BUBBLE FORMATION AT A PUNCTURE IN A SUBMERGED RUBBER MEMBRANE

Very large enhancements in volumetric mass transfer coefficients have recently been reported using a new type of sparger which is comprised of a punctured rubber membrane. The punctured sheet has been reported to produce very uniform emulsions of small bubbles, which leads to large apparent increases in gas voidage and mass transfer area. Flooding(slugging) is presumably repressed owing to the “elastic hole” phenomenom whereby the rubber sheet balloons and expands as applied pressure increases. Under conditions of expansion, a puncture in the sheet also expands thereby mitigating the occurence of jetting. In the present effort, we study a single puncture in the center of circular rubber sheets of 2, 3, and 4 inch diameters. By measuring bubble frequency and flow rate, we compute average bubble size. These results for flow rates from 0.01 to 2.0 cc/sec suggest that bubble size is practically constant over a nearly two decades of flow rate, until a flow of around 0.5 cc/sec, thence bubbles tend to follow the empirical correlation of L. Davidson and Amick (1956) and the inviscid theory of J.F. Davidson and Schuler (1960) both of which predict bubble volume increases as the 6/5 power of flow.

Using the “point source” model of J.F. Davidson for bubble growth, we include additional effects of surface tension to derive the required detachment-time. This leads to a theory which includes inertial, buoyancy and surface tension effects. The theory gives flow rate as a function of final bubble size and agrees quite well with the 180 experiments reported. The new theory approaches the inviscid models in the limit of large gas flow rates. Finally, we present results which clearly suggest that hole area increases linearly with increasing plenum chamber pressure.     

COMPREHENSIVE STUDY OF THE GAS HOLD UP AND BUBBLE SIZE DISTRIBUTION IN HIGHLY VISCOUS LIQUIDS I. GLYCEROL SOLUTIONS

The overall gas hold up, E_G, and bubble size distribution were separated into the particular gas hold up, E_GK, and Sauter diameter. d_SG. due to “small bubbles” as well as E_GG and d_SG, due to “intermediate to large bubbles.” Bubbles are defined to be “small” if they remain in the bubbling layer 15 seconds after the gas flow is turned off. The bubbles which leave the layer during this time are considered to be “intermediate to large bubbles.” The time dependences of E_G E_GK and E_GG, as well as of bubble size distribution after initiating the aeration of the liquid, is investigated. The steady state E_G, E_GK and E_GG, Sauter diameter and specific geometrical surface area of “small” and “intermediate to large” bubbles as well as of the entire bubble population were determined in bubble columns employing 50, 70, 90 and 95% glycerol solutions and perforated plates with different hole diameters (d_H = 0.5. 1.0 and 3.0 mm) respectively. In highly viscous media the “small” and “very large” bubble fractions are high. A comparison of the specific geometrical bubble surface areas with the corresponding volumetric mass transfer coefficients, k_La's, measured earlier indicate that the “small” bubbles do not contribute to k_La. The influence of the “small” bubbles on the fluiddynamics of the two phase system is discussed.     

Dispersion and hold-up in bubble columns — comparison of rigid and flexible spargers

The performance of a new type of bubble generating device, the rubber sheet sparger, is contrasted and compared with rigid spargers. Impulse response tests were analyzed using the weighted-moments method to determine voidage and dispersion coefficients in counter-current bubble columns of nominal diameters two, four, six and twelve inches. The flexible rubber sheet sparger produced more uniform emulsions, smaller bubbles and larger voidages than perforated plates, while dispersion coefficients were reduced for a range of superficial gas velocities. The dispersion data seem to fit the isotropic turbulence model, with slight modifications. It is demonstrated that the rubber sheet sparger is self-regulating, with hole size increasing in direct proportion to pressure drop across the sparger.     

Oscillations in gas-fluidized beds: Ultra-fast magnetic resonance imaging and pressure sensor measurements

Ultra-fast Magnetic Resonance Imaging (MRI) and pressure sensor measurements have been applied to study: (i) pressure fluctuations, (ii) the eruption of bubbles at the top of a bed and (iii) the formation of bubbles in a gas-fluidized bed. Ultra-fast MRI has been applied for the first time to study the formation and eruption of bubbles; the technique is non-intrusive and provides measurements with good temporal and spatial resolutions. The MRI measurements revealed that bubbles are formed periodically, rather than randomly at a distributor, which in this case was a perforated plate. The frequency at which bubbles erupted from the top of the bed matched the frequency of the pressure fluctuations measured just above the distributor, where the measured pressure is predicted very well for the case of slug flow by Kehoe and Davidson's [P.W.K. Kehoe, J.F. Davidson, Pressure fluctuations in slugging fluidized beds, AIChE Symp. Ser. 128 (69) (1973) 34-40] correlation, originally developed for locations high up a bed. Both findings lead to the conclusion that the passage and eruption of bubbles at the top of a bed are the dominant cause of the pressure fluctuations, which are subsequently propagated downwards through the bed. Two new correlations are proposed for predicting the frequency of pressure fluctuations in a bubbling bed; both correlations agree well with experimental measurements. A modification of Baeyens and Geldart's [J. Baeyens, D. Geldart, An investigation into slugging fluidized beds, Chem. Eng. Sci. 29 (1974) 255-265] correlation predicts the frequency of pressure fluctuations when slugs are formed, but are not fully developed. The frequency of bubble formation, as measured by MRI, is equal to or higher than both the frequency of bubble eruption at the top of the bed and the frequency of pressure fluctuations, depending on the depth of the bed. The frequency of bubble formation is significantly lower than predicted by Davidson and Schüler's [J.F. Davidson, B.O.G. Schüler, Bubble formation at an orifice in an inviscid liquid, Trans. Inst. Chem. Eng. 38 (1960) 335-342] equation, originally developed for gas-liquid systems.     

A visualized investigation of bubble breakup in a swirl-venturi bubble generator

The dynamics and breakup of bubbles in swirl-venturi bubble generator (SVBG) are explored in this work. The three-dimensional movement process and breakup phenomena of bubbles are captured by one high-speed camera system with two cameras while the distribution of swirling flow field is recorded through Particle Image Velocimetry technology. It is revealed that bubbles have two motion trajectories, which are deeply related to bubble breakup. One trajectory is that mother bubble moves upward in an axial direction of the SVBG to the diverging section, and the other trajectory is that mother bubble rotates obliquely upward to another side-wall along the radial direction. Meanwhile, binary breakup, shear-off-induced breakup, static erosive breakup, and dynamic erosive breakup are observed. For relatively high liquid Reynolds number, vortex flow regions are extended and the bubble size is reduced. Furthermore, it is worth noting that the number of microbubbles increases significantly for intensive swirling flow.     

On the measurement of bubble size distribution in gas–liquid contactors via light sheet and image analysis

Particle image velocimetry techniques coupled with advanced image processing tools are receiving an increasing interest for measuring flow quantities and local bubble-size distributions in gas–liquid mechanically agitated vessels.When trying to analyze image information the problem arises that bubble sizes are generally underestimated, due to the fact that the laser sheet used for lighting the system randomly cuts bubbles over non-diametrical planes, leading to an apparent bubble size distribution even in the ideal case of single sized bubbles. Clearly in the case of bubbles with a size distribution the experimental information obtained is affected by the superposition of effects.Aim of this work is that of providing a numerical procedure able to reconstruct actual bubble size distributions from relevant apparent size distributions obtained by laser sheet illumination and image analysis. The procedure proposed is robust and viable and can account for laser sheet thickness. The procedure is shown to provide fully satisfactory results even with quite extreme distributions. BSD resolution dependence on the numerousness of raw data processed is discussed. Use of the proposed procedure for extracting BSD from bubble chord raw data obtained by other devices, such as point probes, is straightforward.     

Controlled electrochemical gas bubble release from electrodes entirely and partially covered with hydrophobic materials

This paper deals with an experimental study on millimetre-size electrochemically evolved hydrogen bubbles. A method to generate gas bubbles controlled in number, size at detachment and place on a flat electrode is reported. Partially wetted composite islands are implemented on a polished metal substrate. As long as the island size is lower than a limit depending on its wettability, only one bubble spreads on the island and its size at detachment is controlled by the island perimeter. The composite, a metal–polytetrafluoroethylene (Ni–PTFE), is obtained by an electrochemical co-deposition process. On the contrary to predictions of available models for co-deposition, at current densities beyond Ni²⁺ limiting current density, the mass ratio of PTFE in the deposit strongly increases. A mechanism is proposed to describe co-deposition when hydrogen bubbles are co-evolved. The observation of gas evolution on fully hydrophobic electrodes highlights the fact that bubbles growth rate on such electrodes differs from growth rates when bubble growth is controlled by mass transport of dissolved gas. The more a bubble grows by coalescence the more its foot expands on the electrode the bigger its size at detachment. This triple line creeping mechanism explains why, when attached bubbles coalesce many times before detaching, their size at detachment increases with current density.     

Inviscid bubble formation on porous plates and sieve plates

We experimentally and theoretically investigate the formation of bubbles on wetted and non-wetted sieves and porous plates, which are submerged in an inviscid liquid. It is assumed that the process of bubble formation occurs as if each bubble were alone on the plate. The interaction between orifices is modeled by estimating the gas flow field caused by a growing bubble. Depending on the material below the plate, a growing bubble influences the formation of bubbles at other orifices either in its vicinity or over the whole plate, and bubbling sites are regularly or irregularly distributed over the plate. Values for the volume fluxes at which the bubbling behavior changes are given, e.g., the minimum gas volume flux at which a disperser becomes effective or the volume flux at which growing bubbles densely populate the plates.For an example system of air in water we discuss the four cases of wetted sieve, non-wetted sieve, wetted porous plate and non-wetted porous plate. We present data for a non-wetted porous plate and find fair agreement between theoretical predictions and experiment.     

A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow

Several models for the daughter bubble/droplet size distribution are reviewed and a detailed discussion is given to get a better understanding of the daughter size distribution. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow, based on an eddy-bubble/droplet collision method, is developed. It takes into account the energy distribution of turbulent eddies, effect of capillary pressure and surface energy increase during bubble/droplet breakup. An increase in the mother bubble/droplet size and energy dissipation rate increases the probability of unequal breakup. The model prediction is in good agreement with experimental results and the underlying physical situation.     

Bubble sizes produced by shear and turbulence in a bubble column

Measurements of bubble sizes for co-current upward air-water flow in a recirculating loop bubble column are described. The bubble sizes were determined with a two electrode conductivity detector. The effectiveness of two different designs of baffle in reducing the bubble size is assessed. The first type of baffle was a perforated plate placed across the air-water flow, which broke the bubbles by the shear flow and turbulence it caused. The measurements with this type of baffle are consistent with a recently developed theory of bubble break-up in shear flow. The second type of baffle consisted of a series of wire arrays placed across the flow. These broke the bubbles by a cutting action. The rate of bubble coalescence downstream of this baffle was determined, over a range of gas hold-up.     

Flowrate effects on the lateral coalescence of two growing bubbles

The coalescence of two growing bubbles presents unique characteristics compared to static bubble coalescence. The gas injection flowrate significantly affects the different stages of bubble evolution, which is poorly understood. In this study, we investigate the flowrate effects on the lateral coalescence of two growing bubbles experimentally. The synchronous bubbling from adjacent needles is achieved using water to push air. During the bubble growth process, we find that the initial nonlinear evolution of bubble volume is because the bubble emerges as a small spherical cap with a large curvature radius and apparent contact angle. As the neck expands after bubble coalescence, the injection flowrate accelerates the neck evolution compared to the case without air injection. We find the neck expansion time decreases linearly with increasing flowrate, while the expansion speed increases with flowrate, but only in the early stage. Moreover, we propose a new theoretical expression that predicts the neck radius well at all the flowrates. At the post-coalescence oscillation stage, the average projection area of the coalesced bubble increases linearly with time, except for periodic oscillations. Besides, we find that the injected air primarily influences the coalesced bubble's height, which in turn affects the projection area.     

气固流化床气泡发生频率的研究

在单孔二维气固流化床中(292mm×16mm)用高灵敏度电容探针研究气泡发生频率.以频谱分析仪分析气泡频率分布曲线.考察了一系列参数对气泡频率功率分布密度曲线的影响,其中包括颗粒直径(0.105—0.590mm),颗粒重度(590—2990kg/m~3),颗粒最小流化速度(0.0072—0.481m/s),床层初始高度(205—565mm),探针离孔口垂直距离,孔口气体流率(0.5—35×10~(-4)m~3/s)以及床层辅助流化气速(0—3倍最小流化速度)等.对于重度低的小颗粒流化床,单孔气泡发生频率符合Davidson和Harrison早先推导的模型.随着颗粒直径和重度的增大,实验数据与上述模型呈有规律的偏差.本文提出气体从形成中气泡的顶半球以最小流化速度值向乳浊相泄漏的模型,推导了气泡发生频率的基本方程.以本研究的泄漏模型,用数值计算方法在计算机上计算的气泡发生频率与实验数据相吻合.     

The pressure beneath a growing rising bubble

On the basis of potential theory, the equations of motion and the associated pressure field are derived for an idealized growing spherical gas bubble rising in an inviscid liquid under the influence of gravity from a horizontal plate-orifice and from a free standing nozzle. The dimensionless pressure (p_N?p₀)/πga at the gas source N (where p₀ is the undisturbed ambient pressure, a the instantaneous bubble radius and π the liquid density) is found to rise to a maximum when the dimensionless bubble position h/a = 1·55 for bubbles formed at a plate orifice and (125/48)^{$\text{1}\text{3}$} ? 1·38 for bubbles formed at a free standing nozzle. These positions of maximum pressure correspond well to experimentally observed positions at which the gas supply to bubbles grown at constant flow rate in water is cut off by the collapse of the neck linking bubble and gas source. The volumes of bubbles at this instant are predicted theoretically and compare well with experimentally determined values.     

A unified theoretical model for breakup of bubbles and droplets in turbulent flows

Pressure has a significant effect on bubble breakup, and bubbles and droplets have very different breakup behaviors. This work aimed to propose a unified breakup model for both bubbles and droplets including the effect of pressure. A mechanism analysis was made on the internal flow through the bubble/droplet neck in the breakup process, and a mathematical model was obtained based on the Young–Laplace and Bernoulli equations. The internal flow behavior strongly depended on the pressure or gas density, and based on this mechanism, a unified breakup model was proposed for both bubbles and droplets. For the first time, this unified breakup model gave good predictions of both the effect of pressure or gas density on the bubble breakup rate and the different daughter size distributions of bubbles and droplets. The effect of the mother bubble/droplet diameter, turbulent energy dissipation rate and surface tension on the breakup rate, and daughter bubble/droplet size distribution was discussed. This bubble breakup model can be further used in a population balance model (PBM) to study the effect of pressure on the bubble size distribution and in a computational fluid dynamics‐population balance model (CFD‐PBM) coupled model to study the hydrodynamic behaviors of a bubble column at elevated pressures. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1391–1403, 2015     

Formation dynamics and size prediction of bubbles for slurry system in T-shape microchannel

The bubble formation dynamics and size manipulation in the slurry of polystyrene microspheres in the microfluidic T-junction were visually investigated by a high-speed camera. Based on the evolution of the bubble neck with time, the formation process of bubbles is divided into three stages: filling, squeezing and pinch-off. The particle concentration has an obvious effect on the squeezing stage, while less impact on the filling and pinch-off stages. In the squeezing stage, the evolution of the dimensionless minimum neck width of bubbles with time could be described by a power-law relationship. The increase of the particle concentration or continuous phase flow rate could lead to the increase of body flow of the continuous phase and the enhancement of the squeezing force acted on the bubble neck, correspondingly, the power-law index α in the squeezing stage enlarges. Moreover, the bubble size increases with the increase of the gas phase flow rate and the decrease of the particle concentration and continuous phase flow rate. However, the effect of the particle concentration on the bubble size weakens with the increase of the continuous phase flow rate. In addition, a new prediction correlation of the bubble size for the slurry system in a T-shape microchannel was proposed with good prediction accuracy.     

Hydrodynamics features of dispersed bubbles in the ventilated wake flow of a cylinder

An experimental study was conducted to investigate the 2D bubbly flow downstream of a cylinder. Sparsely distributed bubbles were produced using the ventilation method. The carrier flow was measured using the particle image velocimetry (PIV) technique. The shadow imaging technique was used to capture instantaneous bubbly flow images. An image-processing code was compiled to identify bubbles in acquired image, calculate the bubble equivalent diameter and the bubble velocity. The effects of Reynolds number and the flow rate of the injected air were considered. The result indicates that the carrier flow is featured by distinct flow structures and the wake region is suppressed as the upstream velocity increases. Regarding the bubbles trapped in the wake flow, the number of small bubbles increases with the upstream velocity. On the whole, the bubble velocity is slightly lower than that of the carrier flow. The consistency between small bubbles and the carrier flow is high in terms of velocity magnitude, which is justified near the wake edge. The difference between the bubble velocity and the carrier flow velocity is remarkable near the wake centerline. For certain Reynolds number, with the increase in the air flow rate, the bubble equivalent diameter increases and the bubble void fraction is elevated.     

Modeling of bubble coalescence in bubbly co-current flows restricted by confined geometry

Principles of kinetic theory are used to model the coalescence of bubbles in horizontal and vertical upflows where bubble movements are restricted by channel geometry. There are four critical variables that determine the rate at which a swarm of small bubbles will coalesce: the initial bubble population, the average initial bubble diameter, the average relative velocity of the bubbles, and the efficiency of bubble collisions. A model based on dimensional considerations is proposed to predict bubble size as a function of flow position. This model agrees well with experimental results for air/water and air/water/glycerin systems performed in a rectangular channel with an aspect ratio of 12.5 and a cross-sectional area of under both vertical and horizontal orientations.     

Bubble mechanisms and characteristics at pore scale in a packed-bed reactor

An image processing technique was used to study dominant bubble mechanisms in a two-dimensional packed-bed at pore level under the bubbly flow regime. Bubble breakup and coalescence were identified as dominant mechanisms using a large number of image samples. Two types of coalescence mechanisms were identified that occur due to compression and deceleration associated with the bubbles and three breakup mechanisms were identified that are result of liquid shear force, bubble acceleration, and bubble impact. Data on various two-phase parameters, such as local void fraction, bubble velocity, size, number, and shape were obtained from the images. Results indicated that when a flow regime changed from bubbly to either trickling or pulsing flow, the number of average sized bubbles significantly decreased and the shape of the majority of the bubbles was no longer spherical. Although a mean bubble velocity of all sized bubbles was uniform for given gas and liquid superficial velocities, individual bubble velocities were quite different depending on the bubble location in the pore. The present bubble size distributions were compared with previous studies and the results on bubble size are in general agreement.     

Dynamic gas disengagement: A new technique for assessing the behaviour of bubble columns

A precise measure of the liquid motion and distribution of bubble sizes is essential for designing gas-liquid reactors for complex reactions in which product distribution may be a function of bubble size. A theoretical approach is presented which shows how the interaction of bubble size distribution and bubble rise velocity functions leads to predictions of the overall steady state hold-up in a bubble column within which the liquid flow is understood. Since this approach is based on a physical understanding of how bubble flow at a given superficial velocity must relate to the static hold-up, the theory can be immediately extended to describe the disengagement of gas bubbles if the gas feed is cut off. Thus the dynamic gas hold-up during gas disengagement can be used to provide new insights into the fundamentals of bubble column behaviour. In this way it becomes possible in principle to inter-relate macroscopic properties such as surface area, gas phase residence time distribution and intensity of mixing in the liquid phase.A new experimental technique is described which measures the dynamic gas hold-up during gas disengagement Experimental results at a nominal 20 mm/s gas superficial velocity are compared with various approaches based upon the theory. The effects of the accompanying induced liquid movements are represented by a simplified core-annulus circulation model. Bubble size distributions and liquid circulation can then be related to both the static and dynamic hold-up behaviour. It is shown that ambiguity due to uncertainty about the relative differences in bubble size distribution in upflow and downflow regions can be resolved from a knowledge of the surface area.