A study of the three‐dimensional particle size segregation structure in a rotating drum

Three‐dimensional particle size segregation structures of binary mixtures of six different size ratios (SR = 1.42–3.37) in a rotating drum are studied. The formation of two smaller particle satellites around the central smaller‐particle rich band after the band formation core‐thickening mechanism is reported for the first time. The binary mixtures of six SRs show three satellite shapes, including the small bump shape, the axe shape, and the hemisphere shape. Except for the binary mixture of SR = 2.01 with the axe satellite shape, the satellite size increases with the increasing of the SR value at the same bed depth. The degrees of mixing of binary mixtures of six different SRs at different bed depths are analyzed using the Lacey mixing index. The degree of mixing at the bed surface and close to the drum cylindrical wall can be explained by the drift‐diffusional model of Savage (1993). © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Experimental study of the mixing kinetics of binary pharmaceutical powder mixtures in a laboratory hoop mixer

As increasingly commented by the literature during the last 5 years, estimating the homogeneity of a powder mixture and following powder mixing processes is not a simple task. In this paper, we present the development and statistical validation of a sampling methodology for defining the number of samples required to provide a reasonable estimation of the homogeneity attained in a laboratory scale tumbler mixer. This method is then used to follow the mixing kinetics of a dilute binary powder mixture in a hoop mixer. Special attention is paid to the statistical meaning of the values obtained and the influence of the physical characteristics such as particle size and shape. The role of the particle shape of the majority powder is particularly emphasised and it is quantitatively demonstrated that spherical particles are harder to mix and more ready to segregate than particles with irregular shapes. The different mixing mechanisms at play are identified; the practical limits of use of such tumbler mixers with pharmaceutical powders are discussed.     

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     

Simulation and modeling of segregating rods in quasi‐2D bounded heap flow

Many products in the chemical and agricultural industries are pelletized in the form of rod‐like particles that often have different aspect ratios. However, the flow, mixing, and segregation of non‐spherical particles such as rod‐like particles are poorly understood. Here, we use the discrete element method (DEM) utilizing super‐ellipsoid particles to simulate the flow and segregation of rod‐like particles differing in length but with the same diameter in a quasi‐2D one‐sided bounded heap. The DEM simulations accurately reproduce the segregation of size bidisperse rod‐like particles in a bounded heap based on comparison with experiments. Rod‐like particles orient themselves along the direction of flow, although bounding walls influence the orientation of the smaller aspect ratio particles. The flow kinematics and segregation of bidisperse rods having identical diameters but different lengths are similar to spherical particles. The segregation velocity of one rod species relative to the mean velocity depends linearly on the concentration of the other species, the shear rate, and a parameter based on the relative lengths of the rods. A continuum model developed for spherical particles that includes advection, diffusion, and segregation effects accurately predicts the segregation of rods in the flowing layer for a range of physical control parameters and particle species concentrations. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1550–1563, 2018     

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.     

Designing minimally segregating granular mixtures for gravity-driven surface flows

In dense flowing bidisperse particle mixtures varying in size or density alone, smaller particles sink (percolation-driven) and lighter particles rise (buoyancy-driven). But when particle species differ from each other in both size and density, percolation and buoyancy can either enhance (large/light and small/heavy) or oppose (large/heavy and small/light) each other. In the latter case, a local equilibrium can exist in which the two mechanisms balance and particles remain mixed: this allows the design of minimally segregating mixtures by specifying particle size ratio, density ratio, and mixture concentration. Using DEM simulations, we show that mixtures specified by the design methodology remain relatively well-mixed in heap and tumbler flows. Furthermore, minimally segregating mixtures prepared in a fully segregated state in a tumbler mix over time and eventually reach a nearly uniform concentration. Tumbler experiments with large steel and small glass particles validate the DEM simulations and the potential for designing minimally segregating mixtures.     

蔗糖三相流态化结晶过程中离集与混合特性的研究

在一总高６５０ｍｍ，直径６０ｍｍ的三相流化床实验装置上，分别采用压降法和取样法测定了不同操作条件下二元混合物蔗糖晶体颗粒浓度沿轴向的分布，并建立了表征颗粒混合与分级程度的数学模型，得到不同条件下的混合系数。结果表明，混合系数即混合程度随气速增加而增大，但随液速增加略有减小；随大颗粒比率的增加，床中的离集程度有所增大。     

Numerical simulation of local and global mixing/segregation characteristics in a gas–solid fluidized bed

Researches on solids mixing and segregation are of great significance for the operation and design of fluidized bed reactors. In this paper, the local and global mixing and segregation characteristics of binary mixtures were investigated in a gas–solid fluidized bed by computational fluid dynamics-discrete element method (CFD-DEM) coupled approach. A methodology based on solids mixing entropy was developed to quantitatively calculate the mixing degree and time of the bed. The mixing curves of global mixing entropy were acquired, and the distribution maps of local mixing entropy and mixing time were also obtained. By comparing different operating conditions, the effects of superficial gas velocity, particle density ratio and size ratio on mixing/segregation behavior were discussed. Results showed that for the partial mixing state, the fluidized bed can be divided into three parts along the bed height: complete segregation area, transition area and stable mixing area. These areas showed different mixing/segregation processes. Increasing gas velocity promoted the local and global mixing of binary mixtures. The increase in particle density ratio and size ratio enlarged the complete segregation area, reduced the mixing degree and increased the mixing time in the stable mixing area.     

An index to characterize gas-solid and solid-solid mixing from average volume fraction fields

A mixing index based on solid volume fraction fields is developed for gas-solid flows. Conventional mixing indices are based on particle realizations of granular mixing and are applicable to experimental data or discrete element method simulations. However, these indices cannot be used as-is for multifluid models, and an index for characterizing mixing in gas-solid flows from continuous fields is needed. The performance of the new mixing index is tested in two applications. The first is a 3D simulation of the mixing of biomass and sand in a fluidized bed reactor, and the second is a 2D simulation of binary particle segregation in a fluidized bed. The simulations are performed using OpenFOAM®. The mixing index is used to quantify gas-solid mixing using solid volume fractions and solid-solid mixing using solid fractions. The formulation of conventional mixing indices is extended to be used with solid volume fractions fields, and methods for performance improvement are presented.     

Classifying the fluidization and segregation behavior of binary mixtures using particle size and density ratios

Experimental investigations show that fluidized binary mixtures exhibit varied pressure drop profiles and segregation patterns, depending on the level of disparity due to size and/or density differences. In this study, different mixture types are mapped on a graph of density versus size ratios. It is found that the ratio of the minimum fluidization velocities of individual components can be used to categorize these mixtures. A simple correlation is developed to compute the ratio of the minimum fluidization velocities based on the density and size ratios. Categorizing the binary mixtures in this manner gives a qualitative understanding of how the different mixtures behave on fluidization. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

内置活动内构件回转窑内二元颗粒的运动混合研究

采用离散单元法（DEM）对内置活动内构件回转窑内二元颗粒的运动混合进行了数值模拟。探讨了添加不同长度活动内构件时（回转窑转速、活动内构件宽度及厚度均固定）示踪颗粒的运动轨迹以及颗粒整体的运动模式。用接触数指标来定量评价颗粒的混合程度,比较了添加不同长度活动内构件时回转窑内二元颗粒的混合程度。结果表明：当活动内构件长度分别为0、13mm、21mm、29mm和37mm时,长度越长,示踪颗粒运动轨迹的遍历区域越大,运动轨迹稀疏区和密集区的差别越小,比起无内构件,添加活动内构件时颗粒的运动方向更加随机,运动轨迹更加紊乱。因活动内构件的存在,颗粒的运动模式由滚落模式变为阶梯模式。活动内构件的扰动和搅拌作用可以有效增强二元颗粒之间的混合。活动内构件存在一个最优长度,过长或过短都不能获得最理想的增混效果。     

Density effect on mixing and segregation processes in a vibrated binary granular mixture

The mixing and segregation processes of binary granular mixture with identical sizes but different densities particles subjected to vertical oscillatory excitation are investigated in this study. The spatial distributions of vibrated binary steel-glass beads mixture are visualized by simulation and the results are similar to the experimental data. The time evolution of pattern formations show that the heavy particles first move toward the center of the bed and then concentrate near the centers of the two convection cells of the vibrated system. The mechanism causing the mixing and segregation is strongly dependent on the momentum exchange of each species which is related to the granular temperature gradients of mixture components. The influences of solid fraction and granular temperature profiles on the mixing of the mixture are examined under different operating conditions. The simulation results show that the granular temperatures of heavy particles are higher than those of light particles, indicating that the granular temperatures do not equilibrate for the mixture system. The convection motion also plays an important role in determining the mixing of the system. For understanding the extent of granular mixing, the segregation intensity was determined to quantify the mixing rate of binary mixtures. The segregation intensity shows that the mixing rate increases with the vibration strength, but decreases with the initial heights of mixture.     

三维喷动床内异径干湿颗粒混合特性数值模拟

基于计算流体力学-离散单元法,建立了三维喷动床内气固两相流数学模型,采用Fortran语言编制了并行数值模拟程序。对三维喷动床内两种不同直径的干颗粒及湿颗粒的混合特性进行了数值模拟,并从颗粒角度分析了双组分颗粒的运动机制。利用Lacey混合指数对床内整体以及特定区域的混合程度进行了定量分析,并研究了液桥体积、颗粒密度比以及表观气速对异径颗粒混合的影响。结果表明：在单孔射流喷动床内,干湿两种颗粒流动方式相似,湿颗粒无明显的聚团现象;液桥力对小直径的颗粒影响较大,使不同直径湿颗粒速度差减小;环隙区内颗粒的混合是影响整床颗粒混合的关键因素;液桥体积对颗粒混合的影响较大,对颗粒密度比以及表观气速的影响有限。     

Effect of blade angle and particle size on powder mixing performance in a rectangular box

This study focuses on the understanding of flow over a single blade and its impact on powder mixing. The Discrete or Distinct Element Method (DEM) is used and the flow of a single blade through a bed of a binary particle mixture is studied. Mixing performance with respect to a blade-rake angle and particle size is investigated using the Modified Generalized Mean Mixing Index (MGMMI) and the maximum mean instantaneous velocities. A wide range of angles and different loading scenarios of the binary particle mixture were studied. Velocity profiles for all these cases were computed, as well as the forces on particles and the blade. The results showed an inverse relation between the interparticle force and blade-rake angle. Systems with a higher number of larger particles experienced a higher interparticle force. Similar results were obtained for the blade force. The results for mixing efficiency showed that if the smaller particles are placed at the top this leads to a higher mixing performance. The mixing performance was highest for blade-rake angles that offered a maximal surface area or maximal resistance to the flow of particles, which occurred for blade-rake angles from 70° to 90°.     

Estimation of mixing index and contact number by spot sampling

Most of the available definitions of the mixing index, which specifies homogeneity or distribution of the composition in a solids mixture, are based on the variance of the concentration of a certain component among spot samples. However, for a solid—solid chemical reaction or any process involving contact between different solid phases, its rate is proportional to the contact points or area among particles of the different phases. Thus a definition of a microscopic and geometric mixing index based on the number of contact points appears to be of practical significance.The contact number is the number of contact points between two different types of particles for one key particles, a particle species which is selected as a reference. In this paper, the estimation of the mean contact number from spot samples is considered. An expression for estimating the contact number from spot samples is derived. Expressions for the expected value (population mean contact number) and the variance of this mean contact number are also derived. To verify these expression, random numbers with a uniform distribution are generated to simulate a binary component mixture in the completely mixed state. Results of the simulation are in reasonably good agreement with the derived expressions. The mixing index based on the mean contact number is able to indicate the homogeneity of a mixture with regular packing arrangement. In such a mixture, particles are packed either cubically or hexagonally in each layer, and therefore it is difficult to estimate the homogeneity of the mixture from the sample variance.     

Numerical Simulation and Analysis of Particle Mixing and Conduction in Wavy Drums

A thermal discrete element method (DEM) is used to simulate particle mixing and heat conduction inside wavy drums to explore the effects of wavy walls. Sinusoidal configurations with different waves on the walls are simulated. The Lacey mixing index is applied to analyze the mixing characteristics. The driven forces from the wavy wall, either positive/negative or effective driven forces, are analyzed to explain the mechanisms of mixing enhancement in the wavy drum. A new control parameter is proposed to explain the mechanism of mixing enhancement. It is found that a locally oscillating effect exists in wavy drums, which is imparted on the bulk rotating motions of particles and enhances the characteristics of particle mixing and heat conduction significantly. Except over large wave numbers and rotating speeds when the flow regime is deteriorated for mixing, the wavy drum is generally beneficial for mixing augmentation as well as conduction enhancement.     

A study of the axial and radial competition segregation in a rotating drum with internal diameter changing

A binary mixture is mixed in a rotating drum composed by 19 rings with different inner diameters. It is found that the larger particles are concentrated in the rings with smaller inner diameters. The collection of the larger particles in these rings is due to the particle dynamic angle of repose. The transition from the particle segregation core pattern at the end wall to the good radial mixing rings is through a transient turning comet segregation pattern. This transition is closely related to the distance from the ring with the smallest inner diameter to the ring with the largest inner diameter. Having a higher fraction of larger particles in a ring requires both the collection ring having a smaller inner diameter and a smoother inner diameter transition to the neighboring rings.     

Simulation study of the effect of wall roughness on the dynamics of granular flows in rotating semicylindrical chutes

A discrete element model (DEM) is used to investigate the behavior of spherical particles flowing down a semicylindrical rotating chute. The DEM simulations are validated by comparing with particle tracking velocimetry results of spherical glass particles flowing through a smooth semicylindrical chute at different rotation rates of the chute. The DEM model predictions agree well with experimental results of surface velocity and particle bed height evolution. The validated DEM model is used to investigate the influence of chute roughness on the flow behavior of monodisperse granular particles in rotating chutes. To emulate different base roughnesses, a rough base is constructed out of a square close packing of fixed spherical particles with a diameter equal to, smaller, or larger than the flowing particles. Finally, the DEM model is used to study segregation in a binary density mixture for different degrees of roughness of the chute. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2117–2135, 2015     

Nano-mixing of dipyridamole drug and excipient nanoparticles by sonication in liquid CO2

Nanoparticles (about 200 nm thick and 600–12000 nm long flakes) of dipyridamole, a poorly water-soluble anti-thrombosis drug, are produced by supercritical antisolvent solvent with enhanced mass transfer method. Applicability of sonication in liquid CO₂ for mixing of drug and excipient nanoparticles is demonstrated for several binary mixtures of drug and excipient. The drug particles are mixed with three different excipients: silica nanoparticles, lactose microparticles, and polyvinylpyrrolidone nanoparticles. To intimately mix at nanoscale, macro mixtures of dipyridamole and excipient particles are sonicated in liquid carbon dioxide. The effects of ultrasonic energy, amplitude, and component weight ratio are studied for the binary mixtures. Characterization of mixing is done using several methods. Scanning electron microscopy is used as a primary method for microscopic analysis. Two macroscopic effects, drug dissolution and blend homogeneity (relative standard deviation), are used to characterize mixing quality of drug/lactose mixture. Results of drug dissolution and blend homogeneity show effectiveness of the proposed mixing method for fine size particles. Material handling properties of drug/silica and lactose/silica mixtures were examined. Upon mixing, the handling properties are significantly improved as measured by compressibility index and Hausner ratio. Liquid CO₂ offers an environmentally benign media for mixing. In addition, the mixture obtained does not contain any residual solvent as compared to the sonication in organic liquids. Upon depressurization, CO₂ is easily removed from the mixture providing a facile recovery of the product.     

Cohesive effects in powder mixing in a tumbling blender

Rotary drums are used as mixers, dryers, kilns and granulators. In all of these systems, powder cohesion deeply affects mixing and segregation, and it is critical in process scale up. In this paper, we focus on the effect of cohesion in mixing and size segregation of binary mixtures of uniform and non-uniform sizes in a partially filled rotating drum. The cohesive force between particle is simulated using a square-well potential and the numerical model is used to characterize flow and mixing properties. The model is validated by comparison to experimental images. Results show a time-dependent spatial distribution of cohesive powder that depends on the magnitude of cohesion and friction. In uniform binary systems, as cohesion increases, the rate of mixing first increases and then decreases, however for the case of non-uniform binary systems, we observe different mixing patterns depending on the relative magnitude of forces acting between particles of same/different sizes. Unlike free flowing material, for cohesive mixtures, a higher rotation speed is found to enhance mixing performance.