Numerical Modeling of Particle Dynamics in a Cylindrical Chamber Containing a Rotating Disk

Numerical modeling was performed to study the submicron particle dynamics in a confined flow field containing a rotating disk, temperature gradient, and various inlet gas flow rates. The Lagrangian model was employed to compute particle trajectories under the temperature gradient, disk rotation speed, and inlet gas flow rate effects. The trajectories of particles with diameters of 1 μm, 0.1 μm, and 0.01 μm were examined in this study. When the inlet gas temperature was lower than that of the disk, particle-free zones were created due to upward thermophoretic force for 1 μm and 0.1 μm particles. Disk rotation was found to depress the size of the particle-free zone. Particle deposition onto the disk for 0.01 μm particles was possible because of the Brownian motion effect. A detailed evaluation of the particle-free zone size as a function of the temperature gradient, disk rotation speed, and inlet gas flow rate was performed. When the inlet gas temperature was higher than the disk temperature, particle deposition onto the disk was enhanced due to the downward thermophoretic force for 1 μm and 0.1 μm particles. Disk rotation was found to increase the deposition rate. For 0.01 μm particles, Brownian motion was more important than thermophoretic force in controlling particle behavior. The particle deposition rates as a function of the temperature gradient, disk rotation speed, and inlet gas flow rate were performed.     

Analysis of gas-particle flow characteristics in impinging streams

A three dimensional Euler–Lagrange model for the gas-particle two-phase impinging streams (GPIS) is developed based on the direct simulation Monte Carlo (DSMC) method with consideration of particle rotation and collision. The gas-particle flow characteristics involved in GPIS as well as the effects of inlet gas velocity and particle rotation are analyzed. The results indicate that two pairs of counter-rotating gas vortices are developed at two sides of the opposite jet flows, which is able to entrain the particles and thus greatly weaken the deposition of particles. Interparticle collisions in the impingement zone produce two effects on the particle behaviors: the direct escaping of particles from impingement zone and the progressive accumulation of particles in impingement zone. Under the same inlet particle mass flow rate, the particle concentration in the impingement zone decreases with increasing inlet velocity of gas due to the increasing impinging reaction of interparticle collisions and growing entrainment of gas vortices. In addition, the rotation of particle provides an additional driving force to push the particles away from the impingement zone, leading to the higher speed of escaping particles and smaller maximum particle concentration at the center of impingement zone than those without particle rotation.     

Investigation of the effect of impeller rotation rate,powder flow rate,and cohesion on powder flow behavior in a continuous blender using PEPT

In this paper, we examine the movement of particles within a continuous powder mixer using PEPT (Positron Emission Particle Tracking). The benefit of the approach is that the particle movement along the vessel can be measured non-invasively. The effect of impeller rotation rate, powder flow rate, and powder cohesion on the particle trajectory, dispersive axial transport coefficient, and residence time is examined. Increase in the impeller rotation rate decreased the residence time, increased the axial dispersion coefficient, and resulted in longer total path length. Effect of flow rate was different at two different rotation rates. At lower rotation rate, increase in flow rate increased the residence time, decreased the axial dispersion, and resulted in longer total path length. At higher rotation rate, increase in flow rate decreased the residence time, increased the total path length and showed a complex dependence on the axial dispersion coefficient. Increasing cohesion (measured using the flow index, dilation, and the Hausner ratio) did not affect the axial dispersion coefficient significantly, but had significant effects on the total particle path length traveled and the residence time. These results, relevant to pharmaceutical powders, provide better physical understanding of the influence of operating parameters on the flow behavior in the continuous mixer. In addition, one of the main obstacles of modeling continuous mixing of particles is to know the appropriate values for the modeling parameters as well as validate modeling approaches. One example is the dispersion coefficient which leads to an analytical solution for the axial dispersion model of a continuous blending process.     

Forces on the surface of small ellipsoidal particles immersed in a linear flow field

Knowledge of the forces which a fluid motion exerts on the surface of suspended material is important for many processes in which the particles are broken apart by the hydrodynamic forces. In this paper, we examine the stresses on a small ellipsoidal particle which is immersed in either a constant, simple shear, two-dimensional straining or axisymmetric straining flow. Calculations have been performed using Oberbeck's and Jeffery's models and have been appropriately visualized. Furthermore, the motion and orientation of the ellipsoid have been examined and the extreme values of stresses have been analyzed. A simple criterion for the break-up of particles is proposed. The analysis shows that the straining flows are particular important for the load on particles. In contrast, simple shear flows are less crucial as the presence of vorticity leads to a rotation of the particles.     

Applying dry powder coatings to pharmaceutical powders using a comil for improving powder flow and bulk density

A method for applying nano-sized silicon dioxide guest particles onto host pharmaceutical particles (a.k.a. “dry-coating” or “nanocoating”) has been developed using conventional pharmaceutical processing equipment. It has been demonstrated that under selected conditions, a comil can be used to induce sufficient shear to disperse silicon dioxide particles onto the surfaces of host particles such as active pharmaceutical ingredients (API) without significant host particle attrition. In accordance with previous studies on dry coating, the dispersed silicon dioxide adheres to the host particle surface through van der Waals attractions, and reduces bulk powder cohesion. In this work, laboratory and pilot scale comils were used to dry coat pharmaceutical API and excipient powders with 1% w/w silicon dioxide by passing them through the mill with an appropriate combination of screen and impeller. In general, the uncoated powders exhibited poor flow and/or low bulk density. After dry coating with a comil, the powders exhibited a considerable and in some cases outstanding improvement in flow performance and bulk density. This coating process was successful at both the laboratory and pilot scale with similar improvements in flow. The superior performance of the coated powders translated to subsequent formulated blends, demonstrating the benefit of using nanocoated powders over uncoated powders. This particle engineering work describes the first successful demonstration of using a traditional pharmaceutical unit operation that can be run continuously to produce uniform nanocoating and highlights the substantial improvements to powder flow properties when this approach is used.     

Theoretical and experimental investigations on particle rotation speed in CFB riser

Particle rotation is a common phenomenon in gas-solid two-phase flows. The paper presents theoretical and experimental investigations on particle rotation speed in the gas-solid flow inside a cold CFB riser. The possible particle rotation speed, caused by non-homogeneous flow field and particle collision, and its variation with time were investigated. The average particle rotation speed was predicted with considerations of particle size, average particle collision velocity, particle collision rate and particle number density. It is found that particle collision is the most significant reason for particle rotation. The maximal and average rotation speed for particles with an average size of several hundred micrometers in the CFB riser under typical working condition may be several thousand revolutions per second and several hundred revolutions per second, respectively. The rotation speed of glass beads with an average size of in the upper dilute zone of a cold CFB riser was measured by using a high speed digital imaging system. The variation of particle rotation speed with time was observed, which is in accordance with the theoretical result. The average rotation speed for glass beads was statistically analyzed based on a large number of particle examples. With several factors taken into account, the experimental result is considered to agree with the theoretical one.     

进料位置与风速对旋风分级器颗粒分级效果的影响

根据旋风分级器内气流速度分布特点进行了进料区域划分,运用非稳态离散相模型和分级实验对比了3个代表性进料位置对颗粒运动轨迹及分级精度的影响,分析了1 μm和10 μm颗粒在不同区域内的受力情况。结果表明,边壁区域进料造成粗组分中细粉夹带现象严重,分级精度差;中部进料区域内流场强度大,粗颗粒受离心力强,细颗粒受轴向气流曳力大,有利于减少颗粒在分级区的停留时间,实现粗、细颗粒的快速分级,对改善分级精度有利;中心位置进料延长了粗颗粒的分级运动路程,增加了粗组分跑损的概率,模拟计算15 μm的粗颗粒进入细组分的质量分数达到11.7%。经实验验证,入口气速在10～22 m·s^-1,中部区域进料时分级后粗、细组分粒度分布曲线重合区面积最小,分级粒径比率值平均提高了25.3%,研究结果为离心气流分级设备的进料位置设计提供了一定的指导。     

Experimental study of particle rotation characteristics with high-speed digital imaging system

Particle rotation plays an important role on several aspects in gas-solid two-phase flow. However, it has not been paid much attention due to a lack of appropriate measurement methods. An attempt has been made in the present paper on the experimental study of particle rotation characteristics in a cold pilot-scale Circulating Fluidized Bed (CFB) riser, by using a high-speed digital imaging measurement system. It is found that one can measure rotation speeds manually for particles with special speckles on their surfaces or irregular shapes by observing particle image sequences. A dual-frequency imaging method was presented to enlarge the maximal measurable rotation speed at finite frame frequency and the measured rotation speeds are validated theoretically. Furthermore, particle rotation characteristics in a cross-section in upper dilute-phase zone were analyzed statistically. The results show that the average particle rotation speed is about 300 rev/s with the top speed of 2000 rev/s, when the superficial gas velocity U_g, external solids mass flux G_s and average particle diameter are 5 m/s, 1.5 kg/(m² s) and 0.5 mm, separately. The average particle rotation speed near the wall area is higher than that in the center area at the testing cross-section. Those particles, with either smaller size or higher radial component of translational speed, may have higher average rotation speed. The average rotation speed of irregular particles is apparently higher than that of the spherical ones.     

Slow and intermediate flow of a frictional bulk powder in the Couette geometry

Most current research in the field of dry, non-aerated powder flows is directed toward rapid granular flows of large particles. Slow, frictional, dense flows of powders in the so-called quasi-static regime were also studied extensively using Soil Mechanics principles. The present paper describes the rheological behavior of powders in the “intermediate” regime lying between the slow and rapid flow regimes. Flows in this regime have direct industrial relevance. Such flows occur when powders move relative to solid walls in hoppers, bins and around inserts or are mixed in high and low shear mixers using moving paddles. A simple geometry that of a Couette device is used as a benchmark of more complicated flows.The constitutive equations derived by Schaeffer [J. Differ. Equ. 66 (1987) 19] for slow, incompressible powder flows were used in a new approach proposed by Savage [J. Fluid Mech. 377 (1998) 1] to describe flows in the intermediate regime. The theory is based on the assumption that both stress and strain-rate fluctuations are present in the powder. Using Savage's approach, we derive an expression for the average stress that reduces to the quasi-static flow limit when fluctuations go to zero while, in the limit of large fluctuations, a “liquid-like”, “viscous” character is manifested by the bulk powder.An analytical solution of the averaged equations for the specific geometry of the Couette device is presented. We calculate both the velocity profile in the powder and the shear stress in the sheared layer and compare these results to experimental data. We show that normal stresses in the sheared layer depend linearly on depth (somewhat like in a fluid) and that the shear stress in the powder is shear rate dependent. We also find that the velocity of the powder in the vicinity of a rough, moving boundary, decays exponentially so that the flow is restricted to a small area adjacent to the wall. The width of this area is of the order of 10-13 particle diameters. In the limit of very small particles, this is tantamount to a shear band-type behavior near the wall.     

Evaluation of apparent viscosity of liquid-containing porous particles by the intrusion method using a conical rotor

The apparent viscosity of a wet powder consisting of porous silica particles and a viscous liquid was evaluated by means of a newly developed powder rheometer in which a rotating conical rotor with grooves on the surface intrudes semi-statically into the powder bed. Using this rheometer, the relationship between the shear torque and the depth of intrusion, i.e., the torque characteristic curve, was measured under various conditions. The shear force acting on a contact point between the particles was estimated from the torque characteristic curve. Above the critical liquid amount in which the pores of the particles were filled with the liquid, the shear force increased with an increase in the thickness of the liquid film formed on the particle surface regardless of the pore volume. From the change of shear force with the physical properties of the liquid, it was clear that the shear force is closely related to the liquid bridge force acting on the contact points between the particles. The apparent viscosity coefficient of the wet powder was determined from the shear rate dependence of the shear force. At the relatively high liquid amounts corresponding to funicular and capillary states, the apparent viscosity coefficient increased sharply with the thickness of the liquid film since the viscosity of the liquid strongly affected the shear flow of the wet powder. Subtle changes of the apparent viscosity due to the liquid amount and the physical properties of the liquid can be sensitively detected by using the rotary-intrusion method.     

基于颗粒间相互作用的细颗粒粉体料仓下料过程分析

以玻璃微珠、流化床裂化催化剂颗粒、褐煤和聚氯乙烯颗粒为实验物料,开展粉体流动性表征与料仓下料实验。研究发现,不同粉体的流动性差异较大,相应的料仓重力下料结果也不同;实验所用粉体的下料流率远低于传统Brown and Richards模型的预测值。分析表明,颗粒间相互作用导致的粉体黏附团聚是阻碍细颗粒粉体下料流动的主要原因。基于上述分析,利用剪切测试结合摩尔应力圆理论获得床层拉伸应力,并借助Rumpf方程构建的颗粒间相互作用与粉体床层应力之间的模型来获得不同粉体的颗粒间作用力;继而采用Bond数对粉体床层空隙率进行修正,揭示了颗粒间相互作用对粉体床层结构的影响,并在此基础上建立了粉体下料流率预测模型。新建立的耦合颗粒间作用力的粉体流率模型,有效改善了传统模型对细颗粒粉体流率预测值偏高的弊端,显著降低了流率预测偏差。     

壁面粗糙度对气粒两相流动中颗粒行为影响的实验研究

The effect of wall roughness on particle behavior in two-phase flows in a horizontal backward-facing step is studied using a phase-Doppler particle anemometer. The results show that the wall roughness widens the particle velocity probability density distribution, enhances the redistribution of particle velocity into different directions,reduces the particle longitudinal mean velocity and increases the longitudinal and transverse fluctuation velocities and Reynolds shear stress. The effect of roughness on particle motion in the recirculation zone is weaker than that in the fully developed flow region. The effect of roughness for small particles is restricted only in the near-wall region, while that for large particle diffuses to the whole flow field.     

Ultrafine cohesive powders: From interparticle contacts to continuum behaviour

Continuum mechanical models and appropriate measuring methods to determine the material parameters are available to describe the flow behaviour of cohesive powders. These methods are successfully applied to design process equipment as silos. In addition, “microscopic” studies on the particle mechanics can give a better physical understanding of essential “macroscopic” constitutive functions describing a powder “continuum”. At present, by means of the discrete element method (DEM), a tool is available that allows one to consider repulsive and frictional as well as attractive adhesion forces in detail. Within the framework of Newton's equations of motion, each particle in the system is tracked, and reacts to the forces acting.The knowledge of the interaction forces between particles is thus a prerequisite for understanding (via DEM) the stability and flow of particulate systems and other phenomena. In this study, macroscopic cohesion and friction are related to their microscopic counterparts, adhesion and contact-friction. The macroscopic cohesion is found to be proportional to the maximal microscopic adhesion force, and the macroscopic friction coefficient is a non-linear function of the contact friction, dependent (or independent) on the preparation procedure for yielding (or steady-state flow).One of the few methods available for the direct measurement of surface and contact-forces is the atomic force microscope (AFM) and, related to it, the so-called particle interaction apparatus (PIA). A contact model for ultrafine cohesive particles (average radius ) is introduced, based on such experiments. Plugged into DEM, consolidation, incipient yielding, and steady-state flow of the model powders are studied. Also the dynamic formation of the shear zone is examined and compared with experimental observations. Eventually, the shear experiments with volumetric strain measurements in a translational shear cell are used for validation.     

Shear-induced orientation in polymer/clay dispersions via in situ X-ray scattering

We report in situ X-ray scattering measurements of shear-induced orientation in polymer-clay dispersions. Two different organically modified clays, montmorillonite and fluorohectorite, are dispersed in a low molecular weight, viscous polymer melt, facilitating studies at room temperature. Orientation measurements are performed in the flow-gradient plane, allowing characterization of both the average degree and direction of particle orientation during shear. In all cases, the orientation angle is finite, indicating systematic misalignment of the particle long axes relative to the flow direction. In concentrated fluorohectorite and montmorillonite dispersions, anisotropy and orientation angle are roughly independent of shear rate, and negligible relaxation is observed upon flow cessation. Conversely, a lower concentration montmorillonite sample exhibits orientation that is more responsive to shear flow, and partially relaxes upon flow cessation. In this sample, the orientation behavior is interpreted in light of rotational diffusion of the clay particles. This same sample exhibits oscillatory structural dynamics upon shear flow reversal, attributed to tumbling rotations of the disk-like clay particles in shear. Large-amplitude oscillatory shear is similarly demonstrated to be capable of inducing significant particle orientation; the degree of orientation is principally determined by the applied strain amplitude. Complementary measurements of rheological properties exhibit many characteristics commonly reported in polymer-clay nanocomposites. Based on the structural measurements reported here, the rheological phenomena are interpreted to arise from a combination of flow-induced particle orientation and rate- and time-dependent destruction or reformation of particle networks.     

Skin-Core morphology and failure of injection-molded specimens of impact-modified polypropylene blends

The structure-property relationship as well as the failure phenomena of injection molded polypropylene (PP) blends modified with ethylene/propylene/diene terpolymer (EPDM) and thermoplastic polyolefinic rubber (TPO) were investigated. Single and double-gated tensile bars were injection molded by different Injection speeds. Microscopic studies on the failure behavior of knit lines were carried out using microtomed sections taken from the doublegated specimens. It was found that during injection molding, a skin-core morphology is formed in both the continuous PP matrix as well as in the modified PP blends containing rubber particles of various deformation. The characteristics of the latter are in agreement with those described by the Tadmor flow model. The skin consists of a thin pure PP layer, whereas the subsurface layer contains more or less elongated rubbery particles due to the elongational flow at the wall. The deformation of the rubbery particles decreases, but their concentration increases with increasing distance from the skin towards the core. The deformed particles are oriented tengentionally to the flow front profile. Failure during tensile and tensile impact loading is initiated in the shear zone along the skin-core boundary. This zone has a transcrystalline character and favors the formation of crazing. Final fracture of the bars depends, however, on how crazing and shear yielding simultaneously interact. Their interaction is a function of the average particle size of the dispersed phase. Above an average particle size of 0.6 μm, crazing is prevented by shear bands. For injection molding of PP/rubber blends a moderate injection speed is recommended, if the melt viscosities of the components are closely matched. In this way a pronounced dispersion gradient of the rubber particles across the plaque thickness is avoided. However, for the blends modified with rubber of high viscosity ratio and greater melt elasticity, use of higher injection speed is advantageous. Here, the higher shear stress field decreases the average particle size taken into the direction perpen dicular to the lead, since the cross section of the stronger deformed particle decreases.     

Rheology of poly(vinyl chloride) plastisol for super‐high‐shear‐rate processing. II

Capillary flow of poly(vinyl chloride) plastisol was examined at low, high, and superhigh shear rates. At the low to intermediate shear rates, the flow was pseudo‐plastic, but the measured viscosity was not reproducible and widely scattered. The flow behavior was explained as the breakup of the particle network into network‐fragments of varying size. At high shear rates, the measured viscosity was reproducible and increased with shear rate, indicating that the particles were, by and large, separated from each other. At superhigh shear rates, the viscosity decreased with the increase of shear rate. The particles cease to participate in flow because rotation becomes more difficult. A plug‐flow ensues with a thin layer of lubricating plasticizer. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

The flooding of a powder — the importance of particle size distribution

This paper reviews the development of a new annular shear cell for the characterisation of aerated powders, and studies in detail the flooding phenomena for an alumina powder. Results have shown a large reduction in shear stress for small quantities of air entrainment and transition from normal Coulomb-solid flow to liquid-like flow at high shear rates. Addition of fine particles is shown to enhance these effects, thereby increasing the likelihood of flooding. Addition of particles of size 40 μm and below is shown to be the main factor. An increase of 10% of particles in this size range shows a similar shear response to that obtained with a sample of alumina known to have flooded, although smaller quantities also have a significant effect. Such low quantities of additional fines could occur due to segregation, resulting in pockets of material with a high chance of flooding under normal powder handling conditions.     

Performance Characteristics of a New Continuous-Flow Electrophoresis Instrument

Abstract

An instrument is described for the continuous separation of particles by means of electrophoresis. The effect of field strength, electrolyte flow rate, and sample flow rate on migration distance and particle band width were investigated. The interrelationships between the various operational parameters and particle band resolution are discussed.     

The Influence of Air Permeation on the Flow Properties of Bulk Solids

This paper considers the influence of low air permeation on the flow properties of slightly consolidated bulk solids in steady state flow. A ring shear device was built that enables the powder sample to be permeated during the shear test from below, upwards with flow velocities below the onset of fluidization. Furthermore, a mathematical model predicting the dependence of both the shear stress as well as the location of the shear zone in the shear cell on the aeration degree was developed. This model predicts a reduction of the shear stress with increasing air feed pressure and a sudden displacement of the shear zone from the cover to the bottom of the shear cell for a high degree of aeration. The good agreement between the measured results and the model predictions proves that the influence of the permeation on the flow properties of bulk solids can be traced back to the change of the normal stresses in the shear zone.     

Adhesion of ultrafine particles—Energy absorption at contact

The mechanical product behaviour of cohesive ultrafine powders is characterized by insufficient flowability and large compressibility. Consequently, a comparatively large energy input is necessary to promote the non-rapid frictional shear flow in powder handling practice. The paper continues the new micromechanical philosophy demonstrated in the last publication [Tomas, J., 2007a. Adhesion of ultrafine particles—a micromechanical approach. Chemical Engineering Science 62, 1997-2010, doi: 10.1016/j.ces.2006.12.055].When two adhesive particles are coming in contact, the constitutive models of four stressing modes, namely by compression and detachment (tension), sliding, rolling and torsion have to be derived. The consequences of elastic-dissipative, elastic-plastic, frictional unloading and reloading paths of normal and tangential forces, rolling and torsional moments are discussed with respect to energy absorption. The total energy absorption comprises contributions by elastic-dissipative hysteresis due to microslip within the contact plane and by fully developed friction work when the friction limits of displacements are exceeded during contact sliding, particle rolling or rotation. With increasing contact flattening by normal load these friction limits, hysteresis and friction work increase. The particle mass related, averaged energy densities of these various stressing modes are found to be 0.4-6 mJ/g. But the enormous, mass of contact zone related energy density amounts to 0.2-20 kJ/g. Besides this, the powder mass related energy consumption characterises the global intensity of energy absorption of macroscopic process within an apparatus, e.g. the specific preshear work of about 1-5 mJ/g. Thus, it is very essential to understand the micromechanics of particle contact behaviour with respect to product quality assessment and process performance in particle technology.