Mathematical modeling of squashing flows of heated polymer particles

A combination of shear and extension is encountered in the squashing flows of heated polymer particles. Extensional rate affects the non-Newtonian viscosity in determining the flow field in the squashing of cylindrical particles, but both the extensional and shear rates are equally important for disc-like particles. A viscous-type constitutive equation is used for simplicity. The solution of the momentum equations satisfying no-slip boundary conditions leads to a particle flattening equation that can predict flattening ratios of nonisothermal particles in terms of rheological parameters and dimensionless groups of process variables. Application of this analysis to roll fusing of toner particles in copiers is described in a companion article in this issue.     

连续流动系统中颗粒返混与反应率计算的Monte Carlo方法

本文是作者在前文的基础上,应用Monte Carlo方法与“随机树式结构图”,模拟分析了复杂连续流动系统的随机返混、多粒度颗粒的未反应率、以及颗粒反应的动态行为.仿真模拟的物理概念直观、简单,程序简短,在计算机上能容易地完成.对简单情况,其结果与已知方法的结果相吻合.而该问题的确定型方法或Markov模型是由一组复杂的、难于求解的随机微分方程组构成.该方法的应用有可能为计算连续流动反应器内颗粒的行为提供一种可行途径.     

Preparation of Novel Core-Shell Nanocomposite Particles by Controlled Polymer Bridging

Ceramics that are composed of nanosized granules show enhanced properties in various applications. A layer-by-layer deposition process is developed in this study to prepare core—shell nanocomposite particles, using controlled polymer adsorption. Submicrometer-sized alumina particles that have been chosen as the starting core particles are first dispersed by pH control and then modified by adsorption of anionic poly(acrylic acid) to facilitate the subsequent deposition of nanoparticles on them. A key step in the processing involves the removal of excess polymer in the supernatant after the adsorption by controlled washing, so that the added nanoparticles do not self-flocculate among themselves. A coating of nanosized particles is indicated by the charge reversal of the micrometer-sized composite particles. The isoelectric point of the composite particle is similar to that of nanosized particles under both low and high coverage conditions. Scanning electron microscopic observation of coated particles shows full monolayer coverage of the nanoparticles on core particles, which confirms the efficiency of the coating scheme that is discussed here. The present study reveals the feasibility of coating nanoparticles onto micrometer-sized core particles, using controlled polymer bridging, for the preparation of the multilayer nanocomposite powders.     

Group C+ particles: Efficiency augmentation of fluidized bed reactor through nano-modulation

Group C⁺ particles, Group C particles after nano-modulation, with extremely large specific surface area, have been shown to exhibit extraordinarily good fluidization quality with superiorly high bed expansion, significantly increasing gas holdup in the bed. As a first attempt, Group C⁺ particles were used as catalysts in a fluidized bed reactor (C-plus FBR) to evaluate the reaction performance and were compared to that using Group A particles. C-plus FBR could achieve a much higher reaction conversion, up to 235% of that using Group A particles. The contact efficiency for Group C⁺ particles is much higher, being 330% more than that for Group A particles. The greater contact efficiency is due to both larger specific surface area and higher bed expansion, providing larger gas–solid interfacial area and longer gas residence time. Conclusively, Group C⁺ particles with superior fluidization quality and reaction performance do have huge potential in gas-phase catalytic reactions.     

Controlled Nucleation Aerosol Reactors: Production of Bulk Silicon

A new type of aerosol reactor is described. By controlling the rate of gas phase reactions such that vapor diffusion to existing particles is favored over homogeneous nucleation, a small number of seed particles can be grown to supermicron sizes. A model for the influence of growing particles on the rate of homogeneous nucleation has been used to design a reactor for the production of silicon particles by thermal decomposition of silane gas. Particles as large as 9 μm mass median diameter have been grown in this two-stage reactor. Silicon aerosol yields ranging from 70% to 83% have been achieved with this system.     

Prediction of minimum fluidization velocity for vibrated fluidized bed

The prediction of minimum fluidization velocity for vibrated fluidized bed was performed. The Geldart group A and C particles were used as the fluidizing particles. The method based on Ergun equation was used to predict the minimum fluidization velocity. The calculated results were compared with the experimental data.The calculated results of minimum fluidization velocity are in good agreement with experimental data for Geldart group A particles. For group C particles, the difference between the calculated results and experimental data is large because of the formation of agglomerates. In this case, the determination of agglomerate diameter is considered to be necessary to predict the minimum fluidization velocity.     

Prediction of pressure drop with steady state pneumatic conveying of solids in horizontal pipes

Current relationships for determination of the pressure drop with pneumatic conveying of solids in pipes are not of general validity. The theoretical considerations underlying these relationships do not take into account the influence of the rotatory motion of the particles. On the other hand, extremely high rotatory speeds of the particles due to wall collision are observed.Therefore a new concept is presented which takes into account the rotatory motion of the particles. A further aim was to represent the data in the form of nondimensional groups which allow meaningful, physical interpretation of the results obtained.A state diagram for the prediction of pressure drop with pneumatic conveying in the form of sliding particles strands is described.Calculation of power loss per particle and of the force and the moment acting on a particle leads to a nondimensional representation of pressure drop in which a normalized pressure drop is combined with a particle Froude number and a Froude number which contains the particle fall velocity and the pipe diameter. This combination of nondimensional groups defines fully suspended flow.The normalized pressure drop is defined in such a way that it represents the nondimensional slip of the particles, too.Comparison with pressure drop measurements for pneumatic transport in horizontal pipes which included changes in particle size, particles density and pipe diameter confirms the physical significance of the parameters used with regard to the prediction of pressure drop and of particles slip velocity.A simple procedure for the prediction of pressure drop in the full range of steady-state pneumatic conveying is proposed.     

Hindered settling velocity of a bimodal mixture of spherical solid particles in a Newtonian fluid

Works describing methods for calculating the settling velocity of a biomodal mixture of solid particles are analyzed. A method for calculating the settling velocity of a bimodal mixture of spherical particles is proposed that takes into account the contact interaction between particles of different sizes due to their collisions. The calculation results are in satisfactory agreement with experimental data on settling of a bimodal mixture of spherical solid particles.     

DSMC prediction of granular temperatures of clusters and dispersed particles in a riser

Flow behavior of gas and particles in a CFB riser is simulated by a Euler-Lagrangian approach. Collisional interaction of particles is modeled by a direct simulation Monte Carlo (DSMC) method. The coefficient of restitution depends on the relative velocity between two particles by taking into account both the viscoelastic and plastic deformations of particles. The Newtonian equations of motion are solved for each simulated particle in the system. The interaction between gas phase and simulated particles is determined by means of Newtonian third law. A criterion proposed by Soong et al. [C.H. Soong, K. Tuzla, J.C. Chen, Experimental determination of clusters size and velocity in circulating fluidized beds, in: J.F. Large, C. Laguerie Eds., Fluidization VIII Engineering Foundation, New York, 1995, pp. 219-227.] is used to obtain information of clusters. A model for the determination of the number of particles inside a cluster is proposed from kinetic theory of granular flow. The flow behavior of clusters and dispersed particles in the riser is numerically predicted. Distributions of granular temperature of clusters and dispersed particles are computed from velocity distributions. The upward moving clusters give a high granular temperature in comparison to the downward moving clusters. The granular temperature of the dispersed particles is an order of magnitude larger than that of the clusters. The computed collision frequencies of dispersed particles and clusters from DSMC are lower than those from kinetic theory of granular flow.     

Nanomechanical characterization of single micron‐sized polymer particles

The mechanical characterization of single micron‐sized polymer particles is very important for understanding the anisotropic conductive adhesives interconnection. In this article, a nanoindentation‐based flat punch method was employed to investigate the mechanical properties of single polymer particles. A diamond flat tip, instead of a commonly used sharp tip for indentation, was specially designed to deform single polymer particles. The maximum applied load is 10 mN and the linear loading/unloading rate is 2 mN/s. Two types of amorphous polymer particles were examined. The polymer particles display significantly different stress–strain behaviors. The material responses at different strain levels were analyzed and compared. A particle size effect, the smaller the diameter, the harder the particle, on the compression stress–strain behavior, was observed. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

An Experimental Investigation for Agglomeration of Aerosols in Alternating Electric Fields

Electrostatic precipitators have a relatively low efficiency for the collection of submicron particles. One way to increase their efficiency is to enforce the agglomeration and thereby form larger particles. In this work, a study has been initiated for enhancing the agglomeration between oppositely charged particles by using an alternating electric field to increase the relative motion between such particles. A simple first order computer model was developed for establishing the magnitude of agglomeration and for characterizing the interdependence of different parameters of importance. A laboratory experimental unit was established for studying various practical configurations for agglomeration in alternating electric field, using finely dispersed limestone powder. For the measurements of particle size distributions, a Berner Low Pressure Impactor was used. The preliminary results have shown a 50% reduction in the mass concentration of submicron particles, for oppositely charged particles in an alternating electric field. On the other hand, no agglomeration was measured by the use of a quadrupole field.     

Thermophoretic acceleration of particle deposition from laminar air streams

A preliminary study is reported of the use of temperature gradients to accelerate the deposition of small particles from laminar air streams. It is shown that appreciable effects can be obtained even with small temperature gradients and particles as large as 30 μm. An empirical correlation is proposed for the thermophoretic force based on the present results and those published previously for smaller particles.     

A Model of Controlled Release of Polymer-dispersed Drug Systems Containing Regulatory Particles

Abstract

A model of controlled release systems using a polymer matrix with mixtures of dispersed drug particles and regulatory particles is considered. The regulatory particles are fillers that release at a slower rate than the drug and open more paths for the passage of the drug. Mathematical analysis shows that both the drug and regulatory particles have Fickian diffusion behaviors. The use of regulatory particles increases the release rate and can make the system responsive to physiological change.     

Role of bed height and amount of dust on the efficiency of sound‐assisted fluidized bed filter/afterburner

A 40‐mm sound‐assisted fluidized bed filter/afterburner for hot gas clean‐up has been characterized in terms of bed saturation time, total amount of collected particles, fraction of fine particles permanently adhered on the coarse bed particles, and efficiency of using a regeneration strategy based on mechanical (attrition) and/or chemical (combustion) action. Experiments have been carried out at ambient temperature as well as at 850°C, with and without application of sound and varying bed height and amount of dust in the gas flow. The controversial effect of the application of sound: not only enhancement of particles interactions but also increase of fines permanently adhering on bed coarse particles is presented and discussed. A simplified model has been developed to obtain rough predictions of bed height which maximize fine particles capture, bed saturation time, total amount of particles collected in the bed, fraction of fine particles loading present as adhered particles on bed particles. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Rational design of metal mesh particles for biological fluidized bed reactors

Utilization of metal mesh particles as a support material in biological waste treatment and fermentation technology offers special advantages over other immobilization methods. A theoretical analysis of fluidized bed bioreactors utilizing metal mesh support particles is presented and optimization of important parameters for rational design of metal mesh particles is discussed.     

A Model of Deposition of Hygroscopic Particles in the Human Lung

Many aerosols in the environment are hygroscopic and grow in size once inhaled into the humid respiratory tract. The deposited amount and the distribution of the deposited particles among airways differ from insoluble particles of the same initial diameter. As particles grow in size, diffusive behavior tends to diminish while impaction and sedimentation effects increase. A multiple-path model for deposition of hygroscopic particles in the respiratory tract was developed for symmetric and asymmetric lung geometries by implementing particle size change in a model of insoluble particle deposition in lungs. Particle growth by molecular diffusion of water vapor to the particle surface was formulated. The growth model included temperature depression, solute, Kelvin, and Fuchs effects. Particle growth during travel time in each lung airway was computed. Average loss efficiency per airway was calculated by incorporating contributions from particles of various sizes acquired in that airway. A mass balance on the number of particles that entered, exited, deposited, or remained suspended was performed per airway to obtain regional and local deposition fractions of particles in the lung. The deposition fractions calculated for salt particles showed a drop for submicrometer particles in the tracheobronchial region and a significant increase in deposition for micrometer particles or larger. Consequently, very few fine and coarse salt particles reached the alveolar region to be available for deposition. Overall, lung deposition of ultrafine particles decreased for salt particles. Deposition for fine and coarse salt particles in the lung was larger than that of insoluble particles of the same initial particle size.     

Entrainment behaviour of high-density Geldart A powders with different shapes

Atomised and milled Ferrosilicon with average particle diameters of 38 and 50 µm respectively were fluidised with air at ambient conditions. The entrainment rate of the more spherical atomised particles was on average six times that of the irregularly shaped milled particles over the range of superficial velocities investigated. In an attempt to decouple the effect of particle size from shape, the bed was divided into theoretically isolated bins based on the distributions of particle sizes. This indicated that the atomised particles had a higher entrainment rate for particles smaller than approximately 25 µm whereas the opposite was true for particles greater than this size. None of the entrainment correlations investigated was able to predict the switch in entrainment behaviour as a function of particle sphericity and diameter. Furthermore, the traditional critical particle diameter associated with cohesive Geldart A particles was not observed for either of the two particle shapes. It is therefore concluded that neither the hydrodynamic nor Van der Waals forces acting on the particles can adequately explain the entrainment rate behaviour of differently shaped high-density Geldart A particles.     

An Electrostatic Lens for Focusing Charged Particles in a Mass Spectrometer

The ability to transmit particles into the ablation region of an aerosol mass spectrometer determines in part the lower size limit for particles that can be analyzed. A large fraction of small particles (< 100 nm) are lost due to processes such as Brownian diffusion that broaden the particle beam. In this work, electrostatic focusing is used to overcome the limits of aerodynamic focusing in the analysis of nanometer-sized particles by aerosol mass spectrometry. A simple tube lens is used to focus charged particles into the ablation laser beam path. The diameter of the focused beam is smaller than the fundamental aerodynamic limit imposed by Brownian motion. Measured enhancements of the hit rate for particles between 21 and 33 nm diameter are between 3 and 6. These values are lower limits for the true enhancements. The lens is also energy selective and can be used to select the mass (size) of the particles being analyzed.     

Effective packing of 3-dimensional voxel-based arbitrarily shaped particles

In many research areas including medicine and paper coating, packing of particles together with numerical simulation is used for understanding important material functionalities such as optical and mass transfer properties. Computational packing of particles allows for analysing those problems not possible or difficult to approach experimentally, e.g., the influence of various shapes and size distributions of particles. In this paper a voxel-based algorithm by Jia et al. [X. Jia, R.A. Williams, A packing algorithm for particles of arbitrary shapes, Powder Technology 2001, vol. 120, pp. 175-186.] enabling the packing of arbitrarily shaped particles, is memory- and speed-optimised to allow for simulating significantly larger problems than before. Algorithmic optimisation is carried out using particle shell area reduction decreasing the amount of time spent on collision detection, fast rotation routines including lookup tables, and a bit packing algorithm to utilise memory effectively. Presently several hundreds of thousands of complex arbitrarily shaped particles can be simulated on a desktop machine in a simulation box consisting of more than 10⁹ voxels.     

The influence of particle size on the flow of initially fluidised powders

When particles are allowed to move over a horizontal surface, the effect of gas flow through them is to increase the distance over which they move, termed their mobility. This has already been shown for cases when gas is continuously passed through a current of particles, but this investigation shows that this is also true when the gas flow is only initially present. Experiments were conducted on a column of fluidised particles that were released into an enclosed channel by the removal of a wall, and the distance travelled by the particles was measured. The behaviour of fine particles (group A in the Geldart classification of fluidised particles) was distinct from that of larger particles.The mobility was modified when they were mixtures of different-sized particles. In particular, when there was no gas flow, the mobility was a maximum when the proportion of fine particles was 30% and the magnitude of this effect increased with the size of the coarser component of the mixture. All the different mixtures of particles acted in a similar manner with increasing mobility for a given gas flow rate with proportion of fine particles until roughly half the mixture was composed of fine particles, and there was then no further increase.