Laminar mixing of shear thinning fluids in a SMX static mixer

Flow and mixing of power-law fluids in a standard SMX static mixer were simulated using computational fluid dynamics (CFD). Results showed that shear thinning reduces the ratio of pressure drop in the static mixer to pressure drop in empty tube as compared to Newtonian fluids. The correlations for pressure drop and friction factor were obtained at Re_MR?100. The friction factor is a function of both Reynolds number and power-law index. A proper apparent strain rate, area-weighted average strain rate on the solid surface in mixing section, was proposed to calculate pressure drop for a non-Newtonian fluid. Particle tracking showed that shear thinning fluids exhibit better mixing quality, lower pressure drop and higher mixing efficiency as compared to a Newtonian fluid in the SMX static mixer.     

Dispersion of high-viscosity liquid-liquid systems by flow through SMX static mixer elements

The pressure drop and the dispersed phase drop size distribution have been measured for flow through SMX static mixer elements, in columns of diameter 41.18 and 15.75 mm, for a continuous phase of aqueous corn syrup and a dispersed phase of silicone oil. For single-phase flow the pressure drops were consistent with known literature correlations. In the presence of the dispersed phase the pressure drops were increased about 20% above the expected single-phase values, showing more short-term fluctuations but with no significant effect of the flow fraction of the dispersed phase. Droplet size distributions were measured by the computer-aided analysis of images from a digital camera. For shorter lengths of packing the distributions showed a significant “tail” at the large-diameter end, but as the packing length was increased the tail decreased or became non-existent. The mean drop sizes have been compared with a new model based on drop formation at equivalent point sources within the packing.     

Liquid phase residence time distribution for gas–liquid flow in Kenics static mixer

The residence time distribution (RTD) of the liquid phase for co-current gas–liquid upflow in a Kenics static mixer (KSM) with air/water and air/non-Newtonian fluid systems was investigated. The effect of liquid and gas superficial velocities on liquid holdup and Peclet number was studied. Experiments were conducted in three KSMs of diameter 2.54 cm with 16 elements and 5.08 cm diameter with 8 and 16 elements, respectively, of constant L_e/D_e = 1.5 for different liquid and gas velocities. A correlation was developed for Peclet number, in terms of generalized liquid Reynolds number, gas Froude number and liquid Galileo number, where as for liquid holdup, a correlation was developed as a function of gas Reynolds number. The axial dispersion model was found to be in good agreement with the experimental data.     

Drop Breakup in an SMX Static Mixer in Laminar Flow

The mechanism of drop breakup inside SMX static mixers in the laminar flow regime was studied using experimental observations and computational fluid dynamics (CFD). The deformation and breakup of a single drop was simulated using the volume of fluid (VOF) model. It was observed that drops break up after collision with the leading edges and cross‐points of the bars in the SMX static mixer. It was found that drop collision with the bar cross‐points of the SMX static mixer elements is most effective for drop breakup. Elongation and folding result in drop breakup at the cross‐points.     

Development of positron emission particle tracking for studying laminar mixing in Kenics static mixer

Positron emission particle tracking (PEPT) is a flow visualisation technique that has found application in a wide range of processes. In this work, PEPT has been used to study laminar flow of a high viscosity Newtonian and non-Newtonian fluid in a Kenics static mixer (KM). Through analysis of the trajectories of many hundreds of passes of the tracer particle through the mixer, it is possible to compute the overall flow field and to visualise how the fluid twists and folds as it passes along the mixer. Eulerian velocity maps plotted for the Newtonian and non-Newtonian fluids showed that the length required for the flow to develop is shorter for the non-Newtonian fluid than the Newtonian. The stretching and folding mechanism of mixing was observed by grouping the trajectories into clusters according to whether the trajectory passes to the left or right of the blade at the transition between elements. Those trajectories making the same L–R–L decision tended to remain in the same striation through two or three elements until that striation became stretched and folded back on itself, sandwiching other layers. It is clear that the PEPT data is rich and powerful. We are hopeful that the techniques we develop for the flow and mixing in the Kenics mixer will be applicable to studying more complex laminar flows.     

高黏度流体在SK型静态混合器内的流动特性

根据流体动力学、非线性动力学及Ottino理论,建立了高黏度流体在SK型静态混合器内的流体流动改进模型,分析二维Navier-Stokes方程基于双极坐标系下流函数形式的边值问题并建立了相应的流体微分运动方程。用Poincare映射方法对静态混合器内的蠕动流的动力学行为进行了数值仿真研究。给出了系统响应随管壁转动角频率变化的分岔图、最大Lyapunov指数曲线图、典型的Poincare截面图和相图。结论表明:高黏度流体在SK型静态混合器内轴截面的径向流动存在混沌特性。     

Residence time distribution and liquid holdup in Kenics KMX static mixer with hydrogenated nitrile butadiene rubber solution and hydrogen gas system

A Kenics^® KMX static mixer that has curved-open blade internal structure was investigated to study its hydrodynamic performance related to residence time distribution and liquid holdup in a gas/liquid system. The static mixer reactor had 24 mixing elements arranged in line along the length of the reactor such that the angle between two neighboring elements is 90°. The length of the reactor was 0.98 m with an internal diameter of 3.8 cm and was operated cocurrently with vertical upflow. The fluids used were hydrogen (gas phase), monochlorobenzene (liquid phase) and hydrogenated nitrile butadiene rubber solution (liquid phase). In all the experiments, the polymer solution was maintained as a continuous phase while hydrogen gas was in the dispersed phase. All experiments were conducted in the laminar flow regime with the liquid side hydraulic Reynolds number in the range of 0.04-0.36 and the gas side hydraulic Reynolds number in the range of 3-18. Different polymer concentrations and different operating conditions with respect to gas/liquid flow rates were used to study the corresponding effects on the hydrodynamic parameters such as Peclet number (Pe) and the liquid holdup (ε_L). Empirical correlations were obtained for the axial dispersion coefficient (D_a) and liquid holdup in liquid system alone and for the gas/liquid system separately. It was observed that the Peclet number decreased with the introduction of gas in to the reactor while in the liquid system alone, an increase in viscosity decreased the Peclet number. The liquid holdup was empirically correlated as a function of the physical properties of the fluids used in addition to the operating flow rates.     

Turbulent liquid–liquid dispersion in SMV static mixer at high dispersed phase concentration

The aim of this paper is to investigate the influence of physico-chemical parameters on liquid–liquid dispersion at high dispersed phase concentration in Sulzer SMV™ mixer. Four different oil-in-water systems involving two different surfactants are used in order to evaluate the effect of interfacial tension, densities and viscosities ratio on mean droplets size diameters. Moreover the influence of the dispersed phase concentration on the pressure drop as well as on the droplet size distribution is investigated. Two different droplets size distribution analysis techniques are used in order to compare the resulting Sauter mean diameters. The comparison between residence time in the mixer and surfactants adsorption kinetics leads to take into account the evolution of the interfacial tension between both phases at short times. Finally experimental results are correlated as a function of dimensionless Reynolds and Weber numbers.     

Formation of O/W emulsions by static mixers for pharmaceutical applications

Oil-in-water (O/W) emulsions produced by static mixers in the laminar flow regime are characterized for their oil drop size spectra. The emulsions are used in the first process step for the production of microspheres for pharmaceutical applications by the emulsion extraction method. However, emulsion generation by static mixers in the laminar flow regime is rarely discussed in the scientific literature. Here we deduce a non-dimensional correlation for predicting the Sauter mean oil drop size as a function of the static mixer operation parameters and the liquid properties. First, the material properties of the organic and water phases are characterized. Second, the oil drop size spectra of the emulsions are measured by laser diffraction. Dimensional analysis is used to describe the relationship between the process parameters of the static mixer and the Sauter mean oil droplet size. Emulsion production experiments using SMX static mixers with two different diameters are carried out with the mixing of the two liquids taking place in the laminar flow regime. We provide results covering a wide range of all process parameters, which were identified influencing the droplet size of the emulsion. The correlation achieved is related to the non-dimensional drop-size based Ohnesorge number of the emulsification process and allows for the prediction of the mean oil droplet size with good accuracy, which is an essential information about the emulsion properties relevant for the pharmaceutical application.     

脉冲式静态混合器压力降分析

测定了雷诺数Ｒｅ从６８变化到１６５１时混合器压力降与雷诺数，摩擦系数与雷诺数的关系曲线和相应的曲线拟合方程。Ｒｅ＜５５０时，摩擦系数ｆ＝１３９．６６Ｒｅ－０．７４２，当Ｒｅ＞５５０时，流动基本处于湍流状态，ｆ＝５．２Ｒｅ－０．２０３。当雷诺数增大时，混合器内元件数量的改变对摩擦系数影响不大。     

Design and assessment of a novel static mixer

This paper examines the performance of a novel static mixer comprising a circular tube fitted with eight alternating equi‐spaced semicircular rigid insert (baffles) as the mixer elements. Experiments were carried out to obtain the coefficient of variance (CoV) for the mixing of two streams of water and brine for Reynolds number between 60 and 700. Decreasing the baffles clearance ratio significantly reduces the CoV but at a cost of an increase in the pressure drop across the static mixer. The presence of the mixing elements (baffles) promotes a non‐laminar, turbulent‐like flow which considerably enhances the mixing. The static mixer described here represents a cost effective, easy to manufacture, low maintenance, and flexible alternative to the more sophisticated static mixers currently in use.     

Power-draw analysis of a coaxial mixer with Newtonian and non-Newtonian fluids in the laminar regime

The power consumption of a new coaxial mixer composed of a wall scraping arm and a series of rods and a pitched-blade turbine mounted on the same axis of revolution and operated in a contra-rotating mode has been characterized. The work is based on experimental measurements and 3D numerical simulations in the case of homogeneous Newtonian and non-Newtonian fluids in the laminar regime. Very good agreements between experimental and numerical results have been obtained. It has been shown that the Metzner-Otto concept can be extended to account for the speed ratio between the impellers, which allows to represent the power consumption results of the coaxial mixer on a single power master curve like with a single agitator mixer.     

SK静态混合器内各截面停留时间分布实验研究

采用脉冲示踪法对SK静态混合器内各截面的停留时间进行了实验测试,比较了流量对各截面停留时间分布的影响.结果表明:在同一截面上,随着流量增加,平均停留时间减小,停留时间分布密度曲线变得高而窄;在相同流量下,沿着轴线方向,平均停留时间增大,量纲一方差减小,流体流动趋向于活塞流.同一截面上,随着流量增加应答峰初期的斜率较陡,...     

New method for the determination of precipitation kinetics using a laminar jet reactor

In this paper a new experimental method for determining the kinetics of fast precipitation reactions is introduced. Use is made of a laminar jet reactor, which is also frequently applied to determine the kinetics of homogeneous gas-liquid reactions. The liquid containing one or more of the precipitating reactants passes a gas-filled reactor as a stagnant jet in which no mixing occurs. The remaining reactant needed for precipitation is supplied in gaseous form and causes the precipitation reaction to occur while it is diffusing into the jet. Hydrodynamics as well as transport phenomena are precisely known for this system, whereas agglomeration can be minimized by adjustment of the concentration of the solute supplied by the gas. The kinetics of the different crystallization steps can be determined by analyzing the size distribution of the produced particles. This new method is experimentally demonstrated for the precipitation of CuS using H₂S gas. The obtained data were successfully used to simulate a packed bed absorber in which H₂S is absorbed by a CuSO₄ solution.     

仿柳叶形静态混合器的流动及混合特性

对仿柳叶形静态混合器内混合气流进行了速度场与浓度场的试验研究,结果表明该混合器内速度场与浓度场偏差均达到了非常理想的效果（优于国家标准偏差值）。同时采用CFD软件对该静态混合器内的流场进行了数值模拟,试验与模拟的数值结果以及两者的浓度云图分布都有着较好的一致性。随后的研究结果表明：在混合元件尾迹区域出现了纵向涡和发卡涡来促进混合;在经过混合元件区域时因为湍流动能耗散率增加形成的高湍流动能耗散率区能够使物质交换更加频繁;整个静态混合器的流动阻力也主要发生在该区域,随之出现的返混现象也在一定程度上加强了混合效果。     

静态混合器中液液分散的实验及CFD模拟

在SK型静态混合器上进行甲苯-水两相混合实验,采用截面直接拍摄法获得分散混合性能指标Sauter平均直径（SMD）。利用Box-Behnken响应面分析设计实验,在Design Expert 7.0平台上拟合实验数据,获得SMD的多项式形式的表达式。建立了与实验相同的静态混合器物理模型,使用Mixture多相流模型、k-ε湍流模型进行了CFD模拟研究,获得了浓度场云图及分布混合指标不均匀系数。模拟所得压降与实验值的相对误差在15%以内,表明模拟结果与实验结果吻合较好。结果表明,静态混合器中液液分散过程是分散混合和分布混合共同作用的结果,两种混合经过6～8个混合单元后共同达到充分发展。充分发展后的SMD受表观流速、分散相分率和静态混合器直径三因素影响,且表观流速的影响最为显著;充分发展后的不均匀系数均达0.05以下,表明静态混合器自身具有较好的分布混合性能。     

Q型静态混合器内液滴群分散特性

静态混合器因具有结构紧凑、强化性能优异和连续性生产等优点被广泛应用于过程工业中,但Q型静态混合器(QSM)内多相流分散混合强化机理不完善制约了其在精细化工和原料药绿色生产中的应用。采用计算流体力学(CFD)耦合群体平衡方程对QSM内相含率α≤5%时液滴分散特性进行数值模拟,分析液液界面张力、动力黏度和相含率对液滴群d32的分散行为的影响。标准旋流静态混合器内的d32数值预测结果与实验结果有良好的一致性。模拟结果表明,在z/l=11.5处不同分散相d32减小73%~96%,RL-90-QSM对不同物性介质的分散混合具有高效性和普适性;在高雷诺数和低相含率下,不同分散相流过z/l=0~2时d32破碎速率最大,在z/l=2.5处d32减小51%~90%,d32随混合时间的增加逐渐减小且在z/l=10后趋于稳定;界面张力对混合结果的影响大于动力黏度。     

Numerical investigation of blade shape in static mixing

The mixing performance of the KMX and SMX static mixers have been compared using 3D high-resolution computational fluid dynamics (CFD) simulations. Although these mixers have a similar design composed of layers of blades, their blade shape is different: curved for the KMX and flat for the SMX. The flow of a Newtonian fluid in steady laminar regime has been considered as the benchmark of the study. The simulation was first validated by assessing the pressure drop vs. the number of mixer elements and the results were found to be in good agreement with experimental data. To evaluate the mixing quality, cross-section stream function, extensional efficiency, mean shear rate, residence time, intensity of segregation, stretching, and Lyapunov exponent have been selected. Analysis of the flow pattern and mixing parameters shows differences between the mixers and it appears that the curved blade is more efficient than the flat blade design at the expense of a slightly higher pressure drop. In practice, the KMX mixer should provide a higher mixing rate at high viscosity ratio than the SMX mixer. © 2004 American Institute of Chemical Engineers AIChE J, 51: 44–58, 2005     

Quantification of laminar mixing in the kenics static mixer: An experimental study

The laminar flow field in a Kenics KM static mixer has been studied using laser induced fluorescence and digital image analysis. Mixing was quantified by measurement of the number average striation thickness, variance of striation widths and interfacial area, for elements of length to diameter (L/D) ratios of 0.8, 1.0, 1.5 with 90° twist per element. From flow visualisations, transitions were observed in the flow where vortices developed above the first and second elements at Reynolds numbers of 43 and 90 for L/D = 0.8 and Reynolds numbers of 55 and 105 for L/D = 1.0. It was found that these vortices did not appreciably enhance mixing based on striation thickness and variance of striation widths measurements after 4 to 5 elements. The influence of viscosity ratio showed a viscosity ratio (dyed stream/bulk stream) of I had faster interfacial area growth and created more uniform mixtures compared to a viscosity ratio of 0.2 for flow rate ratio of 0.2.