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.     

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     

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.     

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     

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.     

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.     

Discrete element reduced‐order modeling of dynamic particulate systems

One of the key technical challenges associated with modeling particulate processes is the ongoing need to develop efficient and accurate predictive models. Often the models that best represent solids handling processes, like discrete element method (DEM) models, are computationally expensive to evaluate. In this work, a reduced‐order modeling (ROM) methodology is proposed that can represent distributed parameter information, like particle velocity profiles, obtained from high‐fidelity (DEM) simulations in a more computationally efficient fashion. The proposed methodology uses principal component analysis (PCA) to reduce the dimensionality of the distributed parameter information, and response surface modeling to map the distributed parameter data to process operating parameters. This PCA‐based ROM approach has been used to model velocity trajectories in a continuous convective mixer, to demonstrate its applicability for pharmaceutical process modeling. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3184–3194, 2014     

Numerical investigation of granular mixing in an intensive mixer:Effect of process and structural parameters on mixing performance and power consumption

Discrete element method (DEM) simulations of particle mixing process in an intensive mixer were con-ducted to study the influence of structural and process parameters on the mixing performance and power consumption. The DEM model was verified by comparing the impeller torque obtained from simulation with that from experiment. Impeller and vessel torque, coordination number (CN) and mixing index (Relative standard deviation) were adopted to qualify the particle dynamics and mixing performance with different parameters. A method based on cubic polynomial fitting was proposed to determine the critical mixing time and critical specific input work during the mixing process. It is found that the mixing performance and energy efficiency increases with the decrease of impeller offset. The mixing perfor-mance is improved slightly with the increase of blade number and the impeller with 3 blades has the highest energy efficiency due to its low input torque. Results indicate that the energy efficiency and the mixing performance increase with the decrease of filling level when the height of granular bed is higher than that of blade.     

Improvement of a gram‐scale mixer for polymer blending

A small‐scale mixer designed by Bryce Maxwell is commercialized by Custom Scientific Instruments, Inc. under the name of MINI‐MAX Molder. It is very useful for the study of polymer blends, especially when the available amount of polymer specimen is limited, for example, less than a few grams. However, it gives essentially shear flow and suffers from poor distribution and dispersion capabilities in comparison with large scale extruder and internal mixers. We propose here an improvement of the mixing and dispersing capabilities of the Maxwell small‐scale mixer by the addition of Teflon disk and steel balls together with the mixed materials. When polypropylene and high impact polystyrene were mixed at 70/30 wt. ratio at 180°C without the disk and balls, the high impact polystyrene particle size (D) was 6.27 μm. A finer dispersion (D = 1.44 μm) was achieved by the introduction of one Teflon disk at the center of mixing cup and three steel balls. Furthermore, with increasing the number of steel balls from three to seven, and with using different sizes of balls, much finer dispersions were achieved (D = 0.58 μm and 0.47 μm). This may be caused by: (1) the addition of Teflon disk eliminates the low shear regions in the mixing cavity, and (2) the addition of steel balls induces asymmetric circulation of the materials, some changes in the flow lines going from the center to the border or from the top to the bottom, some reorientation of the materials, and higher shear fields. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 1–5, 2006     

新型静态混合器湍流特性数值模拟

结合新型静态混合器的结构特点,利用CFD软件采用标准的k-ε湍流模型对新型静态混合器内的湍流状态下的三维不可压缩流场进行数值模拟。通过研究新型静态混合器脉动速度分布的对称性及其间歇性发现:新型静态混合器内3个方向速度分量的偏斜因子和平坦因子分布具有周期性;x和z2个方向的速度概率密度分布存在较小不对称性且其平坦因子数值在2.3—5.7变化,径向偏斜因子的数量级均较轴向小1个数量级。采用新的数据处理方法计算和分析得到了不同长径比下新型静态混合器湍流流动阻力统一特性曲线及其关联式。     

Full‐physics simulations of spray‐particle interaction in a bubbling fluidized bed

Numerical simulations of a gas‐particle‐droplet system were performed using an Euler‐Lagrange approach. Models accounting for (1) the interaction between droplets and particles, (2) evaporation from the droplet spray, as well as (3) evaporation of liquid from the surface of non‐porous particles were considered. The implemented models were verified for a packed bed, as well as other standard flow configurations. The developed models were then applied for the simulation of flow, as well as heat and mass transfer in a fluidized bed with droplet injection. The relative importance of droplet evaporation vs. evaporation from the particle surface was quantified. It was proved that spray evaporation competes with droplet deposition and evaporation from the particle surface. Moreover, we show that adopting a suitable surface coverage model is vital when attempting to make accurate predictions of the particle's liquid content. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2569–2587, 2017