and the dimensionless wall shear stress are proposed showing the significance of these main dimensionless parameters and support other important theoretical and experimental work available in the literature.

Pulsed jets driven by two interacting cavitation bubbles produced at different times

An experiment is performed using high-speed photography to elucidate the behaviours of jets formed by the interactions of two laser-induced tandem bubbles produced axisymmetrically for a range of dimensionless interaction parameters such as the bubble size ratio, $\unicode[STIX]{x1D709}$, the distance between the two cavitation bubbles, $l_{0}^{\ast }$, and the time difference in bubble generation, $\unicode[STIX]{x0394}\unicode[STIX]{x1D703}^{\ast }$. A strong interaction occurs for $l_{0}^{\ast }<1$. The first bubble produced (bubble A) deforms because of the rapid growth of the second bubble (bubble B) to create a pulsed conical jet, sometimes with spray formation at the tip, formed by the small amount of water confined between the two bubbles. This phenomenon is followed by bubble penetration, toroidal bubble collapse, and the subsequent fast contraction of bubble B accompanied by a fine jet. The formation mechanism of the conical jet is similar to that of a water spike developed in air from a deformed free surface of a single growing bubble; however, the pressures of the gases surrounding each type of jet differ. The jet behaviours can be controlled by manipulating the interaction parameters; the jet velocity is significantly affected by $\unicode[STIX]{x1D709}$ and $l_{0}^{\ast }$, but less so by $\unicode[STIX]{x0394}\unicode[STIX]{x1D703}^{\ast }$ for $\unicode[STIX]{x0394}\unicode[STIX]{x1D703}^{\ast }>\unicode[STIX]{x0394}\unicode[STIX]{x1D703}_{c}^{\ast }$ ($\unicode[STIX]{x0394}\unicode[STIX]{x1D703}_{c}^{\ast }$ being the critical birth-time difference). The optimum time of jet impact, at which bubble A reaches its maximum volume, depends on $\unicode[STIX]{x0394}\unicode[STIX]{x1D703}^{\ast }$. It is generally later for larger values of $\unicode[STIX]{x1D709}$. A pulsed jet could be used to create small pores in a cell membrane; therefore, the reported method may be useful for application in tandem-bubble sonoporation.

Behaviour and dynamics of two bubbles in conjunct condition in high‐viscosity liquids

AbstractTwo bubbles in conjunct condition are often encountered in high‐viscosity liquids, but have received very little attention in the literature. The conjunct bubbles rise together with unchanged shapes and constant velocities, showing some unique properties compared to single bubbles. The current research built on the previous work of Cai et al.,[1] and extended the bubble size ratio (κ) to the range 1.0–1.2. The formation and motion characteristics of conjunct bubbles made by direct collision of two in‐line bubbles were investigated, including the effects of bubble volume, bubble size ratio, and liquid viscosity. Models for the conjunct bubbles and the single bubbles were provided for predicting the projected area diameters and the rising velocities respectively, and the predicted values closely agreed with the measurements in glycerol‐water solutions with Morton numbers in the range of 1.690–661.8. The dynamic forces on the conjunct bubbles were analyzed, and a succinct algorithm was proposed for calculating the drag forces on the conjunct bubbles and the interaction force between the two bubbles.

Temporal evolution of microstructure and rheology of sheared two-dimensional foams

We measure the shear rheology of two-dimensional liquid foams in a Couette device, and correlate the variation of the shear stress with the evolution of the foam microstructure. For a monodisperse foam, inception of shearing results in a rapid rise of the shear stress, which then saturates into a quasi-steady state of fluctuations about a time-independent mean value. The dominant frequency of the oscillation correlates closely with the time scale of one row of bubbles sliding past the next row. The mean stress decreases with increasing bubble size. In bidisperse foams, the shear stress exhibits two regimes of transient behavior. If the shear rate and the large-to-small bubble size ratio are both below certain thresholds, the stress behaves similarly to that in a monodisperse foam. Above these thresholds, however, the instantaneous shear stress oscillates around a mean value that declines gradually over several minutes. The foam eventually approaches a quasi-steady state similar to that of a monodisperse foam. This gradual decrease in shear stress can be attributed to the size-based segregation of bubbles. Finally, we propose a mixing rule that relates the effective viscosity of a bidisperse foam in the quasi-steady state to those of monodisperse foams made of the two constituent bubble sizes.

Hydrodynamic feedback on bubble breakup at a T‐junction within an asymmetric loop

Bubble breakup at a microfluidic T‐junction by taking into consideration the hydrodynamic feedback at the downstream channels is presented. Experiments are conducted in square microchannels with 400 μm in width. The splitting ratio of the bubble size in the bifurcations varies nonmonotonically with the flow rate ratio of gas/liquid phases, and it is also affected by the liquid viscosity. A critical size of the mother bubble determines the variation trend of the splitting ratio of bubble size with flow rates of both phases and the liquid viscosity, which is related to the different breakup mechanisms for long and short bubbles at the junction and the different additional resistances induced by long and short bubbles in downstream channels. A theoretical model is proposed to predict the tailoring size of bubbles at the T‐junction by taking into account of the additional resistance in the presence of bubbles in downstream channels. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1920–1929, 2014

Size Segregation in Sheared Two-Dimensional Polydisperse Foam

We report experiments on simple shear of a monolayer of bidisperse and polydisperse bubbles in a Couette device. The bubbles segregate according to their sizes, with larger ones in the middle of the gap and smaller ones closer to the walls, when the shear rate and the bubble size ratio are each above a threshold. The spatial distribution of the larger bubbles becomes flatter across the gap as its area fraction increases. To explain these observations, we adapt a model for monodisperse emulsions that predicts the spatial distribution of droplets as an outcome of the competition between migration away from the walls and shear-induced diffusion. The dense packing of bubbles in our foam intensifies bubble-bubble interaction, which manifests itself both in lateral migration due to wall repulsion and in collision-induced diffusion. After accounting for this difference via an effective capillary number based on the deformation of the bubbles, the model predicts the observed bubble distributions accurately.

Quenching of a highly superheated porous medium by injection of water

Understanding of two-phase flow through porous medium with intense phase change is of interest in many situations, including nuclear, chemical or geophysical applications. Intense boiling occurs when the liquid is injected into a highly superheated medium. Under such conditions, the heat flux extracted by the fluid from the porous medium is mainly governed by the nucleation of bubbles and by the evaporation of thin liquid films. Both configurations are possible, depending on local flow conditions and on the ratio of bubble size to pore size. The present study is motivated by the safety evaluation of light water nuclear reactors in case of a severe accident scenario, such as the one that happened in Fukushima Dai-ichi plant in March, 2011. If water sources are not available for a long period of time, the reactor core heats up due to the residual power and eventually becomes significantly damaged due to intense oxidation of metals and fragmentation of fuel rods resulting in the formation of a porous medium where the particles have a characteristic length-scale of 1 to 5 mm. The coolability of the porous medium will depend on the water flow rate which can enter the medium under the available driving head and on the geometrical features of the porous matrix (average pore size, porosity). Therefore, it is of high interest to evaluate the conditions for which the injection of water in such porous medium is likely to stop the progression of the accident. The present paper addresses the issue of modelling two-phase flow and heat transfers in a porous medium initially dry, where water is injected. The medium is initially at a temperature well above the saturation temperature of water. In a first part, a summary of existing knowledge is provided, showing the scarcity of models and experimental data. In a second part, new experimental results obtained in an IRSN facility are analysed. The experiment consists in a bed of steel particles that are heated up to 700°Cbefore injecting water. The facility is briefly described. The velocity of the "quench front" (location where particles are quickly cooled down) and the total pressure drop across the medium are estimated. The dependencies of those quantities with respect to the inlet water flow rate, the initial temperature of the medium and the diameter of particles are obtained. In a third part, a model is proposed, based on a previously developed model which is improved in order to take into account intense boiling regimes (in particular nucleate boiling). The model includes a function that takes into account the contact area between water and the particles which depends on the temperature of particles and on the void fraction. That function affects the local intensity of phase change. The model involves a few parameters which cannot be evaluated analytically. Those parameters are bounded, following the analysis of experimental data. Finally, the model is assessed by comparison of calculations with those new experimental data. The satisfactory agreement shows that the model is almost predictive in the range of parameters studied. The experimental results also show that the quench front becomes unstable under certain conditions. This is also analysed and compared with the predictions of the model.

Size-Differentiated Lateral Migration of Bubbles in Couette Flow of Two-Dimensional Foam

We report experiments on lateral migration of bubbles in a two-dimensional foam sheared in a narrow-gap Couette device. A larger bubble in an otherwise monodisperse bubble raft migrates toward the center of the gap as long as the bubble size ratio and the shear rate are each above a threshold. The migration speed is roughly two orders of magnitude higher than that of a single bubble, and increases with the shear rate and the size ratio. The bubble also deforms much more than an isolated one at the same shear rate. Modifying the Chan-Leal solution for the migration of a single submerged bubble or drop, we derive a formula that successfully predicts all the migration trajectories recorded in the experiment. The threshold for migration corresponds to the wall repulsion force overcoming the capillary force in the two-dimensional foam. The size-differentiated bubble migration provides an explanation for previously observed size segregation in sheared three-dimensional polydisperse foams.

The effects of outgassing on the transition between effusive and explosive silicic eruptions

The eruption style of silicic magmas is affected by the loss of gas (outgassing) during ascent. We investigate outgassing using a numerical model for one-dimensional, two-phase, steady flow in a volcanic conduit. By implementing Forchheimer's equation rather than Darcy's equation for outgassing we are able to investigate the relative influence of Darcian and inertial permeability on the transition between effusive and explosive eruptions. These permeabilities are defined by constitutive equations obtained from textural analysis of pyroclasts and determined by bubble number density, throat–bubble size ratio, tortuosity, and roughness. The efficiency of outgassing as a function of these parameters can be quantified by two dimensionless quantities: the Stokes number, the ratio of the response time of the magma and the characteristic time of gas flow, and the Forchheimer number, the ratio of the viscous and inertial forces inside the bubble network. A small Stokes number indicates strong coupling between gas and magma and thus promotes explosive eruption. A large Forchheimer number signifies that gas escape from the bubble network is dominated by inertial effects, which leads to explosive behaviour. To provide context we compare model predictions to the May 18, 1980 Mount St. Helens and the August–September 1997 Soufrière Hills eruptions. We show that inertial effects dominate outgassing during both effusive and explosive eruptions, and that in this case the eruptive regime is determined by a new dimensionless quantity defined by the ratio of Stokes and Forchheimer number. Of the considered textural parameters, the bubble number density has the strongest influence on this quantity. This result has implications for permeability studies and conduit modelling.

Effect of interface contamination on particle–bubble collision

This study focuses on the impact of the interface contamination on the collision efficiency between bubbles and inertial particles. The bubble's surface mobility has been integrated into the collision modelling by using the hydrodynamics stagnant-cap model, in which the clean angle θclean is used to characterise the interface contamination level. Direct numerical simulations have been performed for various bubble's Reynolds numbers (1≤Reb≤100), particle to bubble size ratio (0.001≤rp/rb≤0.02) and particle's Stokes numbers (0.001<Stp<1). The Lagrangian tracking was performed for the solid particles by solving the full particle trajectory equation, in order to find the critical grazing trajectory. The collision efficiency was then calculated, as the ratio of the number of particles located in the body of revolution made by critical trajectory to that of particles located in the cylinder formed by bubble's projection area. The magnitude of hydrodynamic force (buoyancy, drag, shear lift, added mass and history forces) as well as surface forces (electrostatic, Van der Waals and hydrophobic forces) are compared to propose a simplified trajectory equation. The surface contamination was found to play an important effect on the behavior of collision efficiency, especially near θclean. Analysis of collision angle showed that there is a critical angle θcrit, depending on the bubble's Reynolds number. For the bubble with θclean>θcrit, the contact point of the “grazing trajectory” can only be situated on the mobile interface, while for θclean<θcrit, the contact point may be on both mobile and immobile part of the interface and only the positive inertial effect is observed. A simple model has been proposed that makes possible the description of collision efficiency for clean or contaminated bubbles.

Ordered packings of bubbles in columns of square cross-section

The introduction of bubbles of equal size into a confined space with dimensions comparable to the bubble diameter generally leads to the formation of ordered foam structures. We present experimental data and computer simulations of the four simplest observed structures in columns of square cross-section. The topology of the ordered structure is dependent upon the ratio of bubble size to cross-sectional area of the enclosing tube. Ordered foam structures are observed to form over a smaller range of this parameter than in the cylindrical case.

Coalescence of Bubbles Translating through a Tube

The results of an experimental study of the interaction and coalescence of two air bubbles translating in a cylindrical tube are presented. Both pressure- and buoyancy-driven motion of the two bubbles in a Newtonian suspending fluid within the tube are considered. The close approach of the two bubbles is examined using image analysis, and measurements of the coalescence time are reported for various bubble size ratios and capillary numbers. For pressure-driven motion of bubbles, coalescence is found to occur in an axisymmetric configuration for all bubble size ratios considered in the experiments. For buoyancy-driven motion, on the other hand, the disturbance flow behind the leading bubble causes the trailing bubble to move radially out toward the tube wall when the trailing bubble size becomes very small compared to the size of the leading bubble. In that case, coalescence occurs in a nonaxisymmetric configuration, with a time scale for coalescence that is substantially larger than that for coalescence in the axisymmetric configuration. When the imposed flow is in the direction of the buoyancy force, coalescence time is independent of bubble size ratio, and decreases as the capillary number increases. Experimental measurements of the radius of the thin liquid film separating the two bubbles are used in conjunction with a simple film drainage model to predict the dependence of the coalescence time on the bubble size ratio.

Interaction of cavitation bubbles with a free surface

The motion of single- and two-cavitation bubbles generated by laser beams directly beneath a free surface is studied experimentally, using high-speed photography, and theoretically using the highly accurate boundary integral method. Favorable comparisons of bubble shape history and centroid motion are observed while the numerical calculations provide information on the pressure field surrounding the bubbles. A range of responses, including the null impulse state, is obtained for the two bubbles depending on the bubble size ratio and the interbubble and bubble-free surface distances, although in all cases reported in this article, the bubble nearest the free surface yields a high-speed liquid jet directed away from the free surface. It is also found that when the free-surface–bubble interaction is strong, a fast free-surface spike is formed for both the single- and two-bubble cases.

K-1436 固体壁面近傍での2個のレーザー生成キャビテーション気泡の非軸対称運動(S16-3 キャビテーションおよび気液系流れのダイナミクス(3))(S16 キャビテーションおよび気液系流れのダイナミクス)

The motion of two laser-produced cavitation bubbles near a solid boundary was studied experimentally using high-speed photography. Two bubbles were mainly generated side by side near a solid wall. Eventually they collapsed non-axisymmetrically due to the Bjerknes force resulting from the bubble-bubble interaction as well as the bubble-boundary interaction. The direction of the liquid jet formed inside a smaller bubble, θ_j was estimated to examine the effect of the bubble size ratio, ξ, resulting in a remarkable decrease in θ_j as decreasing ξ, especially in the region of ξ<0.6.

Statistical method to calculate local interfacial variables in two-phase bubbly flows using intrusive crossing probes

This paper presents a statistical method to calculate local interfacial variables in two-phase gas–liquid bubbly flows from data taken with double-sensor intrusive probes. Firstly, one derives the geometrical relationship existing between the apparent and actual bubble velocity for a single spherical bubble flowing in a multidimensional flow field. The apparent variables are obtained from the experimental data when one assumes that the bubble trajectory is aligned with the probe axis. A similar relationship exists for the intersected chord length and bubble diameter. Then, the analysis is extended to a swarm of bubbles. The ratio between the apparent to the actual bubble velocity and the intersected chord length to the bubble diameter appear now as probability density functions. The experimental data were taken for air–water bubbly flow regime in a vertical round pipe with a double tip electrical probe. Processing the phase density function generated by the bubble events, one determines distribution function of the bubble velocity and intersected chord length, termed the apparent distributions. The variables of interest, actual bubble velocity and diameter, come out of the solution of a linear system of equations relating the probability function of the measured and estimated bubble velocity and bubble size ratio. The probability density function of the actual bubble velocity and bubble diameter, plus the bubble frequency, add up to various interfacial properties calculated with this technique: the void fraction, the bubble velocity, the bubble size, the interfacial area density and the interface velocity fluctuation intensity. To validate the method, the paper compares local and area averaged quantities with previously published results, volumetric measurements and extensively used correlation.