Approximate theoretical solution for the Sherwood number of oscillating bubbles at different Reynolds numbers

In this paper a theoretical approach to the effect of bubble oscillations on the mass transfer rates has been carried out to get a better understanding of the effect of bubble oscillations in multiphase gas–liquid contactors. The perturbation method has been used to approximate the velocity profile surrounding the bubbles while they oscillate. The shape of the oscillating bubble was modelled taking into account the effect of the liquid viscosity on bubble oscillation frequency and amplitude. The modelled shapes match the photographs of bubbles oscillating in liquids with different viscosities. As a result, new approximate theoretical models for the Sherwood number in viscous fluids at different flow regimes have been proposed. The models extend the work already available in the literature for mass transfer rates from oscillating bubbles in inviscid fluids and provides good results in predicting the Sherwood number at high and moderate Reynolds numbers, the preferred regimes in many industrial operations where, as a result of the hydrodynamics processes involving the bubbles. Their oscillations do not completely decay.     

搅拌槽内中高黏物系的气液分散特性研究进展

从实验和数值模拟两方面对搅拌槽内中高黏物系条件下的气含率、气泡尺寸大小和传质特性等进行综述。讨论了搅拌桨型、操作条件、黏度或非牛顿性对气液分散特性的影响。阐明了径流式搅拌桨和上翻式轴流桨的组合能减小气穴,更适合中低黏物系的搅拌;搅拌转速比通气量的影响效果更明显,转速增加使气泡的分布均匀性变好,而提高通气速度会产生大气泡,使气泡分布不均匀程度增加;黏度或非牛顿性的增加可以改变气泡的碰撞频率,气泡平均尺寸减小。最后讨论了针对中高黏物系的计算流体力学模型的修正方法,并且展望了此领域的研究发展方向。     

Gas-liquid mass transfer in bubble columns with a T-junction nozzle for gas dispersion

Bubble break-up, gas holdup, and the gas-liquid volumetric mass transfer coefficient are studied in a bubble column reactor with simultaneous injection of a gas and liquid through a T-junction nozzle. The theoretical dependence of bubble break-up and the volumetric mass transfer coefficient on liquid velocity in the nozzle is developed on the basis of isotropic turbulence theory. It is shown that correlations which are developed based on liquid jet kinetic power per nozzle volume explain average gas holdup and the volumetric mass transfer coefficient within an error of 15% for all gas and liquid flow rates and nozzle diameters used. Experiments with a larger scale column, height 4.64 m and diameter 0.98 m, show a transition from homogeneous to heterogeneous flow at a certain liquid flow rate through the nozzle. Liquid composition was found to have a significant effect on gas-liquid mass transfer. A phenol concentration of 10–30 mg/l in water increases the volumetric mass transfer coefficient of oxygen by 100%. This phenomenon may have significance in the chemical oxidation of wastewater.     

THREE-PHASE FLUIDIZED BEDS WITH VISCOUS LIQUID: HYDRODYNAMICS AND MASS TRANSFER†

Hydrodynamics and gas/fiquid mass transfer in fluidized beds of glass spheres (3-8 mm diameter)were studied employing viscous aqueous solutions (16-53 mPas) Increasing liquid viscosity reduced the bubble disintegration capability of the particle beds. The most pronounced consequence was a strong decrease in the volumetric mass transfer coefficients (k_La) From a comparison of k_La in Newtonian and pseudoplastic liquids it is concluded that the effective shear rates in three-phase fluidized beds are higher than in bubble columns.     

Solid—liquid mass transfer in a resonant bubble contactor

The resonant bubble contactor is a device in which a column of liquid is made to oscillate in a vertical direction, thereby entraining gas bubbles which are carried to the bottom of the column by Bjerknes forces. Large volumes of gas can be entrained, and the fluid becomes highly agitated.In this work, mass transfer to small solid particles in the contactor has been investigated. A study of the effect of frequency of oscillation and diameter of particle on solid—liquid mass transfer rates has been made. The results show a considerable increase in mass transfer coefficient over those normally observed in stirred tanks. Correlations were obtained to represent the data when bubble cycling does and does not occur in the system.     

CFD modeling of gas dispersion and bubble size in a double turbine stirred tank

In the present paper, gas dispersion in a double turbine baffled stirred tank is modeled using a commercial computational fluid dynamics (CFD) code FLUENT 6.1 (Fluent Inc., USA). A bubble number density equation is implemented in order to account for the combined effect of bubble break-up and coalescence in the tank. In the proposed work, the impellers are explicitly described in three dimensions using multiple reference frame model. Dispersed gas and bubbles dynamics in the turbulent water are modeled using an Eulerian-Eulerian approach with dispersed k-ε turbulent model and modified standard drag coefficient for the momentum exchange. The model predicts spatial distribution of gas holdup, average local bubble size and flow structure. The results are compared with experimental and numerical finding reported in the literature and good agreement between the present model and measurements of Alves et al. [Gas liquid mass transfer coefficient in stirred tanks interpreted through bubble contamination kinetics. Chemical Engineering Science, 2002, 57, 487-496] is achieved.     

Theoretical modelling of the effect of surface active species on the mass transfer rates in bubble column reactors

The complex composition of the liquid media in bubble column reactors makes their understanding and theoretical modelling challenging. In this work we have studied the effect of surface tension and contaminants, salts, on the mass transfer rates from a theoretical point of view, looking for a deeper understanding on the effect of surface active species which usually reduce surface tension and modify bubble surface behaviour. The specific contact area is obtained using a population balance where the effect of the presence of contaminants is addressed by the proper theoretical closures for bubble coalescence efficiency, for partially and fully immobile surfaces, and bubble break-up. Meanwhile, the contribution of contaminants to the liquid-film resistance is implemented as function of the coverage of the surface of the bubbles. It was found that the degree of bubble surface coverage not only affects bubble coalescence but also their break-up. The ion strength defines bubbles stability and the critical Weber number can be predicted as function of ion strength. Furthermore, the mass transfer rates are function of the surface coverage by the electrolytes. The model was able to predict k_La taking into account the fact that the concentration profiles surrounding individual bubbles are not completely developed due to the presence of other bubbles, in agreement with previous results from the literature.     

Gas holdup of rotating foam reactors measured by γ‐tomography—effect of solid foam pore size and liquid viscosity

Rotating foam reactors have already shown to give high mass transfer rates compared to stirred tank reactors. For a deeper insight into the hydrodynamics of these reactors, the hydrodynamics of rotating foam reactors were studied using γ‐ray tomography. The two‐phase flow through the foam block stirrer is mainly influenced by the solid foam pore size and the liquid viscosity. For low viscosity, the optimal foam block pore size was identified in the range between 10 and 20 pores per inch (ppi). With smaller pore size, the gas holdup inside the foam block strongly increases due to bubble entrapment. For higher viscosity, pore sizes larger than 10 ppi have to be used to achieve a sufficient liquid flow rate through the foam block to avoid a strong gradient over the reactor height. The effect of the hydrodynamics on the gas–liquid and liquid–solid mass transfer and the reactor performance are discussed. © 2012 American Institute of Chemical Engineers AIChE J, 59: 146–154, 2013     

HYDRODYNAMICS AND MASS TRANSFER IN BUBBLE COLUMNS: EFFECT OF SOLIDS

The hydrodynamics and mass transfer in a large diameter bubble column (D_c 0.305 m), specifically, the effects of gas velocity and the presence of solids on the gas holdup structure, gas-liquid interfacial area, and volumetric mass transfer coefficients in viscous as well as low viscosity solutions are studied. The sulfite oxidation technique was employed to measure the gas-liquid interfacial area. Volumetric mass transfer coefficients were measured using a chemical method (sulfite oxidation) as well as physical absorption of oxygen from air, and the overall gas holdups were measured using the hydrostatic head technique. The effect of solids on the gas holdup structure was examined using the dynamic gas disengagement method. With the addition of polystyrene particles, the gas-liquid interfacial area decreased for low viscosity systems, whereas it increased for viscous systems. This was shown to be due to the effect of solids on bubble coalescence. The wettability characteristics of solid surfaces in the presence of different liquids have been suggested as the reason for the effect of solids on coalescence. Oil shale slurries presented a special case because of the mineral dissolution effect.     

Influence of medium composition on oxygen transfer rate in animal cell culture

Experiments were conducted in a 0.25 m diameter bubble column to investigate the effect of medium composition on oxygen transfer rate. Aqueous solutions, the composition of which mimics a mammalian cell culture medium, are used. The effect on oxygen transfer rate of additives used to protect cells against local hydrodynamic stresses induced by bubble coalescence and bursting is addressed, in the range of operating conditions (aeration rates) met in animal cell cultures. The mass transfer coefficient, the liquid viscosity and surface tension, and the bubble size distribution are measured as a function of liquid composition and of gas superficial velocity, allowing to decouple the effects of the different additive on k_L and on a.     

搅拌槽内粘稠物系中气液相间氧传递

以发酵罐中气液相间氧传递为背景，考察了搅拌槽内搅拌器形式、物系流变性质、通气搅拌操作条件等对假塑性粘稠物系中氧传递过程的影响。结果表明，这些因素主要通过改变气体分散状态和相间传质面积来影响氧传递速率。根据气泡在搅拌槽内不均匀分布现象，多层搅拌下气液相间传质过程可以用气泡运动分区分布模型来描述。它说明了采用轴向流桨和涡轮桨组合的搅拌形式在氧传递方面的优越性，为强化发酵罐中供氧指明一条有效途径     

HYDRODYNAMICS AND MASS TRANSFER IN BUBBLE COLUMNS: EFFECT OF SOLIDS

The hydrodynamics and mass transfer in a large diameter bubble column (D_c 0.305 m), specifically, the effects of gas velocity and the presence of solids on the gas holdup structure, gas-liquid interfacial area, and volumetric mass transfer coefficients in viscous as well as low viscosity solutions are studied. The sulfite oxidation technique was employed to measure the gas-liquid interfacial area. Volumetric mass transfer coefficients were measured using a chemical method (sulfite oxidation) as well as physical absorption of oxygen from air, and the overall gas holdups were measured using the hydrostatic head technique. The effect of solids on the gas holdup structure was examined using the dynamic gas disengagement method. With the addition of polystyrene particles, the gas-liquid interfacial area decreased for low viscosity systems, whereas it increased for viscous systems. This was shown to be due to the effect of solids on bubble coalescence. The wettability characteristics of solid surfaces in the presence of different liquids have been suggested as the reason for the effect of solids on coalescence. Oil shale slurries presented a special case because of the mineral dissolution effect.     

Sectionalised bubble column: Gas hold-up and wall side solid—Liquid mass transfer coefficient

The effect of gas sparger type, clear liquid height, liquid viscosity and addition of electrolyte on fractional gas hold-up in a 0.38 m i.d. sectionalised bubble column (SBC) was studied for superficial gas velocities ranging from 0.03 to 0.15 m s⁻¹. A study of the wall side solid–liquid mass transfer coefficient, k_SL, has been made by considering the dissolution of copper in acidic dichromate solutions. The variation of k_SL with axial distance in a section for different gas velocities has been explained. A comparison between the performance of sectionalised bubble columns and conventional bubble columns has been presented. In some cases, the SBC may prove to be superior to bubble columns in practice.     

Mass Transfer in a Flat Gas/Liquid Interface using non‐Newtonian Media

Gas/liquid mass transfer has been investigated using a stirred vessel gas/liquid contactor using non‐Newtonian media and carbon dioxide as absorbent and gas phase, respectively. The volumetric mass transfer coefficients at different operational variables have been determined. Non‐Newtonian media (liquid phase) were prepared as aqueous solutions of sodium carboxymethyl cellulose salt. The influence of the rheological properties, polymer concentration, stirring rate, and gas flow rate on mass transfer was studied for these liquid phases. Kinematic viscosity and density experimental data were used to calculate the average molecular weight corresponding to the polymer employed. The Ostwald model has been used to fit the rheological behavior of aqueous solutions of the polymer employed as absorbent phase. Reasonably good agreement was found between the predictions of the proposed models and the experimental data of mass transfer coefficients.     

Experimental and Numerical Study of Gas-Liquid Flow in a Sectionalized External-Loop Airlift Reactor

The external loop airlift reactor(EL-ALR) is widely used for gas-liquid reactions. It's advantage of good heat and mass transfer rates compared to conventional bubble column reactors. In the case of fermentation application where a medium is highly viscous and coalescing in nature, internal in riser helps in the improvement of the interfacial area as well as in the reduction of liquid-phase back mixing. The computational fluid dynamic(CFD) as a tool is used to design and scale-up of sectionalized external loop airlift reactor. The present work deals with computational fluid dynamics(CFD) techniques and experimental measurement of a gas hold-up, liquid circulation velocity, liquid axial velocity, Sauter mean bubble diameter over a broad range of superficial gas velocity 0.0024≤U_G≤0.0168 m·s~(-1). The correlation has been made for bubble size distribution with specific power consumption for different plate configurations. The effects of an internal on different mass transfer models have been completed to assess their suitability.The predicted local mass transfer coefficient has been found higher in the sectionalized external loop airlift reactor than the conventional EL-ALR.     

有无静态混合器时的机械搅拌气升式环流反应器传递特性研究

The mechanically stirred internal loop airlift reactors equipped with or without static mixers are devised for intensification of gas-liquid mass transfer rate. The influences of superficial gas velocity, agitation or static mixers on gas hold-up, mixing time, liquid circulating velocity and volumetric mass transfer coefficient have been investigated with tap water and carboxymethyl cellulose (CMC) aqueous solution. The experimental results indicate that mechanical agitation is more efficacious than static mixer in highly viscous media for improving mass transfer in airlift reactors. The empirical correlation of volumetric mass transfer coefficient with apparent viscosity, and energy consumption for mechanical agitation and aeration is developed.     

Gas Holdup and Solid‐Liquid Mass Transfer in Newtonian and non‐Newtonian Fluids in Bubble Columns

Gas holdup and surface‐liquid mass transfer rate in a bubble column have been experimentally investigated. De‐mineralized water, 0.5 and 1.0% aqueous solutions of carboxy methyl cellulose (CMC), and 60% aqueous propylene glycol have been used as the test liquids. Effects of column diameter, liquid height to column diameter ratio, superficial gas velocity and liquid phase viscosity on gas holdup and mass transfer rate are studied. Generalized correlations for the average gas holdup and wall to liquid heat and mass transfer coefficients are proposed. These are valid for both Newtonian and pseudoplastic non‐Newtonian fluids.     

Investigations on hydrodynamics and mass transfer in gas–liquid stirred reactor using computational fluid dynamics

In this work, the hydrodynamics and mass transfer in a gas–liquid dual turbine stirred tank reactor are investigated using multiphase computational fluid dynamics coupled with population balance method (CFD–PBM). A steady state method of multiple frame of reference (MFR) approach is used to model the impeller and tank regions. The population balance for bubbles is considered using both homogeneous and inhomogeneous polydispersed flow (MUSIG) equations to account for bubble size distribution due to breakup and coalescence of bubbles. The gas–liquid mass transfer is implemented simultaneously along with the hydrodynamic simulation and the mass transfer coefficient is obtained theoretically using the equation based on the various approaches like penetration theory, slip velocity, eddy cell model and rigid based model. The CFD model predictions of local hydrodynamic parameters such as gas holdup, Sauter mean bubble diameter and interfacial area as well as averaged quantities of hydrodynamic and mass transfer parameters for different mass transfer theoretical models are compared with the reported experimental data of [Alves et al., 2002a] and [Alves et al., 2002b] . The predicted hydrodynamic and mass transfer parameters are in reasonable agreement with the experimental data.     

On the growth of a non‐ideal gas bubble in a solvent‐polymer solution

A model for the growth of an ideal and a non‐ideal spherical gas bubble in a quiescent viscous liquid is presented. The growth of the bubble is assumed to be controlled by both mass transfer and viscous forces. Using the integral method, the differential momentum and binary mass balances were transformed into ordinary differential equations, which were numerically solved. Some analytical solutions for simple cases are also presented. The relevance of this work to the process of polymer melt devolatilization is discussed.     

Mathematical modeling of gas-liquid mass transfer rate in bubble columns operated in the heterogeneous regime

In this paper, a multi-scale approach is followed to study gas-liquid mass transfer in bubble columns. First, a single bubble of equivalent diameter d is considered. Its morphology and its gas to liquid relative velocity are related to the bubble diameter through the use of known correlations. Then, the gas-liquid mass transfer between the bubble and the surrounding liquid is studied theoretically. An equation describing the transport of the transferred species in the viscous boundary layer around the bubble is solved. In a second step, a bubble column of 6-10 m height is studied experimentally. The gas phase in the column is characterized experimentally by means of a gammametric technique. Finally, the two studies are linked, yielding a 1D mathematical model able to predict the gas-liquid mass transfer rate in a bubble column operated in the heterogeneous regime.