Analysis of the advection–diffusion mixing by the mapping method formalism in 3D open‐flow devices

This article extends the analysis of laminar mixing driven by a chaotic flow in the presence of diffusion to three‐dimensional open‐flow devices by means of the mapping‐matrix method. The extended formulation of the mapping matrix recently proposed by Gorodetskyi et al. (2012) allows inclusion of the molecular diffusion in the mixing process. This provides an efficient numerical tool for understanding the interplay between a chaotic advective field and diffusion, especially for high Péclet numbers. As a prototypical open‐flow device we consider the partitioned‐pipe mixer. Results deriving from the application of the extended mapping method are compared with Galerkin simulations, and a close agreement is found. Short‐term properties in the evolution of the concentration and the effect of axial diffusion are also addressed. © 2013 American Institute of Chemical Engineers AIChE J, 60: 387–407, 2014     

Use of an areal distribution of mixing intensity to describe blending of non‐newtonian fluids in a kenics KM static mixer using PLIF

The performance of KM static mixers has been assessed for the blending of Newtonian and time‐independent non‐Newtonian fluids using planar laser induced fluorescence (PLIF). A stream of dye is injected at the mixer inlet and the distribution of dye at the mixer outlet is analyzed from images obtained across the pipe cross section. The effect of number of mixing elements, fluid rheology, and apparent viscosity ratio for two‐fluid blending have been investigated at constant mixture superficial velocity of 0.3 m s^?1. Aqueous solutions of glycerol and Carbopol 940 are used as the working fluids, the latter possessing Herschel–Bulkley rheology. The PLIF images have been analyzed to determine log variance and maximum striation thickness to represent the intensity and scale of segregation, respectively. Conflicting trends are revealed in the experiments, leading to the development of an areal‐based distribution of mixing intensity. For two‐fluid blending, the addition of a high viscosity stream into the lower viscosity main flow causes very poor mixing performance, with unmixed spots of this component observable in the PLIF image. © 2013 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 60: 332–342, 2014     

Fouling mitigation in crossflow filtration using chaotic advection: A numerical study

Fouling mitigation in a crossflow filtration system using chaotic advection is numerically studied. A barrier-embedded partitioned pipe mixer (BPPM) is selected as a static mixer, creating chaotic advection in a laminar flow regime. Mixing characteristics are controlled via two design parameters, the mixing protocol and the dimensionless barrier height (β). The average dimensionless concentration boundary layer thickness () and the surface-averaged dimensionless wall concentration () dramatically decrease with the introduction of the BPPM, incorporating a chaotic flow system. and decrease as β increases, and the largest reduction of is observed in the counter-rotational protocol. A semi-ring configuration is revealed to be the most appropriate configuration to characterize mixing near the membrane surface. It is found that a filtration system with a globally chaotic flow shows the best mixing performance and the largest reduction of fouling.     

The influence of cam geometry and operating conditions on chaotic mixing of viscous fluids in a twin cam mixer

Smooth particle hydrodynamica (SPH) simulations were used to better understand the mixing performance of a class of two‐dimensional Twin Cam mixers. The chaotic manifolds of the flow are used to describe the mixing and to identify isolated regions. For an equilateral triangle cam geometry, a figure‐eight manifold structure traps a layer of fluid against the cam boundaries. Changes in the differential rotation and phase offsets between the cams results in modest improvements in the mixing rate across the manifold barrier. Reducing the apex angle of the triangle changes the manifold structure and allows the trapped layer of fluid to mix more effectively with the rest of the domain. This article shows that examining the chaotic manifolds within a typical industrial mixer can provide valuable insight into both the transient and long‐term mixing processes, leading to a more focused exploration of possible mixer configurations and to practical improvements in mixing efficiency. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Effect of Solids Loading on Resonant Mixed Al‐Bi2O3 Nanothermite Powders

Sensitive nanoenergetic powders, such as nanothermites, have traditionally been processed by ultrasonic mixing of very low solids loaded suspensions in organic solvents, which has restricted their use and application due to high solvent content and associated handling issues. In this work, we report on the performance and mixing quality of nanothermite mixtures prepared in a LabRAM resonant mixer at high solids loadings as compared to ultrasonic mixing. Specifically, the aluminum‐bismuth(III) oxide (Al/Bi₂O₃) system processed in the polar solvent N,N‐dimethylformamide (DMF) was investigated. It was found that the performance and overall quality of mixing was strongly correlated to the volumetric solids loading during processing; increasing volumetric solids loading decreases separation of particles, leading to more particle interaction and more intimate mixing. The measured performance of this system processed at 30 vol‐% was similar to traditionally ultrasonicated mixtures. Increasing the solids loading above 30 vol‐% yielded diminishing returns in performance and may introduce additional safety concerns since dry powders are very sensitive to electrostatic discharge. This mixing approach uses significantly less solvent than traditional ultrasonic mixing, results in a higher density final material, and is amenable to scaling. In addition, solvent wetted nanothermite mixed at 30 vol‐% solids loading can be mixed and deposited from a single applicator and was observed to be over five orders of magnitude less sensitive to electrostatic discharge than dry powders. This relative insensitivity enables the safe deposition of high density nanothermite ink onto devices.     

Scaling inline static mixers for flocculation of oil sand mature fine tailings

Operations to reclaim mature fine tailings (MFT) ponds involve flocculation using high‐molecular‐weight polymers, for which inline static mixers are suited. Three different commercial static mixers were utilized to determine mixing parameters corresponding to optimal dewatering performance of flocculated MFT. MFT was treated with polymer solution under different mixing conditions. The dewatering rates passed through a peak with increasing mean velocity, V and Reynolds number, Re of the fluid. The greater the number of mixer elements, the lower the V and Re at which the peak dewatering rate occurred. Mixing parameters such as G‐value, residence time, and mixing energy dissipation rate of the most rapidly dewatering flocculated MFT were dependent on mixer type and setup. In contrast, peak dewatering rates converged when scaled with respect to specific mixing energy, E, demonstrating that E is a suitable scale‐up parameter for inline static mixing to produce optimally dewatering MFT. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4402–4411, 2015     

旋转流化床粉体混合机混合效果数值模拟和实验验证

为了对旋转流化床粉体混合机进行优化设计,采用CFD-DEM联合仿真的方法,对旋转流化床粉体混合机内球形颗粒的混合过程进行数值模拟,通过Lacey指数具体评价颗粒的混合效果,研究了进气管倾斜角度、进气管布置方式、进气方式对球形颗粒混合效果的影响,并进行球形颗粒混合实验验证。结果表明,进气管最合适的倾斜角度应保证气流作用区域面积恰好为底部颗粒物料区域面积的一半。进气管水平布置时能够保证很好的混合质量及较快的混合速率。脉冲及连续方式进气均能实现均匀混合,脉冲进气方式比连续进气方式耗气量更低。颗粒混合实验有很好的混合效果,与数值模拟的结果具有较高的一致性,从而获得了一种混合效果优越的结构形式,进气管倾斜角度α=35°,水平布置。     

稀释水掺混用薄板式静态混合器结构设计与优化

稀释水掺混是油田或炼油厂原油电脱盐系统的关键环节,直接影响电脱盐的效率和运行能耗。为进一步简化设备结构、助力系统降本增效,提出将薄板式静态混合器应用于稀释水掺混环节。在对薄板式静态混合器进行初步结构设计的基础上,对油水混合情况进行计算流体动力学(CFD)三维数值模拟,以离析强度的平方根(IOS0.5)、管路压降(Δp)等作为评价指标,考察了注水管长度、注水管?弯曲薄板间距、弯曲薄板导向位置、弯曲薄板厚度四个结构参数对油水两相混合程度及运行能耗的影响。以混合管路内径D为基准参照,借助响应曲面法(RSM)对关键结构参数进行优化,并对最优结构参数组合下的混合性能进行预测。优化所得最优结构参数组合为注水管长度为1/3D、注水管-弯曲薄板间距为4/25D、弯曲薄板导向位置为1/8π、弯曲薄板厚度为1/25D,结构优化后的IOS0.5相比优化前降低了43.06%。定性分析薄板式混合器内的水相速度云图和流线图可知,当注水比为2%时,油水两相在注水管下游3D处即可达到均匀混合状态,可见薄板式静态混合器能够在小注水比下快速实现油水均匀混合。     

多孔错流喷射混合器内液体射流轨迹线

利用平面激光诱导荧光测试技术对多孔错流喷射混合器内液体混合过程进行了研究,考察了操作条件（射流速度比r、混合流股Reynolds数Re_M）和混合器的结构参数（射流小孔直径d、孔径管径比d/D、射流小孔个数n）对射流轨迹线的影响。结果表明,混合流股Reynolds数对射流轨迹线影响较小,射流速度比和混合器的结构参数是影响射流轨迹线的主要因素。建立了射流轨迹线的数学模型,并利用实验结果回归了模型参数。模型预测的液体混合过程射流轨迹线与实验结果基本吻合。     

Characterization of feeder effects on continuous solid mixing using fourier series analysis

Variance reduction ratio (VRR) is generally considered as an important index in characterizing the continuous powder mixing. Although the capacity of the mixer to smooth out feeder fluctuations can be expressed by the VRR, few studies are performed quantitatively in this area. The feeder effects are investigated on the solid mixer through the Fourier series analysis. The VRR is deduced quantitatively using the Fourier series of the feed rate variability and the residence time distribution (RTD), which facilitate the explicit decomposition of VRR into intensities of different frequency components. It provides a novel model to determine whether the integrated feeder‐mixer system satisfies specific solid mixing performance criteria, and provides guidelines of system improvement. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

缩放螺旋混合器在层流区的混合性能研究简

A contraction-expansion helical mixer which combines several features, viz. helical pipes for induction of secondary flows and sudden expansion and contraction array tor expansion vortices, has been designed to en- hance flow mixing. A fast competitive-consecutive diazo coupling reaction is used to test the mixing efficiency of contraction-expansion helical mixer. Furthermore, an image processing technique is applied for data visualization and monitoring the extent of mixing. The mixing performance is found to be superior in comparison to the regular helical mixer in the range of Reynolds number from 170 to 1540. Moreover, the mixing time of contraction-expansion helical mixer was found to be reduced by more than 25% compared to the regular helical pipe. Finally, a simple correlation is proposed for predicting the mixing time.     

Combined static mixers for high viscous fluids mixing

A new static mixer Cross-over-Disc has been invented to strip off the boundary layer and to make strong radial mixing. The pressure drop of Cross-over-Disc is 12-26 times as large as that of empty pipe with equivalent diameter and length. The mixing performance of Cross-over-Disc with 14 elements has been investigated in the viscosity range of 190–250 Pa·s by decoloration method, and the gray analysis of images shows that mixing inhomogeneity is about 7.5% and 9.4% for the mixing ratio of 5:1 and 10:1, respectively. Furthermore, mixing inhomogeneity for a combination of static mixing elements (four from Cross-over-Disc and three pairs from Sulzer-type) can be decreased to 2.1%–3.1% within a reasonable range of pressure drop.     

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。     

Discrete element simulation of free flowing grains in a four‐bladed mixer

Numerical simulations of granular flow in a cylindrical vessel agitated by a four‐blade impeller were performed using the discrete element method. Velocity, density, and stress profiles within the mixer displayed a periodic behavior with a fluctuation frequency equal to that of the blade rotation. Blade orientation was found to affect flow patterns and mixing kinetics. For an obtuse blade pitch orientation, a three‐dimensional recirculation zone develops in‐front of the blade due to formation of heaps where the blades are present. This flow pattern promotes vertical and radial mixing. No recirculation zone was observed when the blade orientation was changed to an acute blade pitch. The system's frictional characteristics are shown to strongly influence the granular behavior within the mixer. At low friction coefficients, the 3‐D recirculation in front of the obtuse blade is not present reducing convective mixing. Higher friction coefficients lead to an increase in granular temperature which is associated with an increase in diffusive mixing. Normal and shear stresses were found to vary with mixer height with maximum values near the bottom plate. Additionally, a strong dependence between the magnitude of the shear stresses and the friction coefficient of the particles was found. The stress tensor characteristics indicate that the granular flow in our simulations occurs in the quasi‐static regime. At the same time, the averaged pressure was found to vary linearly with bed height and could be predicted by a simple hydrostatic approximation. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Effect of mixer geometry and operating conditions on flow mixing of shear thinning fluids with yield stress

Flow mixing of a non‐Newtonian fluid in a stirred tank equipped with a side‐entry impeller was observed using particle image velocimetry (PIV). The effects of some geometrical parameters including the mixer shape and impeller type and position on the flow pattern were studied on velocity fields obtained at different locations inside the mixing domain. The different flow structures revealed that the ratio of inertial and viscous forces largely defines the flow pattern. Dead zones were observed inside the tank due to the rheological properties of the fluid. The size of the dynamic regions and the average velocity near the impeller were enhanced by increasing the suction area. Likewise, large pitch ratios were found to improve the active mixing zone and the axial discharge. Curves for the power and pumping numbers are reported for different axial flow impellers. © 2013 American Institute of Chemical Engineers AIChE J, 60: 1156–1167, 2014     

Three‐dimensional flow measurements in a static mixer

Laminar heat and mass transfer are central to a wide range of industrial processes, encompassing (thermal) processing of viscous fluids, compact equipment for process intensification, and emerging microfluidic devices. Many of these applications incorporate the “static‐mixing principle” (stirring of a throughflow by internal elements) for mixing and heat‐transfer enhancement. Investigations on static mixers primarily concern numerical simulations. Experimental studies, on the other hand, are relatively rare and to date restricted to visualization of mixing patterns or integral quantities as for example, pressure drop and heat‐transfer coefficients. The present study expands on this by quantitative experimental analysis of three‐dimensional (3‐D) flow fields and streamline patterns in a representative static mixer using 3‐D particle‐tracking velocimetry. This necessitates tackling of (internal) refractions and reflections caused by the complex mixer geometry. Comparison of experimental results with numerical predictions reveals a good agreement. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1746–1761, 2013     

无序环流混合器的流体力学特性和颗粒混合特性

在内径为Φ286 mm的无序环流混合器装置中,研究了无序环流混合器的流体力学特性和颗粒混合特性。以催化裂化(FCC)平衡剂为颗粒相,在中心区表观气速为0.3~0.5 m/s,边壁区表观气速为0.1 m/s,系统循环强度为0.25~1.00 kg/s的操作条件下,采用PV-6D型颗粒速度密度测量仪测量了混合器内床层各截面密度,并给出不同操作条件下的截面不均匀指数(RNI);采用热颗粒示踪技术给出了混合器内各测量截面的无因次温度分布,并引入混合指数用来定量描述不同操作条件下的颗粒混合程度,同时对比了传统环流混合器与无序环流混合器的混合能力。结果表明,无序环流混合器内部床层密度呈现中心低,边壁高的分布模式。随着循环强度的增加,RNI先减小后增大,随着表观气速的增加,RNI增大。预混合区混合指数为0.7~0.9,在高循环量,低中心区表观气速条件下(G_s为1.00 kg/s,u_(gd)为0.3 m/s),下料管进料影响区的截面混合指数低于其他操作条件。另外,无序环流混合器混合能力优于传统环流混合器。     

Design and characterization of a Low-pressure-drop static mixer

Four-blade static mixer was designed for inline mixing of Newtonian fluids at Reynolds numbers from 700 to 6800. The mixer consists of four equally spaced blades mounted on cylindrical housing with 45° rotation relative to the circumference. It was tested in three different compartments of 6, 8, and 10 mixing elements; each element rotated 45° relative to the adjacent one. Multipoint sampling was used to measure concentration downstream the mixer. The mixing quality was measured by the coefficient of variance (CoV). The CoV decreases as the energy input per unit mass increases. This effect is more pronounced when the number of mixing elements increases. For the case of 10 mixing elements, a good mixing performance (typically more than 95% mixedness or CoV < 0.05) achieved, although a marginally good mixing performance could also be achieved by eight mixing elements. The friction factors were correlated as f = C₁/Re + C₂/Reⁿ with an average deviation of ±10% from experimental data. Furthermore, experimental friction factors were compared with existing models. For a wide range of Reynolds numbers, the friction factors are apparently smaller than those from SMV, KMX, and baffle-type static mixers. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1126–1133, 2019     

Characterization of continuous convective powder mixing processes

The Process Analytical Technology (PAT) initiative has encouraged the development of new technology to improve upon the current manufacturing paradigm. As a result substantial attention has recently focused on continuous processing due to the ability to control disturbances online, avoiding the loss of processing materials and enabling effective process scale-up. In this paper, a pharmaceutical formulation is blended using a continuous flow “high shear” mixer utilizing different operating and design parameters. The mixing efficiency is characterized by extracting samples at the discharge of the blender, and analyzing them using Near Infrared Spectroscopy to determine compositional distribution. Operational conditions such as the inclination angle of the mixer and impeller rotation rate were investigated and showed to affect the mean residence time. The effects of mixer angle, agitation speed, number of blades, blade angle, number of passes through the mixer on the mixing performance of a powder continuous convective mixer are also examined and shown to affect mixing performance whereas the cohesive properties of the material did not significantly affect the mixing operation.     

Effects of blade rake angle and gap on particle mixing in a cylindrical mixer

Performance optimization of a mixer is an issue of great significance in many industrial technologies dealing with particulate materials. By means of Discrete Element Method (DEM), this work examines how the mixing performance of a cylindrical mixer is affected by the two design parameters: blade rake angle and blade gap at the vessel bottom, extending our previous work on particulate mixing. The flow and mixing performance are quantified using the following: velocity fields in vertical cylindrical sections, Lacey’s mixing index, inter-particle forces in vertical cylindrical sections through the particle bed and the applied torque on the blade. Simulation results show that the mixing rate is the fastest for a blade of 90° rake angle, but inter-particle forces are large. Conversely, the inter-particle forces are small for a blade of 135° rake angle, but the mixing rate is slow. The simulation results also indicate that the force applied on particles, velocity field and mixing are interrelated in that order.