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 formation from a free-standing tube in microgravity

The bubble characteristics and the bubble detachment mechanisms during injection of air from a free-standing capillary tube submerged in water were studied in microgravity. The experiments were conducted in the 2.2-s drop tower at the NASA Glenn Research Center. A tube, 0.51 mm in diameter and 150 mm long, in a rectangular test section ( long) served as the injector. Images of the bubbles during the drops were acquired using a high-speed camera for various gas flow rates. Bubble detachment was observed for all the Weber numbers tested (0.28-31.12). This observation was different from previous studies using plate orifices in microgravity when bubble detachment was observed only for Weber numbers larger than 8. In order to resolve these differences, experiments were carried out using plate orifices. It was found that the bubbles detached from the orifice for all Weber numbers and that the bubbles formed were larger than those formed with the tube injector, particularly at low gas flow rates. The availability of a large area for the bubble to anchor itself and the presence of the chamber underneath the orifice could cause these differences. The effects of the chamber volume on the unsteadiness of bubble formation in plate-orifices at low gas flow rates are discussed.     

On the formation of Taylor bubbles in small tubes

The formation of Taylor bubbles and resulting bubble lengths were studied in a ID vertical tube for air-water and air-octane systems. In the co-flow tube/nozzle arrangement two nozzle sizes were used as gas inlets. Superficial velocities varied between 0.001- for the liquid and 0.002- for the gas. Three different mechanisms of initial bubble formation were observed. Of the three mechanisms, mechanism 3 is periodic (with period consisting of a bubble and a liquid slug), reproducible and can be simply modelled. After initial bubble formation further modifications may occur in the formed bubble size by coalescence or pairing. Bubble pairing is encouraged by smaller nozzles and liquid flow rates, while coalescence is observed only for cases where non-Taylor bubbles form initially.Two simple models have been proposed, the first predicts the size of the Taylor bubbles formed by mechanism 3 while the second attempts to predict the condition for bubble pairing to occur. Reasonable agreement with experimental results validates the predictions of the first model for a strong dependence of the volume of Taylor bubbles formed on the gas and liquid flow rates, a moderate dependence on nozzle diameter and a weak dependence (if at all) on the surface tension of the liquid used. Mismatch with the experimental results is caused (at least in part) by the experimental setup where there was no perfect axial alignment of the gas inlet. The experiments also suffered from problems at the outlet at low flow rates where smooth bubble disengagement could not be ensured for long Taylor bubbles. The second model for pairing predicts its occurrence for concentric tube/nozzle arrangements as a function of flow rates and channel diameters. The model over-predicted the range of liquid flow rates at which pairing was observed experimentally, but it captured the form of the boundary between different bubble volume modification mechanisms when represented on superficial velocity graphs.     

Small bubble formation via a coalescence dependent break-up mechanism

A mechanism has been elucidated for the coalescence-mediated break-up of bubbles in gas-liquid systems. Images taken from dynamic systems (a coalescence cell and laboratory-scale bubble columns) show that in some instances the coalescence of two bubbles is accompanied by the formation of a much smaller daughter bubble. Following the coalescence process an annular wave is formed due to the very rapid expansion of the hole following the instant of film rupture. As the wave moves along the length of the bubble, away from the point of rupture it causes a rippling effect which distorts the newly coalesced bubble and may result in the formation of an unstable extension. Instabilities due to the annular wave pinch off a portion of this extension, resulting in the generation of a small daughter bubble. In coalescence dominated systems the process results in the generation of significant numbers of bubbles much smaller (100- diameter) than the Sauter mean diameter (3-).     

Bubble sizes in agitated solvent/reactant mixtures used in heterogeneous catalytic hydrogenation of 2-butyne-1,4-diol

Catalytic hydrogenations reactions are frequently conducted in “dead-end” multiphase stirred reactors with the reactant dissolved either in an alcohol, or in water or a mixture of the two. In such systems, the rate of gas-liquid mass transfer, which depends on bubble size, may well be the overall rate-limiting step. However, a study of bubble sizes across the whole range of solvent compositions from entirely water to entirely organic has not been reported. Here, for the first time, a systematic investigation has been made in a 3 L, closed vessel simulating a “dead-end” reactor containing 1% by volume of air which is dispersed by a Rushton turbine in water, isopropanol (IPA) and mixtures of the two, with and without 2-butyne-1,4-diol simulating a reactant. Mean specific energy dissipation rates, , up to have been used and bubbles size distributions and mean size were measured using a video-microscope-computer technique. In the single component solvents (water, ; IPA, though the interfacial tensions are very different, irregular, relatively large bubbles of similar sizes were observed ( in IPA, and in water) with a wide size distribution. In the mixed aqueous/organic solvents, and especially at the lower concentrations of IPA (1%, 5%, 10%), the bubbles were spherical, much smaller (d₃₂ from 50 to ) with a narrow size distribution. The addition of the reactant (0.2 M 2-butyne-1,4-diol) to the mixed solvents had little effect on the mean size, shape or distribution. However, addition to water (thus producing a mixed aqueous/organic liquid phase) led to small spherical bubbles of narrow size distribution. Neither Weber number nor surface tension was suitable for correlating bubble sizes since σ decreased steadily from pure water to IPA whilst bubble size passed through a minimum at around 5% IPA. For any particular fluid composition, the functionality between d₃₂ and was similar, i.e. . The above observations are explained in terms of the polarisation of bubble surfaces in miscible mixed aqueous/organic liquids caused by preferential directional adsorption at low concentrations of the organic component with its hydrophilic part directed into the aqueous phase and its hydrophobic part into the gas phase. As a result, coalescence is heavily suppressed in the low-concentration miscible alcohol (or diol)/aqueous systems whilst strong coalescence dominates bubble sizes in water and the alcohol and at high concentrations of the latter.     

Bubble-wall interactions in a vertical gas-liquid flow: Bouncing, sliding and bubble deformations

The paper presents the results of a study on the motion of single (individual) bubbles rising in upward shear liquid flow in the vicinity of a vertical wall. Bubbles were found to slide along the wall when their diameter is small. Bubbles could also experience multiple collisions with the wall at certain experimental parameters (geometry of a channel, range of superficial liquid velocity, bubble size, etc). The latter was theoretically predicted by solving the equation of the bubble motion for the lateral direction in the boundary layer of the channel. For this, constitutive models available in the literature for the interfacial forces acting on a bubble in the vicinity of the wall were used. A simplified 1D model predicting bubble lateral displacement near the wall and taking into account the balance of drag and non-drag forces acting on a bubble was proposed. The numerical results were verified against the experimental ones obtained by non-intrusive high-speed video observations and subsequent image processing.The experiments on the bubble motion were conducted in a vertical acrylic duct having a square cross-section of and a height of approximately 1.3 m. Desalinated water and air both taken at room temperature were used in the experiments. All measurements on the bubble motion were performed at channel heights between 0.8 and 1 m above the gas injection point.     

Chaos in bubbling—nonlinear analysis and modelling

In the present paper, nonlinear features and analytical results for the chaotic bubbling from a submerged orifice are described. A chain of air bubbles was produced from the single orifice of in diameter and micro-convection induced by the bubble generation was recorded using hot-probe anemometer located close to the orifice. The air flow rate was varied widely from q=100 to and the aspects of bubbling were observed by high-speed video. The nonlinear analysis is performed for the time series data of hot-probe anemometer especially in the range of q=435-. The calculated largest Lyapunov exponent shows that with increase of air volume flow rate, the time period for the process of liquid flow to lose stability becomes shorter and at high air flow rate such as , it is shorter than the time period between subsequent bubbles. To explain such chaotic behaviors of bubbling, a simple model has been proposed. The model simulates the process of interaction between the elastic bubble wall and liquid. Simulation results compared well with the analytical results of experimental data. Summarizing, it is concluded that one of the reasons for chaos appearance is the nonlinear character of interaction between an elastic bubble wall and the liquid stream.     

Hydrodynamics and steel tube wastage in a fluidized bed at elevated temperature

Hydrodynamic measurements were made in a bubbling fluidized bed operated at 550°C at three different excess gas velocities (0.15, 0.40 and ). The bed has a cross-sectional area of with an immersed tube bank consisting of 59 horizontal stainless steel tubes (AISI 304L), 21 of which are exchangeable, thus allowing erosion studies. Capacitance probe analysis was used to determine the mean bubble rise velocity, the mean bubble frequency, the mean pierced bubble length, the mean bubble volume fraction and the mean visible bubble flow rate. Tube wastage was calculated from roundness profiles obtained by stylus profilometry.A redistribution of the bubble flow towards the center of the bed occurs when the excess gas velocity is increased. Measurements along a target tube, situated next to the capacitance probe, usually show greater material wastage at the central part of the tube, since the mean bubble rise velocity and the mean visible bubble flow rate are higher there. It is suggested that the greater material degradation is also an effect of the through-flow of a particle-transporting gas stream in the bubbles. With increasing height above the distributor plate the circumferential wastage profiles for the lowest excess gas velocity show a gradual change from an erosion pattern with one maximum (Type B behavior) to a pattern with two maxima (Type A behavior). Power spectral density distributions of the fluctuating pressure signals show that this is a result of the formation of larger bubbles, when the fluidization regime is changed in the upper part of the bed. At the highest excess gas velocity the bubble flow becomes more constrained due to a more rapid coalescence of the bubbles and the tubes show Type A wastage profiles throughout the bed.     

Coalescence during bubble formation at two neighbouring pores: An experimental study in microscopic scale

This work studies the effect of the liquid properties and the operating conditions on the interactions between under-formation bubbles in a cell equipped with two adjacent micro-tubes (i.d. ) for the gas injection, placed 210, 700 and apart. This set-up simulates, though in a simplified manner, the operation of the porous sparger in a bubble column, and it is used to study the bubble interactions observed on the sparger surface. Various liquids covering a wide range of surface tension and viscosity values are employed, while the gas phase is atmospheric air. A fast video recording technique is used both for the visual observations of the phenomena occurring onto the tubes and for the bubble size measurements. The experiments reveal that the interactions between under-formation bubbles as well as the coalescence time depend strongly on the liquid properties, the distance between the tubes and the gas flow rate. Two correlations, which can be found helpful for the bubble column design, have also been formulated and are in good agreement with the available experimental data.     

The bubbling behavior of cohesive particles in the 2D fluidized beds

The present work focuses on a fully statistical analysis of bubbling behavior in the two-dimensional (2D) fluidized beds with cohesive particles. Various significant bubble properties such as bubble size, rising velocity, aspect ratio, bed expansion and bubble hold-up, etc., were investigated. An equation for bubble diameter is developed, , and the observed bubbles are generally smaller than the ones generated in the beds with A or B type powders. Both the average bubble size and rising velocity initially increase with the elevation above the distributor and keep constant beyond certain heights. The bubbles exhibit oblong with the most density aspect ratio (β) equal to 0.7. In addition, the bubble rising velocity coefficient ranges from 0.8 to 1.5. Two core-annular flows form in the large diameter, shallow fluidized bed used in this experiment.     

Research on formation mechanisms and control of external and inner bubble morphology in microcellular injection molding

This study investigates the formation mechanisms and control of external and inner bubble morphology in MIM. First, the related theories about foaming and filling flow are analyzed. Second, the assumptions for the formation of inner bubble morphology, external bubble morphology, and the compact skin layer in MIM process are proposed based on theoretical analysis. Finally, experiments of MIM process are conducted to verify the theoretical assumptions. In addition, gas counter pressure (GCP) and rapid mold heating and cooling (RMHC) technology are used for control of bubble morphology. It is found that foaming process in MIM can be divided into foaming during filling and foaming during cooling. Foaming during filling produce oriented and deformed bubbles while foaming during cooling produce spherical or polygonal bubbles. As the bubbles formed by foaming during filling can reach melt flow front, they will be pushed to the cavity surface where they are stretched further and frozen to generate the silver or swirl marks. The compact skin layer is formed due to the redissolution of the gases within bubbles into polymer melt and also restraint of foaming by high cavity pressure. GCP and RMHC are two effective methods for controlling external and inner bubble morphology. POLYM. ENG. SCI., 55:807–835, 2015. © 2014 Society of Plastics Engineers     

Digital image analysis of hydrodynamics two-dimensional bubbling fluidized beds

A new method of digital image analysis has been developed to study the hydrodynamics of two-dimensional bubbling fluidized beds with a digital video camera. The method comprises simultaneous of the size and velocity of gas bubbles, and the axial and radial distribution of bubble voidage. It provides a better estimation of the visible bubble flow than from local probe methods. Also a good estimation of the throughflow can be gotten, which is of great importance for combustor applications.Parallel to the approach of Darton et al. (Transactions of the Institution Chemical Engineering 55 (1977) 274) for three-dimensional fluidized beds, an equation for the bubble diameter of two-dimensional beds is developed,

     

Physical modelling and similitude of air bubble entrainment at vertical circular plunging jets

When a plunging jet impinges into a pool of liquid, air bubble entrainment takes place if the inflow velocity exceeds a threshold velocity. This study investigates air entrainment and bubble dispersion in the developing flow region of vertical circular plunging jets. Three scale models were used and detailed air-water measurements (void fraction, bubble count rate, bubble sizes) were performed systematically for identical inflow Froude numbers. The results highlight that the modelling of plunging jet based upon a Froude similitude is affected by significant scale effects when the approach flow conditions satisfied We₁<1E+3, while some lesser scale effect was noticed for V₁/u_r<10 and We₁>1E+3. Bubble chord time measurements showed pseudo-chord sizes of entrained bubbles ranging from less than to more than with an average pseudo-chord size were between 4 and . However, bubble size data could not be scaled properly.     

Spargers for controlled bubble size by means of the multiple slot disperser (MSD)

Sparging technology is crucial in the dispersion of gases in liquids. In this work, it was demonstrated that an effective, controllable sparger can be made by assembling an array of flat parallel slot-nozzles which may offer new options for sparger design and operation. To illustrate the technique, a compact, ‘multiple slot disperser’ (MSD) having a slot width of and a total slot length of 1.26 m was assembled from a series of 5-mm-thick graphite plates. In water containing a low concentration of frother, a dense three-dimensional bubble plume was produced. The MSD generated consistently narrow bubble size distributions with well-defined median bubble diameters in the range 2.6-3.1 mm, equivalent to a range of gas flow rate from 11 to 26 std l/min. The bubble sizes were readily predictable from established single slot bubble size correlations. The method of construction also allows for simple maintenance, repair and replacement of individual components as needed.     

Modelling the effect of liquid motion on bubble nucleation during beer dispense

Beer dispense involves ejecting supersaturated beer under gas pressure, from a nozzle into a receiving vessel. Bubble nucleation therefore occurs in a flowing liquid. This situation is encountered in other processes, but is not accounted for in current nucleation models. An experimental system was developed to measure bubble production rates and sizes in laboratory scale beer dispense. Experimental results indicate that bubble nucleation is affected by both liquid flow rate and dissolved gas composition. Pre-existing gas nuclei models have been adapted using bubble and droplet detachment models to include the effect of liquid motion and gas composition. The adapted nucleation models were compared to the experimental results. Predicted bubble detachment radii and overall nucleation rates were affected by liquid flow rate, direction of liquid flow, dissolved gas composition, the contact radius and the level of contact angle hysteresis. Accurate predictions were achieved for different surface orientations and liquid flow directions. Accurate predictions occurred at hysteresis levels of 3.5°, 7.5° and 20° for liquid flow rates of 0.6, 2.2 and , respectively. It is clear that the predicted overall nucleation rate however, also depended on the number of nucleation sites and how many of these were active; although values for these parameters were not experimentally determined in this case. Further understanding of the exact number and size of nucleation sites available and the contact angle for the particular combination of liquid and solid used is required to improve the fit of the model to the experimental data.     

Gas back-mixing studies in membrane assisted bubbling fluidized beds

Fluidized beds employing fine powders are finding increased application in the chemical and petrochemical industry because of their excellent mass and heat transfer characteristics. However, in fluidized bed chemical reactors axial gas back mixing can strongly decrease the conversion and selectivity. By insertion of membranes in fluidized beds large improvements in conversion and selectivity can be achieved, firstly by optimizing axial concentration profiles via distributive feeding of one of the reactants or selective withdrawal of one of the products, and secondly, by decreasing the effective axial dispersion via compartmentalization of the fluidized bed. Moreover, insertion of membrane bundles in a suitable configuration impedes bubble growth, thereby reducing reactant by-pass via rapidly rising large bubbles. In this work the influence of the presence and configuration of membrane bundles and the effect of gas addition via the membranes on the effective axial dispersion was studied experimentally.Steady state concentration profiles were measured where a CO₂-tracer was injected at different locations through a probe (point injection) or via the membranes (line injection) into a square fluidized bed containing glass particles (75-, 2550 kg/m³) fluidized with nitrogen distributed via a porous plate. Different bed configurations, viz. without internals, with vertical or horizontal membrane bundles were investigated and the effects of overall fluidization velocity and gas flow ratio of gas fed through the membrane bundles and the porous plate distributor were studied.Experimental results revealed that the insertion of vertical and horizontal membrane bundles decreases the effective axial dispersion considerably compared to a bed without internals. The point injection experiments indicated the importance of a non-uniform lateral emulsion phase velocity profile. The line injection experiments clearly pointed out the importance of bubble-to-emulsion phase mass transfer limitations. Gas addition through the membrane bundles decreases the effective axial gas dispersion enormously by almost annihilating the solids down flow along the walls and by decreasing the average bubble size and bubble fraction.     

Experimental determination of particles capture efficiency in flotation

A single bubble experiment is developed for the determination of the capture efficiency by rising bubbles in a uniform concentration of small inertialess glass particles under carefully controlled hydrodynamics and physico-chemical conditions. Air bubbles (0.35-1.3 mm in diameter) rise and reach their terminal velocity in clean water before passing through a suspension of particles (15- in size), where capture takes place. After passing through another zone containing pure water to remove particles trapped in their wake, bubbles release captured particles at the surface from where the particles are collected and counted. A capture efficiency is then calculated as the ratio of the number of particles captured by one rising bubble to the number of particles present in the volume swept out by this bubble. Capture efficiencies range between 10^-3 and 5×10^-1 and are in the order of magnitude of the experimental results presented by Ralston and Dukhin [1999. The interaction between particles and bubbles. Colloids and Surfaces A: Physicochemical and Engineering Aspects 151, 3-14] as well as of numerical results for collision efficiency presented by Sarrot et al. [2005. Determination of the collision frequency between bubbles and particles in flotation. Chemical Engineering Sciene 60 (22), 6107-6117].     

Demonstration of a minimum in the recovery of nanoparticles by flotation: Theory and experiment

The flotation of nano- and submicron particles does not follow the conventional collection theory based on the interception and collision mechanisms, which predicts extremely low collection efficiency for particles smaller than 10-μm. Brownian diffusion and colloidal forces strongly influence the collection of such particles by air bubbles in flotation. In this paper, a theoretical model is presented for predicting the collection efficiency of nanoparticles. The theory incorporates mass transfer by Brownian diffusion, microhydrodynamics of particles in the vicinity of a slip surface of rising air bubbles, and colloidal interactions that come into effect at small separation distances. The governing equation was solved numerically using the Crank-Nicolson method with variable step size. A finite difference scheme with mesh refinement in the vicinity of the air bubble surface was used to discretise the stiff partial differential equation for the particle concentration. The mesh refinement produced correct numerical solutions without oscillation in the particle concentration distribution, which otherwise occurred due to the stiffness of the differential equation and coarseness of the numerical mesh. Predictions from the model were compared with experimental results obtained with a small laboratory column cell, in which colloidal silica particles with diameters in the range were floated using fine bubbles of typical average diameter . The particle concentration in the pulp was about 1% by weight. Cetyltrimethyl ammonium bromide and Dowfroth 250 were used as the flotation collector and frother, respectively. Both the theory and experiment show significant effect of the electrical double-layer and non-DLVO hydrophobic attractive forces on the collection of nanoparticles by air bubbles. The theoretical and experimental results show the collection efficiency to have a minimum at a particle size in the order of . With larger particles, the interception and collision mechanisms predominate, while the diffusion and colloidal forces control the collection of particles with a size smaller than the transition size.