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.     

Squeezing-to-dripping transition for bubble formation in a microfluidic T-junction

The aim of this paper is to investigate the squeezing-to-dripping transition for bubble formation in a microfluidic T-junction by cross-flowing rupture technique using a high-speed digital camera. Experiments were conducted in a glass microfluidic T-junction with the cross-section of the microchannel of 120 μm wide and 40 μm deep. N₂ bubbles were generated in glycerol–water mixtures with several concentrations of surfactant sodium dodecyl sulfate (SDS). Three different regimes were identified for generating different kinds of bubbles: squeezing, dripping and transition regimes. Various forces exerted on the gaseous thread in different regimes were analyzed. Long slug bubbles were formed in the squeezing regime, while dispersed bubbles in the dripping regime. The transition regime formed short slug bubbles. The bubble sizes in various regimes could be correlated with several dimensionless numbers such as the ratio of gas/liquid flow rates and capillary number. The two-step model for droplets (Steegmans et al., 2009) was extended to describe the bubble formation.     

非对称Y型分岔微通道内气泡破裂与分配规律

利用高速摄像仪对气泡在非对称Y型微通道分岔口的破裂行为和分配规律进行了实验研究。采用氮气（N₂）作为分散相,含0.3%表面活性剂十二烷基硫酸钠（SDS）的蒸馏水-甘油（质量分数分别为20%、40%、50%）溶液为连续相。在分岔口处观察到了3种不同的气泡行为：无间隙的不对称破裂、有间隙的不对称破裂以及不破裂。考察了气泡破裂和不破裂行为之间的转变,并与文献进行了比较。考察了两相流率及物性对破裂气泡分配规律的影响。结果表明：破裂后两个子气泡的长度均随气相流量与气泡长度的增大而增大,随液相流量和黏度的增大而减小。随液相速度和黏度的增大,气泡破裂的不对称程度减弱。     

Quantifying sub-grid scale (SGS) turbulent dispersion force and its effect using one-equation SGS large eddy simulation (LES) model in a gas–liquid and a liquid–liquid system

The one-equation SGS LES model has shown promise in revealing flow details as compared to the Dynamic model, with the additional benefit of providing information on the modelled SGS-turbulent kinetic energy (Niceno et al., 2008). This information on SGS-turbulent kinetic energy (SGS-TKE) offers the possibility to more accurately model the physical phenomena at the sub-grid level, especially the modelling of the SGS-turbulent dispersion force (SGS-TDF). The use of SGS-TDF force has the potential to account for the dispersion of particles by sub-grid scale eddies in an LES framework, and through its use, one expects to overcome the conceptual drawback faced by Eulerian–Eulerian LES models. But, no work has ever been carried out to study this aspect. Niceno et al. (2008) could not study the impact of SGS-TDF effect as their grid size was comparable to the dispersed bubble diameter. A proper extension of research ahead would be to quantify the effect of sub-grid scale turbulent dispersion force for different particle systems, where the particle sizes would be smaller than filter-size. This work attempts to apply the concept developed by Lopez de Bertodano (1991) to approximate the turbulent diffusion of the particles by the sub-grid scale liquid eddies. This numerical experimentation has been done for a gas–liquid bubble column system (Tabib et al., 2008) and a liquid–liquid solvent extraction pump-mixer system ( [Tabib et al., 2010] and [28] ). In liquid–liquid extraction system, the organic droplet size is around 0.5 mm, and in bubble columns, the bubble size is around 3–5 mm. The simulations were run with mesh size coarser than droplet size in pump-mixer, and for bubble column, two simulations were run with mesh size finer and coarser than bubble diameter. The magnitude of SGS-TDF values in all the cases were compared with magnitude of other interfacial forces (like drag force, lift force, resolved turbulent dispersion force, force due to momentum advection and pressure). The results show that the relative magnitude of SGS-TDF as compared to other forces were higher for the pump-mixer than for the coarser and finer mesh bubble column simulations. This was because in the pump-mixer, the ratio of “dispersed phase particle diameter to the grid-size” was smaller than that for the bubble column runs. Also, the inclusion of SGS-TDF affected the radial hold-up, even though the magnitudes of these SGS-TDF forces appeared to be small. These results confirms that (a) the inclusion of SGS-TDF will have more pronounced effect for those Eulerian–Eulerian LES simulation where grid-size happens to be more than the particle size, and (b) that the SGS-TDF in combination with one-equation-SGS-TKE LES model serves as a tool to overcome a conceptual drawback of Eulerian–Eulerian LES model.     

Gas–liquid flows in medium and large vertical pipes

Gas–liquid bubbly flows with wide range of bubble sizes are commonly encountered in many industrial gas–liquid flow systems. To assess the performances of two population balance approaches – Average Bubble Number Density (ABND) and Inhomogeneous MUlti-SIze-Group (MUSIG) models – in tracking the changes of gas volume fraction and bubble size distribution under complex flow conditions, numerical studies have been performed to validate predictions from both models against experimental data of Lucas et al. (2005) and Prasser et al. (2007) measured in the Forschungszentrum Dresden-Rossendorf FZD facility. These experiments have been strategically chosen because of flow conditions yielding opposite trend of bubble size evolution, which provided the means of carrying out a thorough examination of existing bubble coalescence and break-up kernels. In general, predictions of both models were in good agreement with experimental data. The encouraging results demonstrated the capability of both models in capturing the dynamical changes of bubbles size due to bubble interactions and the transition from “wall peak” to “core peak” gas volume fraction profiles caused by the presence of small and large bubbles. Predictions of the inhomogeneous MUSIG model appeared marginally superior to those of ABND model. Nevertheless, through the comparison of axial gas volume fraction and Sauter mean bubble diameter profiles, ABND model may be considered an alternative approach for industrial applications of gas–liquid flow systems.     

Bubble formation in non-Newtonian fluids in a microfluidic T-junction

The aim of this work is to investigate the bubble formation in non-Newtonian fluids in a microfluidic T-junction by crossflowing rupture technique, using a high-speed digital camera. Experiments were conducted in a glass microchannel with 120 μm wide and 40 μm deep. N₂ bubbles were generated in different concentrations of polyacrylamide (PAAm) solutions. Various flow patterns were observed at the T-junction by varying gas and liquid flow rates. The breakup mechanism for bubbles was investigated to gain insight into the effects of flow rates and concentrations of PAAm solutions on bubble size. The gaseous thread collapses at a constant speed in the collapse stage; while during the final pinch-off stage, the variation of the minimum width W_m of the gaseous thread with the remaining time (T − t) could be scaled as W_m ∼ (T − t)^0.21. The bubble size increases non-linearly with the gas/liquid flow rates ratio, and decreases with the concentration of PAAm solutions.     

Y型微通道内纳米颗粒稳定气泡的完全阻塞破裂动力学

研究了Y型微通道吸附型纳米颗粒稳定气泡的完全阻塞破裂的动力学,破裂过程可划分为挤压阶段和快速夹断阶段,两阶段内无量纲气泡最小颈部宽度与时间均呈幂率关系。气泡破裂过程的颈部动力学表明颗粒的存在并不影响两阶段转变的临界颈部宽度,但吸附在气泡表面的颗粒层会减弱挤压阶段中连续相对气泡颈部的挤压作用,以及快速夹断阶段角区中连续相液体回流对气泡的挤压作用,进而阻碍气泡颈部的形变,延长了气泡的破裂过程。纳米颗粒稳定的气泡的指前因子m及幂率指数α均小于常规气泡,但其差值随着毛细管数Ca和气泡长度l₀的增大而减小,颗粒对气泡破裂过程的影响逐渐减弱。此外,纳米颗粒稳定的气泡的头部曲率略小于常规气泡,颗粒对完全阻塞破裂过程气泡头部动力学的影响可以忽略。     

Slug bubble deformation and its influence on bubble breakup dynamics in microchannel

The deformation of moving slug bubbles and its influence on the bubble breakup dynamics in microchannel were studied. Three bubble morphologies were found in the experiment: slug, dumbbell and grenade shapes. The viscosity effect of continuous phase aggravates the velocity difference between the fluid near the wall and the bubble, resulting in that the continuous phase near the bubble head flows towards and squeezes the bubble tail, which causes the deformation of bubbles. Moreover, the experimental results show that the deformation of bubbles could significantly prolong the bubble breakup period at the downstream Y-junction. There exists the critical capillary number Ca_Cr for the asymmetric breakup of grenade bubbles, Ca_Cr increases with the rise of flow rate and viscosity of the continuous phase.     

Bubble breakup with permanent obstruction in an asymmetric microfluidic T‐junction

Bubble breakup with permanent obstruction in an asymmetric microfluidic T‐junction is investigated experimentally. The breakup process of bubbles can be divided into three stages: squeezing, transition, and pinch‐off stages. In the squeezing stage, the thinning of the bubble neck is mainly controlled by the velocity of the fluid flowing into the T‐junction, and the increase of the liquid viscosity can promote this process. In the transition stage, the minimum width of bubble neck decreases linearly with time. In the pinch‐off stage, the effect of the velocity of the fluid flowing into the T‐junction on the thinning of the bubble neck becomes weaker, and the increase of the liquid viscosity would delay this process. The evolution of the minimum width of the bubble neck with the remaining time before the breakup can be scaled by a power–law relationship. The bubble length has little influence on the whole breakup process of bubbles. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1081–1091, 2015     

Mass transfer and shear in an airlift bioreactor: Using a mathematical model to improve reactor design and performance

Several studies have shown a strong relationship between morphology and agitation ( [Cui et al., 1997] and [Berzins et al., 2001] ). The shear stress distribution and mass transfer are the important parameters which can improve the performance of bioreactor. In this work, a mathematical model using computational fluid dynamics (CFD) techniques is used to study the gas–liquid dispersion in an airlift reactor. Multiple rotating frame (MRF) technique is used to approximate the movement of the impeller in the stationary reactor. Population balance modeling (PBM) is used to describe the dynamics of the time and space variation of bubble sizes in the reactor. The PBM equation is solved using an approximate method known as the class method (CM) and the bubble sizes are approximated through a discrete number of size ‘bins’, including transport, and different bubble phenomena. These equations of the CM are then written as scalar transport equations and added to the multiphase fluid mechanical equations describing the dynamics of the flow. All these equations are solved using control volume formulation through the use of an open-source CFD package OpenFOAM. The model is used to analyze an existing geometry of an airlift bioreactor and validate the modification on the initial design. The new design of airlift gives a clear performance by the increase of the global and local mass transfer and the decrease of the shear stress.     

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

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

Breakup dynamics of slender bubbles in non‐newtonian fluids in microfluidic flow‐focusing devices

This study aims to investigate the breakup of slender bubbles in non‐Newtonian fluids in microfluidic flow‐focusing devices using a high‐speed camera and a microparticle image velocimetry (micro‐PIV) system. Experiments were conducted in 400‐ and 600‐μm square microchannels. The variation of the minimum width of gaseous thread with the remaining time before pinch‐off could be scaled as a power‐law relationship with an exponent less than 1/3, obtained for the pinch‐off of bubbles in Newtonian fluids. The velocity field and spatial viscosity distribution in the liquid phase around the gaseous thread were determined by micro‐PIV to understand the bubble breakup mechanism. A scaling law was proposed to describe the size of bubbles generated in these non‐Newtonian fluids at microscale. The results revealed that the rheological properties of the continuous phase affect significantly the bubble breakup in such microdevices. © 2012 American Institute of Chemical Engineers AIChE J,, 2012     

High-frequency formation of bubble with short length in a capillary embedded step T-junction microdevice

The performances of slug flow gas–liquid reactors are mostly determined by slug length, especially for the high gas–liquid flow rate ratio condition. This work is the first time to report the short bubble generated with high frequency in a capillary embedded step T-junction microdevice. The aspect ratio of bubble could be around 0.5 with a frequency higher than 750 s⁻¹ when the gas–liquid flow rate ratio is even higher than 5. The specific surface area of the generated gas–liquid microdispersion system is larger than 10,400 m²/m³. The short bubble formation process includes two periods, and its formation mechanism is mainly because of the relatively higher pressure drop in the step T-junction, which provides a much higher breakup force for the squeezing flow. Finally, two models are developed to predict the bubble frequency and volume. This work provides a highly promising dispersion technology for the gas–liquid process intensification in microreactors.     

Experimental investigation on two-phase air/high-viscosity-oil flow in a horizontal pipe

The flow of very-viscous-oil and air through a horizontal pipe (inner diameter 22 mm) is experimentally studied. We first build and analyze the flow pattern map; a comparison between the air–water and the air–oil flow pattern maps shows a strong influence of the fluid properties. The experimental flow maps are compared with empirical and theoretical ones – Baker (1954), Mandhane et al. (1974), and Petalas and Aziz (1998) – showing a poor agreement. Experimental pressure gradients are also reported and compared with theoretical model, but also in this case the agreement is not very satisfactory. Finally, the elongated bubble velocity and length are measured and compared to model present in the literature. We conclude that the high viscosity of the liquid phase has a strong influence on the results and that the current models are not able to predict the flow features satisfactorily.     

Liquid flow pattern around Taylor bubbles in an etched rectangular microchannel

Liquid flow around Taylor bubbles and the motion of bubble interface in a rectangular microchannel etched on a microfluidic chip were investigated using a three-dimensional particle tracking method. The Taylor bubbles were generated by releasing the dissolved air in working the liquid (water) through heating the microfluidic chip to 35–55 °C and had low velocities (15–1500 μm/s). Three-dimensional velocity distributions of liquid recirculation flows surrounding the Taylor bubble head and tail were obtained by tracking submicron fluorescent particles seeded in the working liquid and the motion of the bubble interface was analyzed by monitoring the motions of the particles attached on the bubble interface. The high velocity film flow through the microchannel corners acted as a liquid jet in front of bubble head and drainage into the corners behind the bubble tail to drive the liquid recirculation flows. The bubble interface near the microchannel corners was also moved by the strong liquid shear induced from the high velocity liquid flow in the microchannel corners. This high velocity liquid flow through the corners could be considered to be driven by the pressure drop over the Taylor bubble. The pressure drop resulted from the decrease of bubble surface mobility due to tracer surfactant in the gas–liquid interface.     

A new experimental method for determining particle capture efficiency in flotation

A single bubble experiment has been developed for the determination of the capture efficiency of particles by bubbles in flotation under well-controlled hydrodynamics and physico-chemical conditions. In a glass column, small single bubbles (d_b=0.22−1.16 mm) are produced in pure water and then rise at their terminal velocity through a suspension consisting of spherical glass particles where bubble–particle capture takes place. The capture efficiency E_capt is calculated as the ratio of the number of particles captured by one bubble to the number of particles present in the volume swept out by this bubble. Images recorded at high optical magnification show that particles slip on the interface, then adhere to air bubbles individually or as aggregates and cover the rear part of bubble surface. The bubble's effective density and interface contamination level are increased by captured particles. As a result, bubble's rising velocity U_b is reduced along the experimental device. By establishing the relationship between capture efficiency E_capt, bubble rise velocity U_b and bubble clean angle θ_clean, a new approach to measure particle–bubble capture efficiency is proposed. This new experimental technique is applied to provide a new set of data for capture efficiency in the case of bubbles with a clean interface. E_capt is found to grow as d_b decreases and d_p increases, within the range between 0.02 and 0.20, which is in the order of magnitude of experimental results of Ralston and Dukhin (1999) as well as of numerical results of Sarrot et al. (2005). These data are favorably compared to numerical modeling of collision efficiency.     

Microjet-Initiated Nano-Gaseous Layer Pinch-Off from the Surface of a Bubble and Subsequent Breakup

This paper describes the first observation and study of the pinch-off and breakup of nano-gaseous layers from the surface of an accelerated bubble by a microjet. The microjet is generated by the interaction between two bubbles in a microfluidic channel. Femtoliter-sized bubbles are developed from the breakup of the nano-gaseous layers due to hydrodynamic instability. The dynamics of this whole process were demonstrated experimentally and studied theoretically. The ability to control the pinch-off and breakup of a thin layer, especially in micro/nanofluidic systems, offers an opportunity to conduct precise manipulation on nanoscale materials for a wide range of cell biological applications.     

聚焦十字型微通道内高黏流体中气泡生成动力学

利用高速摄像仪观察了聚焦十字型微通道内高黏度（630 mPa·s）的甘油-水溶液中氮气气泡的生成过程。研究了气泡生成过程以及气泡体积和最小颈部半径的变化规律。结果表明,高黏流体内气泡生成过程可分为回缩、膨胀、挤压和最终破裂4个阶段。气泡体积在膨胀和挤压阶段均随时间线性增长,但挤压阶段的斜率大于膨胀阶段的斜率。气泡最小颈部半径随时间变化分为两个不同的阶段：在挤压阶段,颈部半径随剩余时间呈幂率关系;而在最终破裂阶段,颈部半径随时间呈线性关系。     

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     

Time scale analysis for fluidized bed melt granulation III: Binder solidification rate

In series I and II of this study ( [Chua et al., 2010a] and [Chua et al., 2010b] ), we discussed the time scale of granule–granule collision, droplet–granule collision and droplet spreading in Fluidized Bed Melt Granulation (FBMG). In this third one, we consider the rate at which binder solidifies. Simple analytical solution, based on classical formulation for conduction across a semi-infinite slab, was used to obtain a generalized equation for binder solidification time. A multi-physics simulation package (Comsol) was used to predict the binder solidification time for various operating conditions usually considered in FBMG. The simulation results were validated with experimental temperature data obtained with a high speed infrared camera during solidification of ‘macroscopic’ (mm scale) droplets. For the range of microscopic droplet size and operating conditions considered for a FBMG process, the binder solidification time was found to fall approximately between 10⁻³ and 10⁻¹ s. This is the slowest compared to the other three major FBMG microscopic events discussed in this series (granule–granule collision, granule–droplet collision and droplet spreading).