Effects of rotational speed and fill level on particle mixing in a stirred tank with different impellers

The particle mixing was studied in a cylindrical stirred tank with elliptical dished bottom by experiments and simulations.The impeller types used were double helical ribbon(HR) + bottom HR,pitched blade ribbon + bottom HR,inner and outer HR + bottom HR,and pitched blade ribbon + Pfaudler + bottom HR labeled as impellers Ⅰ to Ⅳ,respectively.The quantitative correlations among the rotational speed,fill level and power consumption for impeller Ⅰ and impeller Ⅱ were obtained by experiments to validate the discrete element method(DEM) simulations.The particle mixing at different operating conditions was simulated via DEM simulations to calculate the mixing index using the Lacey method,which is a statistical method to provide a mathematical understanding of the mixing state in a binary mixture.The simulation results reveal that as the rotational speed increases,the final mixing index increases,and as the fill level increases,the final mixing index decreases.At the same operating conditions,impeller Ⅲ is the optimal combination,which provides the highest mixing index at the same revolutions.

Effect of drum structure on particle mixing behavior based on DEM method

The optimization of the drum structure is beneficial to improve the particle motion and mixing in rotary drums.In this work,two kinds of drum structures,Lacy cylinder drum(LC)and Lacy-lifters cylinder drum(LLC),are developed on the basic of cylinder drum to enhance the heat transfer area.The particle motion and mixing process are simulated by DEM method.Based on the grid independence and model validation,the contact number between particles and wall,particle velocity profile,thickness of active layer,particle exchange coefficient,particle concentration profile and mixing index are demonstrated.The influences of the drum structure and the operation parameters are further evaluated.The results show that the contact number between particles and wall is improved in LC and LLC compared to cylinder drum.The particle velocity in LC is higher than that in cylinder drum at high rotating speed,and the particle velocity of the particle falling region is significantly improved in LLC.Compared to cylinder drum and LC,the thickness of active layer in LLC is smaller,while the local particle mixing quality is proved to be the best in the active region.In addition,the particle exchange coefficients between static region and active region in the three drums are compared and LLC is found tending to weaken the particle flow.Besides,the fluctuations of particle concentration in the active region,static region,and boundary region are weakened in LLC,and the equilibrium state is reached earlier.In addition,the overall particle mixing performance in cylinder drum,LC and LLC is analyzed.The particle mixing performance in cylinder drum is the worst,while the difference in mixing quality of LC and LLC depends on the operation conditions.

DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured. The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.

NUMERICAL PREDICTION OF PARTICLE MIXING BEHAVIOR IN A BUBBLING FLUIDIZED BED

In this article the hard-sphere Discrete Particle Model （DPM） is used to study the mixing behavior of particles in the 2-D fluidized bed. Different flow patterns in the bed for two kinds of inlet configurations, namely free bubbling and jet bubbling mode, are captured by the numerical model, under specific superficial gas velocities. To examine the degree of particle mixing, the Fan index is applied. The numerical results show that the rate of particle mixing is larger in the jet bubbling than that in the free bubbling mode. The gross circulations of particles in the jet bubbling bed give a higher degree of mixing because of the involvement of a greater number of particles.

Numerical simulation of tetrahedral particle mixing and motion in rotating drums

A regular tetrahedron is the simplest three-dimensional structure and has the largest non-sphericity. Mixing of tetrahedral particles in a thin drum mixer was studied by the soft-sphere-imbedded pseudo- hard particle model and compared with that of spherical particles. The two particle types were simulated with different rotation speeds and drum filling levels. The Lacey mixing index and Shannon information entropy were used to explore the effects of sphericity on the mixing and motion of particles. Moreover, the probability density functions and mean values and variances of motion velocities, including translational and rotational, were computed to quantify the differences between the motion features of tetrahedra and spheres. We found that the flow regime depended on the particle shape in addition to the rotation speed and filling level of the drum. The mixing of tetrahedral particles was better than that of spherical particles in the rolling and cascading regimes at a high filling level, whereas it may be poorer when the filling level was low. The Shannon information entropy is better than the Lacey mixing index to evaluate mixing because it can reflect the real change of flow regime from the cataracting to the centrifugal regime, whereas the mixing index cannot.

DEM analysis of the effect of electrostatic interaction on particle mixing for carrier-based dry powder inhaler formulations

Particle interactions play a significant role in controlling the performance of dry powder inhalers （DPIs）, which mainly arise through van der Waals potentials, electrostatic interactions, and capillary forces. Our aim is to investigate the influence of electrostatic charge on the performance of DPIs as a basis for improv- ing the formulation of the particle ingredients. The mixing process of carrier and active pharmaceutical ingredient （API） particles in a vibrating container is investigated using a discrete element method （DEM）. The number of APl particles attaching to the carrier particle （i.e., contact number） increases with increas- ing charge and decreases with increasing container size. The contact number decreases with increasing vibrational velocity amplitude and frequency. Moreover, a mechanism governed by the electrostatic force is proposed for the mixing process. This mechanism is different from that previously proposed for the mixing process governed by van der Waals forces, indicating that long-range and short-range adhesive forces can result in different mixing behaviours.

Effect of the distributor plugging ways on fluidization quality and particle stratification in air dense medium fluidized bed

Gas-solid fluidized bed separation is a highly efficient and clean technique for coal separation,and can effectively remove ash and sulfur contained gangue minerals from coal.However,the fine coal plugging distributor often leads to uneven fluidization and affects the separation effect.In this paper,different plugging ways were designed to study their effects on the fluidization characteristics and particle mixing.It was found that when the plugging phenomenon occurs,the minimum fluidization velocity of the fluidized bed gradually decreases as the plugging area enlarges.The difference between the top and the bottom of the bed minimum fluidization velocity increases accordingly,and a“stagnation phenomenon”occurs in the bed.The standard deviation of pressure fluctuations at the top of the bed is smaller than that at the bottom of the bed,which is the opposite of normal conditions.As the area of the plugging increases,the dead zone on the side wall of the fluidized bed significantly increases.The size of the dead zone is rapid reducing at the initial stage.It was noticed that the stratification of the low-density products is particularly affected by plugging,whereas the stratification of high-density products is not obviously influenced by certain conditions.

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 conducted 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 performance 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.

The effect of side walls on particles mixing in rotating drums

In this paper, we study the effects of the presence and shape of side walls and of the overall length of rotating cylindrical drums on the mixing of particles with differing sizes by application of the discrete element method (DEM). By varying the semi-axis of the spheroidally shaped side walls and the length of the overall drum, we observe the formation of circulation patterns near the side walls. Although there is a vast amount of literature studying mixing regimes in rotating drums, little is known about the effect of the side walls of the drum on particle mixing. The results of our study demonstrate that introducing curved side walls induces a strong circulation pattern near these side walls, but has, paradoxically, a negative impact on mixing and actually promotes segregation. The cause for this segregation is the difference in velocity of differently sized particles near the curved side walls. Large particles accumulate at the curved side walls, whereas small particles move away from the curved side walls. When the length of the drum is increased, the overall effect of the side walls is decreased, although it does remain observable, even in very large drums.

Enhancing mixing of particles by baffies in a rotating drum mixer

Baffles with shape of ＂-＂ （single baffle）, ＂＋＂ （cross-baffles with four arms） and （baffles with 6 arms） are used to enhance the mixing of particles in a rotating drum mixer. A micro-dynamics study of mixing and segregation ofa bi-disperse system of two particle sizes in the rotating drum with these three kinds of baffles is carried out using the discrete element method （DEM）. The effect of the baffles on mixing, and the mechanisms of mixing enhancement by the baffles are discussed and analyzed. Simulation results show that in an unbaffled drum mixer, particle convection, particle diffusion, and size segregation of hi- disperse particles, all play important roles in the mixing process; whereas size segregation will be largely restrained when the drum mixer has a baffle, regardless of its shape, and the degree of mixing is higher than that in an unbaffled drum mixer. The different mixing characteristics for ＂-＂ shaped baffle, ＂＋＂ baffle, and baffle are revealed by the simulation results. For ＂＋＂ or style baffles, there is an optimal size of baffles for the mixing of particles, and the ootimal mixing efficiency is higher than that for ＂-＂ baffle.

Effects of material properties on the competition mechanism of heat transfer of a granular bed in rotary cylinders

Mixing and heat transfer processes of the granular materials within rotary cylinders play a key role in industrial processes. The numerical simulation is carried out by using the discrete element method （DEM） to investigate the influences of material properties on the bed mixing and heat transfer process, including heat conductivity, heat capacity, and shear modulus. Moreover, a new Prclet number is derived to determine the dominant mechanism of the heating rate within the particle bed, which is directly related to thermal and mechanical properties. The system exhibits a faster heating rate with the increase of ratio of thermal conductivity and heat capacity, or the decrease of shear modulus when inter-particle conduction dominates the heating rate; conversely, it shows a fast-mixing bed when particle convection governs the heating rate. The simulation results show good agreement with the theoretical predictions.

Enhancing mixing of cohesive particles by baffles in a rotary drum

A soft-sphere discrete cohesive powder model was used to simulate the transverse mixing of particles in a rotary drum. Using this model, the effect of cohesion strength and baffle length was investigated. Mixing time （tR） and mixing entropy were used to characterize the mixing behavior. The results showed that increasing particle cohesiveness increases tR. Baffles enhanced transverse mixing, especially for high- cohesive particles. Moreover, the baffle length played a significant role on mixing. An optimized length of 0.50 （L/R） enhances transverse mixing for high-cohesive particles, Further increases in baffle length only decreases the mixing rate by impeding the surface flow layer. In contrast to high-cohesive particles, low-cohesive particles needed much shorter baffles.A soft-sphere discrete cohesive powder model was used to simulate the transverse mixing of particles in a rotary drum. Using this model, the effect of cohesion strength and baffle length was investigated. Mixing time （tR） and mixing entropy were used to characterize the mixing behavior. The results showed that increasing particle cohesiveness increases tR. Baffles enhanced transverse mixing, especially for high- cohesive particles. Moreover, the baffle length played a significant role on mixing. An optimized length of 0.50 （L/R） enhances transverse mixing for high-cohesive particles. Further increases in baffle length only decreases the mixing rate by impeding the surface flow layer. In contrast to high-cohesive particles, low-cohesive particles needed much shorter baffles.

Using the discrete element method to assess the mixing of polydisperse solid particles in a rotary drum

Despite the wide applications of powder and solid mixing in industry, knowledge on the mixing of polydisperse solid particles in rotary drum blenders is lacking. This study investigates the mixing of monodisperse, bidisperse, tridisperse, and polydisperse solid particles in a rotary drum using the dis- crete element method. To validate the model developed in this study, experimental and simulation results were compared. The validated model was then employed to investigate the effects of the drum rotational speed, particle size, and initial loading method on the mixing quality. The degree of mixing of polydis- perse particles was smaller than that for monodisperse particles owing to the segregation phenomenon. The mixing index increased from an initial value to a maximum and decreased slightly before reaching a plateau for bidisperse, tridisperse, and polydisperse particles as a direct result of the segregation of par- ticles of different sizes. Final mixing indices were higher for polydisperse particles than for tridisperse and bidisperse particles. Additionally, segregation was weakened by introducing additional particles of intermediate size. The best mixing of bidisperse and tridisperse particles was achieved for top-bottom smaller-to-larger initial loading, while that of polydisperse systems was achieved using top-bottom smaller-to-larger and top-bottom larger-to-smaller initial loading methods.

Effect of mixing structure on the hygroscopic behavior of ultrafine ammonium sulfate particles mixed with succinic acid and levoglucosan

Understanding the interactions between water and atmospheric aerosols is critical for estimating their impact on the radiation budget and cloud formation. The hygroscopic behavior of ultrafine （〈100nm） ammonium sulfate particles internally mixed with either succinic acid （slightly soluble） or levoglucosan （soluble） in different mixing structures （core-shell vs. well-mixed} were measured using a hygroscopicity tandem differential mobility analyzer （HTDMA）. During the hydration process （6-92% relative humidity （RH））, the size of core-shell particles （ammonium sulfate and succinic acid） remained unchanged until a slow increase in particle size occurred at 79Y~ RH; however, an abrupt increase in size （i.e., a clear deliquescence） was observed at ~72% RH for well-mixed particles with a similar volume fraction to the core-shell particles （80：20 by volume）. This increase might occur because the shell hindered the complete dissolution of the core-shell particles below 92% RH. The onset RH value was lower for the ammonium sulfate/levoglucosan core-shell particles than the ammonium sulfate/succinic acid core-shell particles due to levoglucosan＇s higher solubility relative to succinic acid. The growth factor （GF） of the core-shell particles was lower than that of the well-mixed particles, while the GF of the ammonium sulfate/levoglucosan particles was higher than that of ammonium sulfate/succinic acid particles with the same volume fractions. As the volume fraction of the organic species increased, the GF decreased. The data suggest that the mixing structure is also important when determining hygroscopic behavior of the mixed particles.

Experimental study by online measurement of the precipitation of nickel hydroxide: Effects of operating conditions

The objective of this work is using the online measurement method to study the process of precipitation of nickel hydroxide in a single-feed semi-batch stirred reactor with an internal diameter ofD = 240mm. The effects of impeller speed, impeller type, impeller diameter and feed location on the mean particle size d43 and particle size distribution （PSD） were investigated, d43 and PSD were measured online using a Malvern Insitec Liquid Pro- cess Sizer every 20 s. It was found that d43 varied between 13 kwh and 26 lain under different operating conditions, and it decreased with increasing impeller diameter. When feeding at the off-bottom distance of D/2 under lower impeller speeds, d43 was significantly smaller than that at D/3. PSDs were slightly influenced by operating conditions.

Simulation of ultrasonic attenuation in theelastic mixing particle system

For the study of predicting ultrasonic attenuation of elastic, spherical mixing par- ticles in the liquid-solid two-phase system, the Monte Carlo method （MCM） is introduced, serving as a probability and statistics technique to evaluate the inside ultrasonic events during the ultrasound propagation. On the basis of ultrasonic scattering and aborption, the continuous ultrasonic waves are represented as discrete and independent phonons. By recording the scat- tering events, tracing the trajectory of a moving phonon and calculating the number of phonons that finally reach the receiving transducer, the ultrasonic attenuation coefficient is obtained to be a frequence-dependent spectrum. Numerical investigations have been carried out to predict and compare the ultrasonic attenuation for a solid-liquid two-phase system with a single type particle. After verifing its feasibility, such a method is then appalied into mixing particle sys- tern, where the mixing iron particles and glass beads with various ratios are set as examples for the purpose of predicting ultrasonic attenuation for the monodisperse and polydisperse mixing particle systems. The results of MCM, the ECAH model, the Lloyd ~z Berry （LB） model and the Waterman model match well when the particle volume concentration is lower than 10%, corresponding to iron particles and glass beads respectively. In the case of two-phase system with mixing particles, it is shown that as the particle volume concentration increases to 10%, the variation of the ultrasonic attenuation coefficient with mixing ratio yields a nonlinear tendency. The physical properties of particles can also influence ultrasonic attenuation significantly.

DEM investigation of mixing indices in a ribbon mixer

Mixing index is an important parameter to understand and assess the mixing state in various mixers including ribbon mixers,the typical food processing devices.Many mixing indices based on either sample variance methods or non-sample variance methods have been proposed and used in the past,however,they were not well compared in the literature to evaluate their accuracy of assessing the final mixing state.In this study,discrete element method(DEM)modelling is used to investigate and compare the accuracy of these mixing indices for mixing of uniform particles in a horizontal cylindrical ribbon mixer.The sample variance methods for mixing indices are first compared both at particle-and macro-scale levels.In addition,non-sample variance methods,namely entropy and non-sampling indices are compared against the results from the sample variance methods.The simulation results indicate that,among the indices considered in this study,Lacey index shows the most accurate results.The Lacey index is regarded to be the most suitable mixing index to evaluate the steady-state mixing state of the ribbon mixer in the real-time(or without stopping the impeller)at both the particle-and macro-scale levels.The study is useful for the selection of a proper mixing index for a specific mixture in a given mixer.

Characteristics of atmospheric single particles during haze periods in a typical urban area of Beijing：A case study in October,2014

To investigate the composition and possible sources of particles, especially during heavy haze pollution, a single particle aerosol mass spectrometer（SPAMS） was deployed to measure the changes of single particle species and sizes during October of 2014, in Beijing. A total of 2,871,431 particles with both positive and negative spectra were collected and characterized in combination with the adaptive resonance theory neural network algorithm（ART-2a）. Eight types of particles were classified： dust particles（dust, 8.1%）, elemental carbon（EC, 29.0%）, organic carbon（OC, 18.0%）, EC and OC combined particles（ECOC, 9.5%）,Na-K containing particles（Na K, 7.9%）, K-containing particles（K, 21.8%）, organic nitrogen and potassium containing particles（KCN, 2.3%）, and metal-containing particles（metal,3.6%）. Three haze pollution events（P1, P2, P3） and one clean period（clean） were analyzed,based on the mass and number concentration of PM_（2.5）and the back trajectory results from the hybrid single particle Lagrangian integrated trajectory model（Hysplit-4 model）. Results showed that EC, OC and K were the major components of single particles during the three haze pollution periods, which showed clearly increased ratios compared with those in the clean period. Results from the mixing state of secondary species of different types of particles showed that sulfate and nitrate were more readily mixed with carbon-containing particles during haze pollution episodes than in clean periods.