On the role of the macroscopic deformation in liquid film drainage between bubbles

The collision of bubbles in multiphase reactors is critical to bubble size distribution. However, the theoretical models that can reasonably predict collision outcomes and the experimental data that can be used to directly verify the models are still very lacking. We studied the collision of two bubbles in clean water through experiments and theoretical modeling, revealing the mechanism that the collision result shifts from coalescence to rebound with increasing collision velocity. The macroscopic deformation (MacrD) of bubbles is associated with the film drainage via a segmented linear equation as a function of the film radius and initial Weber number. Thus, the current model can reflect the effect of MacrD in a self-consistent way. The coalescence times and critical coalescence velocities predicted by the model were in good agreement with the experiments. This work provides novel insights into bubble coalescence modeling and serves to improve the accuracy of reactor simulations.     

CFD Simulations of a Bubble Column Operating in the Homogeneous and Heterogeneous Flow Regimes

Bubble columns are operated either in the homogeneous or heterogeneous flow regime. In the homogeneous flow regime, the bubbles are nearly uniform in size and shape. In the heterogeneous flow regime, a distribution of bubble sizes exists. In this paper, a CFD model is developed to describe the hydrodynamics of bubble columns operating in either of the two flow regimes. The heterogeneous flow regime is assumed to consist of two bubble classes: “small” and “large” bubbles. For the air‐water system, appropriate drag relations are suggested for these two bubble classes. Interactions between both bubble populations and the liquid are taken into account in terms of momentum exchange, or drag‐, coefficients, which differ for the “small” and “large” bubbles. Direct interactions between the large and small bubble phases are ignored. The turbulence in the liquid phase is described using the k‐ϵ model. For a 0.1 m diameter column operating with the air‐water system, CFD simulations have been carried out for superficial gas velocities, U, in the range 0.006–0.08 m/s, spanning both regimes. These simulations reveal some of the characteristic features of homogeneous and heterogeneous flow regimes, and of regime transition.     

Localized nature of the luminescence during galvanostatic anodizing of high purity aluminium in inorganic electrolytes

Luminescence during galvanostatic anodizing of high purity aluminium containing Fe, Si and Cu as major impurities in inorganic electrolytes, typically an aqueous solution of ammonium borate, was found to be a local phenomenon which takes place at “flaws” in the growing oxide film. The intensity of the luminescence was found to be closely correlated to the concentration of “flaws” in the film: the intensity of the luminescence being roughly proportional to the concentration of “flaws” in the film. Rough estimate of the concentration of ”flaws“ in the film formed on “as received”, “chemically cleaned” and “electropolished” aluminium plate was 2 × 10⁸.3 × 10⁷ and 10⁵/cm², respectively. Any mechanism deeming the luminescence to be an electroluminescence in a homogeneous oxide with the collision excitation of the impurities or with the recombination at impurity centres has been rejected.     

Eulerian–Lagrangian simulation of bubble coalescence in bubbly flow using the spring-dashpot model

The Eulerian–Lagrangian simulation of bubbly flow has the advantage of tracking the motion of bubbles in continuous fluid, and hence the position and velocity of each bubble could be accurately acquired. Previous simulation usually used the hard-sphere model for bubble–bubble interactions, assuming that bubbles are rigid spheres and the collisions between bubbles are instantaneous. The bubble contact time during collision processes is not directly taken into account in the collision model. However, the contact time is physically a prerequisite for bubbles to coalesce, and should be long enough for liquid film drainage. In this work we applied the spring-dashpot model to model the bubble collisions and the bubble contact time, and then integrated the spring-dashpot model with the film drainage model for coalescence and a bubble breakage model. The bubble contact time is therefore accurately recorded during the collisions. We investigated the performance of the spring-dashpot model and the effect of the normal stiffness coefficient on bubble coalescence in the simulation.The results indicate that the spring-dashpot model together with the bubble coalescence and breakage model could reasonably reproduce the two-phase flow field, bubble coalescence and bubble size distribution. The influence of normal stiffness coefficient on simulation is also discussed.     

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.     

Three‐dimensional numerical simulation of coalescence and interactions of multiple horizontal bubbles rising in shear‐thinning fluids

The dynamics of multiple horizontal bubbles rising from different orifice arrangements in shear‐thinning fluids was simulated numerically by three‐dimensional Volume of Fluid method. The effects of bubble size, rheological properties of shear‐thinning fluids, and orifice structure arrangements on multiple bubbles interaction and coalescence were analyzed, and the mechanisms of bubble coalescence and breakup were fully discussed and elucidated. The variation of bubble rising velocity during coalescence process and freely rising processes for different orifice arrangements was also deeply investigated. The critical initial horizontal intervals for coalescence of multiple horizontal bubbles with various orifice arrangements were attained by simulation, which could serve as the critical criterion of bubble coalescence or noncoalescence. Furthermore, the critical bubble interval was predicted based on the film drainage model, the prediction accords well with the simulation result and is quite conducive for the design and optimization of perforated gas–liquid contact equipment. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3528–3546, 2015     

Gas holdup,bubble size distribution,and mass transfer in an airlift reactor with ceramic membrane and perforated plate distributor

The airlift reactor is one of the most commonly used gas–liquid two-phase reactors in chemical and biological processes. The objective of this study is to generate different-sized bubbles in an internal loop airlift reactor and characterize the behaviours of the bubbly flows. The bubble size, gas holdup, liquid circulation velocity, and the volumetric mass transfer coefficient of gas–liquid two-phase co-current flow in an internal loop airlift reactor equipped with a ceramic membrane module (CMM) and a perforated-plate distributor (PPD) are measured. Experimental results show that CMM can generate small bubbles with Sauter mean diameter d₃₂ less than 2.5 mm. As the liquid inlet velocity increases, the bubble size decreases and the gas holdup increases. In contrast, PPD can generate large bubbles with 4 mm < d₃₂ < 10 mm. The bubble size and liquid circulation velocity increase as the superficial gas velocity increases. Multiscale bubbles with 0.5 mm < d₃₂ < 10 mm can be generated by the CMM and PPD together. The volumetric mass transfer coefficient k_La of the multiscale bubbles is 0.033–0.062 s⁻¹, while that of small bubbles is 0.011–0.057 s⁻¹. Under the same flow rate of oxygen, the k_La of the multiscale bubbles increases by up to 160% in comparison to that of the small bubbles. Finally, empirical correlations for k_La are obtained.     

Improvement of energy density in SrTiO3 film capacitor via self-repairing behavior

Self-repairing behavior of SrTiO₃ film capacitor was explored to improve the energy density. With Au and Al being deposited on SrTiO₃ thin films as top electrode, the breakdown processes were investigated by a real-time optical microscope system. A high electric field of the electrode edge attributed to edge effect provided the “trigger factor” for the self-repairing behavior. Absorbed water not only provided “mobile phase” for self-repairing process which significantly enhanced breakdown strength but also, and equally important, it supplied additional polarization charges to raise dielectric constant. As a result of the concurrent increase in E_b and ε_r, a higher energy density of 15.7 J/cm³ is achieved. A leakage current platform was observed in the self-repairing process and the thickness of a new layer Al₂O₃ film generated from self-repairing process was estimated according to Ohm's law and breakdown strength. Using relative humidity dependence of breakdown voltage, the maximum breakdown field was explored to realize the optimum self-repairing capability.     

The coalescence of H2S and CO2 bubbles in water

Coalescence times are reported for bubbles of H₂S and CO₂ formed on adjacent nozzles in water. With CO₂, times were small (1–3 ms) at pressures below 2 MPa, and rose to 20 ms at 3.4 MPa. With H₂S, the logarithm of the coalescence time was proportional to pressure, and coalescence times reached 100 ms at 1.7 MPa. Film stretching rates were calculated assuming that the film surfaces were slightly immobile. By using a form of Vrij's theory for the inherent breaking time of films of constant thickness, the effective number of immobile layers could be calculated. Since these were in the range 10^?2 to 10^?3, only a small amount of “stiffness” in the film surface is enough to cause large changes in coalescence time.     

COALESCENCE BETWEEN SMALL BUBBLES: EFFECTS OF SURFACE TENSION GRADIENT

1 INTRODUCTIONThe rate of coalescence between bubbles is important to the stability of foams,the mo-bility control in tertiary oil recovery,and a broad class of operations in which gas orvapor is the dispersed phase.Therefore,it is very important that the mechanism of thecoalescence process be understood,so that the effects of the physical properties oncoalescence can be assessed.     

Highly deacetylated chitosan and its properties

A preparative method has been established for obtaining chitosan products which have a desired degree of deacetylation of up to virtually 100%. Effective deacetylation was attained by intermitently washing the intermediate product in water two or more times during the alkali treatment. The weight average molecular weight (M?_w) of the product, which was measured by gel permeation liquid chromatography, was about 5 × 10⁵ at the highest deacetylation of nearly 100%, and the degradation of the molecular chain was not so significant. Tensile strength of the wet film increased markedly with increasing degree of deacetylation, while the dry film did not show a corresponding significant increase of the tensile strength. In the infrared spectra of chitosan film new sharp bands appeared especially at the high degree of deacetylation. This was attributed to increased “crystallization” brought about by high deacetylation.     

Photocatalytic degradation of malic acid using a thin coated TiO2‐film: Insights on the mechanism of photocatalysis

Decontamination of opaque fluids using photocatalysts and near Ultraviolet (UV) irradiation involves major technical challenges. This study considers a thin TiO₂ layer placed in a new Chemical Reactor Engineering Centre (CREC)‐photoreactor cell. This new photoreactor cell is used for the photocatalytic degradation of malic and malonic acids, typical apple juice components. Conversion of organic species can only proceed through the “dark side” of the TiO₂ layer, which is in direct contact with the fluid. Under the selected operating conditions both external mass‐transfer limitations and photolysis are found to be negligible. Macroscopic radiation balance shows that 92% of near UV radiation is absorbed by the ‘back side” of the TiO₂‐film. Photocatalytic degradation experiments with 10, 20, 30, and 40 ppm malic acid initial concentrations, show that malonic acid is a main intermediate. Complete malic acid conversion occurs after 5–8 h of irradiation. Kinetic modeling of malic and malonic acid photodegradation with kinetic parameter estimation is performed using both an “in series” and an “in series‐parallel” reaction networks. The “in series‐parallel” reaction network displays better ability for predicting CO₂ formation, showing maximum quantum yields of 14.2%. Given that in the CREC‐photoreactor cell with a thin TiO₂‐film, photocatalysis can only proceed via the transfer of mobile “h⁺” sites from the irradiated side to the “dark side', this study demonstrates the significance of this step on the overall photocatalysis mechanism. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3286–3299, 2014     

A kinetic model for pyrolysis of cellulose

It has been shown that the pyrolysis of cellulose at low pressure (1.5 Torr) can be described by a three reaction model. In this model, it is assumed that an “initiation reaction” leads to formation of an “active cellulose” which subsequently decomposes by two competitive first-order reactions, one yielding volatiles and the other char and a gaseous fraction. Over the temperature range of 259–341°C, the rate constants of these reactions, k_i (for cellulose → “active cellulose”), k_v (for “active cellulose” → “volatiles”), and k_c (for “active cellulose” → char + the gaseous fraction) are given by k_i = 1.7 × 10²¹e^{? (58,000/RT)} min ^?1, k_v = 1.9 × 10¹⁶e^{? (47,300/RT)} min^?1, and k_c = 7.9 × 10¹¹e^{? (36,600/RT)} min^?1, respectively.     

Influence of bubbles characteristics on the skin friction and velocity gradient on solid sphere

A detailed study of the effects of individual bubbles at high gas flow‐rate has shown, that the dominant influence on skin friction over a solid sphere is the bubble volume in compared to bubble frequency. Nevertheless the bubble frequency is very important in case of low gas flow‐rate. Referring to bubbles produced by a gas distributor, statistical and spectral analyses were performed to study the influence of bubbling on exposure time and magnitude of fluctuations. Referring to a calibrated bubble train, the existence of critical frequency is demonstrated. A bubble with larger volume and a mobile, oscillatory surface generates larger velocity gradient. In the case of gas distribution, histograms of the velocity gradient for a 2 mm glass sphere creating bubble coalescence reveal the maximum exceeds 48 000 s^?1 in the front zone and 2000 s^?1 in the rear zone (θ = 180°). For 5 mm plastic spheres creating bubble break‐up, the maximum of the velocity gradient is only 8100 s^?1 for the front part of the sphere and 2000 s^?1 in the rear zone.     

Hydrodynamics and mass transfer of gas–liquid flow in a falling film microreactor

In this article, flow pattern of liquid film and flooding phenomena of a falling film microreactor (FFMR) were investigated using high‐speed CCD camera. Three flow regimes were identified as “corner rivulet flow,” “falling film flow with dry patches,” and “complete falling film flow” when liquid flow rate increased gradually. Besides liquid film flow in microchannels, a flooding presented as the flow of liquid along the side wall of gas chamber in FFMR was found at high liquid flow rate. Moreover, the flooding could be initiated at lower flow rate with the reduction of the depth of the gas chamber. CO₂ absorption was then investigated under the complete falling flow regime in FFMR, where the effects of liquid viscosity and surface tension on mass transfer were demonstrated. The experimental results indicate that k_L is in the range of 5.83 to 13.4 × 10^?5 m s^?1 and an empirical correlation was proposed to predict k_L in FFMR. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

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].     

Analogous description of the hydrodynamics of gas-solid fluidized beds and bubble columns

In this paper we stress analogies in the hydrodynamic behaviour of gassolid fluidized beds and bubble columns. Using published experimental data, it is demonstrated that the analogous hydrodynamic-behaviour is not only qualitative but also quantitative in nature. Specifically, we show the following.(1) The gas holdup in the homogeneous regimes of bubble columns and fluidized beds can be modelled in a unified way using V_slip = υ_∞(1 − ϵ_d)ⁿ⁻¹, where V_slip refers to the slip velocity between the dispersed (bubbles or particles) and continuous phases and ϵ_d the dispersed phase holdup. The Richardson-Zaki exponent n decreases with increasing gas density.(2) The transition from homogeneous to heterogeneous flow regimes in gasliquid bubble columns and gassolid fluid beds is delayed by increasing system pressure. Extrapolation of the influence of increased gas density allows us to consider liquidliquid dispersions and liquidsolid fluid beds as limiting cases.(3) In the heterogeneous flow regime of operation the classic two-phase theory of fluidized beds can be applied with profit to also describe the hydrodynamics of gasliquid bubble columns provided that the “dilute” phase is identified with the fast-rising large bubbles and the “dense” phase is identified with the liquid phase containing entrained “small” bubbles. Tentative analogies can also be drawn for the interphase mass transfer processes.(4) The “dense” phase backmixing can be modelled in a unified manner.(5) The two-phase theory can be extended to describe slurry reactors.It is argued that, because of cross-fertilization of concepts and information, appreciation of analogies can be invaluable tool in scaling up.     

Two‐step photodegradation process of poly(ethylene terephthalate)

After investigating kinetics of the UV photodegradation of PET film samples having a thickness of 4.4 µm, we found that the photodegradation process takes place in two steps: a very rapid initial step followed by a normal step. This phenomenon is explained by using a concept of “weak links.” We have obtained the rate constants of degradation of the “normal links” k_N = 9.0 × 10⁻⁷ h⁻¹ and “weak links” k_W = 0.46 h⁻¹ and the number of scissions of weak links per molecules P_W = 0.22. For the samples treated by a UV stabilizer, we found k_N = 2.0 × 10⁻⁷ h⁻¹, k_W = 0.11 h⁻¹, and P_W = 0.27. The ratios of the rate constants of the untreated to treated samples are 4.2 for k_W and 4.5 for k_N. These results indicate that the UV stabilizer slows down the photodegradation rate of each step to the same extent, but hardly affects the number of scissions of weak links. Importantly, it is an implication that the lifetime of the PET thin film can be prolonged by a factor of 4.2 to 4.5 in the irradiation conditions used after being treated by the UV stabilizer. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 306–310, 1999     

Micromechanics of agglomeration forced by the capillary bridge: The restitution of momentum

The formation of capillary bridge formed by a liquid adsorbate is one of the main reasons for agglomeration in multiphase flows. Agglomeration takes place when the relative momentum of two colliding particles is fully consumed by the bridge. This article presents a theoretical study of the collisions of particles with adsorbed liquid taking into account the influence of capillary and viscous dissipative forces. The article proposes an approximate analytical solution for the dynamics of the bridge formed during the collision, together with a more complete numerical model, which is validated with experimental data. The restitution of the relative momentum of the colliding particles, depending on a series of dimensionless parameters characterizing the bridge, is investigated. A criterion for prediction of agglomeration, or “collision efficiency,” in a flow involving cohesive particles is given. An expression is proposed for the coefficient of restitution for the case of collision via a liquid bridge. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4045–4057, 2013