The effect of mixer properties and fill level on granular flow in a bladed mixer

The discrete element method was used to study the effect of mixer properties and fill level on the granular flow of monodisperse, cohesionless spheres in a bladed mixer. For fill levels just covering the span of the blades, a three‐dimensional (3‐D) recirculation zone develops in front of the blades, which promotes vertical and radial mixing. Increasing fill level reduces the size of the recirculation zone, decreases bed dilation and hinders particle diffusivities. However, above a critical fill level, the behavior of the particles within the span of the blade is found to be invariant of fill level. At low‐fill levels, the pressure within the particle bed varies linearly with bed height and can be approximated by hydrostatics. At higher fill levels, a constant pressure region develops within the span of the blades due to the angled pitch of the blades. Cylinder wall friction is shown to significantly influence granular behavior in bladed mixers. At low‐wall friction, the 3‐D recirculation zone observed for high‐wall friction conditions does not develop. High‐wall friction leads to an increase in convective and diffusive particle mixing. Shear stresses are shown to be a function of wall friction. Blade position along the vertical axis is shown to influence flow patterns, granular temperature and stress. The effect of increasing the mixer diameter at a constant particle diameter was also studied. When the mixer diameter is larger than a critical size such that wall effects are minimized, the observed granular behavior follows simple scaling relations. Particle velocities and diffusivities scale linearly with mixer size and blade speed. Normal and shear stress profiles are found to scale linearly with the total weight of the particle bed. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Wet granular flows in a bladed mixer: Experiments and simulations of monodisperse spheres

The flow and agglomeration of wet particles in a bladed mixer was studied experimentally using particle image velocimetry and computationally using the discrete element method. The experimental and computational work showed that particle beds at low moisture contents are characterized by enhanced convective and diffusive particle motion as well as enhanced mixing kinetics when compared to dry particle beds. This behavior is attributed to the development of small particle agglomerates which behave like rough, nonspherical particles and enable the transfer of energy from the blades to the particle bed. At higher moisture contents, a different behavior was observed. Particle convective and diffusive motion was hindered by the presence of moisture at higher levels leading to a decrease in mixing performance. This occurs as large agglomerates are formed and are not broken apart by shear leading to poor mixing. Pressure and shear stress profiles were shown to be affected by the amount of moisture in the system. The extent of agglomeration at different moisture contents was quantified via the discrete element simulations. Agglomerate size distributions and morphology were shown to be strong functions of moisture content. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Mixing characteristics of wet granular matter in a bladed mixer

We performed numerical simulations of dry and wet granular flow inside a four-bladed mixer using the discrete element method (DEM). A capillary force model was incorporated to mimic the complex effects of pendular liquid bridges on particle flow. The simulations are able to capture the main features of granular flow, which is substantiated by the comparison of our results with experimental data.It was found that mean and fluctuating velocity fields for wet and dry particles differ significantly from each other. Our results indicate a strong increase in heap formation for wet particles and hence velocity fluctuations in the vertical direction become more pronounced. We observe that mixing in bladed mixers is strongly heterogeneous for wet granular matter due to the formation of different flow regimes within the mixer. The analysis of mixing quality shows that the spatial distribution of mixing intensity is influenced by the moisture content. This can lead to locally and even globally higher mixing rates for wet particles compared to dry granular matter.     

Infrared temperature measurements and DEM simulations of heat transfer in a bladed mixer

An understanding of heat transfer in a bladed mixer is important for drying of pharmaceutical drug crystals. This study presents thermal imaging experiments of the particle bed surface in a bladed mixer to investigate how the impeller speed influences the rate and the uniformity of heat transfer. Next, the process is simulated using the discrete element method. The bed thermal properties are lumped into an effective thermal conductivity, that is calibrated for one impeller speed. The experiments and the simulations show the same trends and generally agree well for all agitated beds. However, to obtain good agreement of the rate of heat transfer between the simulations and experiments in a static bed, we need to adopt a higher thermal conductivity than for the agitated beds. Finally, we discuss the implications of these results for the design of operating protocols.     

Polydisperse granular flows in a bladed mixer: Experiments and simulations of cohesionless spheres

The flow and segregation of polydisperse, spherical particle mixtures in a bladed mixer was investigated using experimental and computational techniques. Discrete element simulations were able to reproduce the qualitative segregation profiles and surface velocities observed experimentally. For a binary system with a 2:1 size ratio, segregation by size occurs due to a sieving mechanism. Segregation in the binary system is fast, with a fully segregated system observed after just 5 revolutions. However, the numerical simulations showed that the extent of segregation in the bladed mixer can be reduced by introducing intermediate particle sizes in between the smallest and the largest particles. Addition of intermediate particle sizes increases convective and diffusive particle motion promoting a mixing mechanism that reduces segregation via the sieving mechanism. Void fraction within the bladed mixer increases as the degree of polydispersity is increased allowing the particles to move more freely throughout the particle bed. Higher void fractions also increase the ability of large particles to penetrate deeper into the particle bed. Normal and shear stresses are also affected by particle size distributions, with lower average values obtained for the system with the largest number of particle species. Differences in the amount of stress generated by each particle species were observed. However, the difference in stresses is reduced as the number of particle species in the system is increased.     

The effect of interparticle cohesion on powder mixing in a ribbon mixer

The effect of interparticle cohesion on powder mixing in a ribbon mixer was studied by means of the discrete element method. It is shown that with an increase in the cohesion, the mixing rate and uniformity of mixing deteriorate, the coordination number increases indicating the loss of the ability of particles to be engaged in free flowing motion, and a majority of particles have a stronger tangential velocity allowing bulk angular motion of particles. Conversely, with a decrease in the cohesion, more particles have larger axial velocities, which will increase convective motion in the axial direction. When the cohesion is reduced, the number of particles having large radial stresses increases, and normal stress in the axial direction remains mostly unchanged. The ribbon mixer can mix cohesive particles in a wide range of the Bond numbers without causing large stresses. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1023–1037, 2016     

Effect of particle size on flow and mixing in a bladed granular mixer

A number of studies have modeled flow and mixing of granular materials using the discrete element method (DEM). In an attempt to reduce computational costs, many of these DEM studies model particles larger than the actual particle size without investigating the implications of this assumption. Using DEM, the influence of the modeled particle size on flow and mixing in a bladed granular mixer is studied. The predicted flow microdynamics, including mixing rates, are strongly dependent on the particle diameter. The effect of particle size on macroscopic advective flow also is significant, particularly for dilute flow regions. These results suggest that the influence of particle size needs to be taken into consideration when using larger particles in DEM mixing simulations. To guide scale‐up efforts, particle‐size‐based scaling relationships for several key flow measurements are presented. © 2014 American Institute of Chemical Engineers AIChE J, 61: 46–57, 2015     

Chaotic mixing in a barrier‐embedded partitioned pipe mixer

Inspired by the partitioned pipe mixer (PPM), a barrier‐embedded partitioned pipe mixer (BPPM) is designed and analyzed using a numerical simulation scheme. The BPPM is a static mixer, composed of orthogonally connected rectangular plates with a pair of barriers, which divide, stretch, and fold fluid elements, leading to chaotic mixing via the baker's transformation. The aspect ratio of the plate (α) and the dimensionless height of the barrier (β) are chosen as design parameters to conduct a parameter study on the mixing performance. The flow characteristics and mixing performance are analyzed using the cross‐sectional velocity vectors, Poincaré section, interface tracking, and the intensity of segregation. The results indicate that several designs of the BPPM significantly enhance the PPM's mixing performance. The best BPPMs are identified with regard to compactness and energy consumption. © 2017 American Institute of Chemical Engineers AIChE J, 64: 717–729, 2018     

Discrete element method simulation of binary blend mixing of cohesive particles in a high-intensity vibration system

The effects of processing intensity, time, and particle surface energy on mixing of binary cohesive powder blends in high-intensity vibration system were investigated via discrete element method simulations. The mixedness was quantified by the coefficient of variation, C_v; lower being better. The mixing rate, which is the speed at which homogeneity was achieved, was inversely proportional to the mixing Bond number, defined as the ratio of particle cohesion to the shear force resulting from the mixing intensity. Results show that both increasing processing intensity and reducing surface energy led to a faster mixing rate. However, the mixedness improved initially as mixing action (the product of mixing rate and mixing time) increased, but later deteriorated upon its further increase. Thus, both mixing rate and mixing intensity need to be tuned for optimum mixing performance depending on the cohesion level of particles; too high or too low mixing action should be avoided.     

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.     

The numerical simulation of a new double swirl static mixer for gas reactants mixing

For the nitrogen oxide removal processes, high performance gas mixer is deeply needed for the injection of NH₃ or O₃. In this study, a new type of double swirl static mixer in gas mixing was investigated using computational fluid dynamics (CFD). The results obtained using Particle Image Velocimetry (PIV) correlated well with the results obtained from simulation. The comparisons in pressure loss between the experimental results and the simulation results showed that the model was suitable and accurate for the simulation of the static mixer. Optimal process conditions and design were investigated. When L/D equaled 4, coefficient of variation (COV) was < 5%. The inlet velocity did not affect the distributions of turbulent kinetic energy. In terms of both COV and pressure loss, the inner connector is important in the design of the static mixer. The nozzle length should be set at 4 cm. Taking both COV and pressure loss into consideration, the optimal oblique degree is 45°. The averaged kinetic energy changed according to process conditions and design. The new static mixer resulted in improved mixing performance in a more compact design. The new static mixer is more energy efficient compared with other SV static mixers. Therefore, the double swirl static mixer is promising in gas mixing.     

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     

Pressure drop and mixing behaviour of non‐Newtonian fluids in a static mixing unit

Static or motionless mixers have received wide application in chemical and allied industries due to their low cost and high efficiency. The pressure drop and mixing behaviour of such mixers have been widely studied. However, the available information for non‐Newtonian fluids is scanty. The results of pressure drop and mixing studies conducted with a locally made motionless mixer (MALAVIYA mixer) and four non‐Newtonian fluids—aq. CMC, PVA, and PEG solutions are reported in this article. The new mixer causes less pressure drop compared to some of the commercial mixers. Mixing behaviour of the unit is more closer to plug flow and a two‐parameter model correlates the dispersion data.     

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     

螺带式混凝土搅拌机混合特性及DEM模拟

采用离散单元法模拟新拌混凝土于搅拌机中的混合过程,研究了双筒螺带式混凝土搅拌机的混合效率。 用Hertz-Mindlin with JKR接触方法建立新拌混凝土离散元模型,模拟了坍落度实验、L箱实验和流变仪实验,将模拟结果与实验结果进行对比,校准模型参数,采用混合系数定量研究了不同初始装填方式下搅拌机的混合效率。结果表明,采用上下装填方式时搅拌机混合效率较高;对任一初始装填方式,左部区域与右部区域、前部区域与后部区域间混合效率无明显差别,而上部区域混合效率比底部区域高,底部出料口处存在搅拌盲区,采用舍弃初始出料的方法可提高新拌混凝土性能。转速较高时混合效率较高,相同旋转圈数时,混合效率基本相同。     

Membrane‐liquid emulsion membrane process using a liquid emulsion membrane process using methane sulfonic acid as a strippant

The application of a liquid emulsion membrane (LEM) process in the recovery of zinc from aqueous solutions is discussed. The role of a stripping agent is very important in the LEM extraction process. Various stripping agents, such as hydrochloric, sulfuric, nitric and methane sulfonic acids, were tested for the stability of membrane. Methane sulfonic acid outperforms the other acids as a strippant. Further importance was given to the stability of the liquid emulsion membrane during the extraction process. The important variables affecting the LEM permeation process of zinc in a mechanically agitated contactor (MAC), such as residence time for extraction, speed of agitation, organic diluents, surfactant concentration and internal strip acid concentration, were systematically investigated. Emulsion swelling and breakage that occurred during these investigations were also described. Finally, the static mixer (SM) device was shown to have a very good potential for LEM extraction of zinc as it outperforms MAC.     

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     

Developing mechanistic understanding of granular behaviour in complex moving geometry using the Discrete Element Method: Part B: Investigation of flow and mixing in the Turbula® mixer

As a consequence of increasing computer power and more readily useable commercial codes, the Discrete Element Method is being used in an increasing range of applications to simulate increasingly complex processes, often for evaluation of machinery prototypes. This presents the additional challenge of analysis of results, in particular to extract flow and mixing mechanisms with a view to improving design or operation.The Turbula mixer is a laboratory scale mixer, which is widely used in industry for the development or testing of new granular products. It comprises a simple vessel geometry (cylinder) that moves with a complex, yet regular, 3D motion giving rise to rapid and thorough mixing of the contents. The mixer presents an ideal system for evaluation of the power of DEM to simulate complex processes and to develop protocols for processing the results of the simulation. Initial results of this investigation, presented in this paper, show that mixing behaviour changes non-monotonically as a function of mixer speed. For the system of monodisperse glass spheres it is shown that mixing rate (in terms of number of mixer revolutions to achieve complete mixing) initially decreases with increasing speed and subsequently increases. The behaviour is suggestive of a transition in the flow process and is the subject of further investigation.     

Large-eddy simulation and laser diagnostic measurements of mixing in a coaxial jet mixer

Numerical and experimental investigation of the turbulent mixing in a coaxial jet mixer is presented. Laser doppler velocimetry (LDV) and planar laser induced fluorescence (PLIF) were applied for measurements of velocity and scalar fields and their fluctuations. Numerical simulations were performed using large-eddy simulation and RANS with different closure models. These results are used for validation of numerical models and a detailed study of flow physics within the recirculation zone.