SEDIMENTATION OF BINARY MIXTURES OF PARTICLES OF UNEQUAL DENSITIES AND OF DIFFERENT SIZES

A model is developed for the sedimentation from a suspension of two particle species of unequal densities and of different sizes. The composition and the thickness of various layers in the sediments are predicted using graphical and analytical methods. The model predictions were in excellent agreement with experimental results, when the particle size ratio was ≥ 108. When size ratio of the particles was 2.60 and 4.31 the agreement occurred in about 50 percent of the cases.     

EFFECT OF PARTICLE SIZE AND INDEX OF REFRACTION ON REFLECTANCE*

The effect of particle size on the reflectance of thin semitransparent layers, such as enamels, was studied by using mixtures containing opacifying particles of definite sizes in an oil of known index of refraction. The mixtures were applied on a black glass plate, and the reflectance was measured. The coefficient of scatter per unit surface of the particles was calculated and was found to decrease slowly as the particle size decreased. On the other hand, for the range of sizes studied, the reflectance of the semitransparent layer increased rapidly as the particle size decreased.     

Effects of Particle-Size Distribution in Initial-Stage Sintering

Diffusion models for the initial-stage sintering of spherical particles were developed for distributions of particle sizes. A linear array of particles with different sizes was treated quantitatively; number, rather than weight, distributions are considered directly to permit summation of particle-pair interactions. Evaluation of a single particle size which will characterize the equivalent shrinkage of the distributed array of random particles yields a size much smaller than that which would designate the division at 50 wt% finer conventionally used. Also, the effective size is smaller for the lattice-diffusion model than for the grain-boundary-diffusion-controlled model. The results show that the rates for binary mixtures are intermediate between the behaviors of the end-member sizes, in accordance with previous experimental findings. A square array of equal spheres with contacting interstitial spheres was also analyzed. Coherent shrinkage requires a retardation of shrinkage along the diagonal contacts (due to tensile loads). Procedures for evaluating the stress transfer were generated for this and similar particle packings. The calculated shrinkage rate is again intermediate between that predicted from previous models and the end-member sizes.     

EFFECTIVE THERMAL CONDUCTIVITY OF BINARY MIXTURES AT HIGH SOLID TO GAS CONDUCTIVITY RATIOS

The effective thermal conductivity of single size and binary mixtures of packed particle beds with stagnant gas at high solid/gas conductivity ratios is determined by a deterministic, unit cell approach. The model results are shown to be in good agreement with experimental data for various gas pressures and solid to gas thermal conductivity ratios up to 1300. A set of correlations for effective conductivity of binary mixtures as a function of gas pressure and particle size is derived. The effect of particle swelling on the effective conductivity of binary mixtures is studied by performing a parametric study of the contact area between the particles     

用无形孔模型研究影响煤粉燃烧的因素

用一种新的孔隙结构模型──无形孔模型来研究影响煤粉燃烧的因素。对该模型进行数值计算，跟踪燃尽过程中温度、氧浓度、燃烧速率等随时间的变化，得到有关曲线。定量探讨整个煤粒内部的燃烧过程。研究挥发分析出和燃烧对煤粉燃烧过程的影响。研究孔隙率、比表面积、粒径等因素对煤粉着火、燃尽的影响。结果表明孔隙率对燃尽的影响较大，而比表面对着火的影响较大。     

The Sedimentation of Bimodal Distributions of Unflocculated Microspheres

Abstract

An improved analysis for sedimentation of binary mixtures (two particle sizes) is proposed and tested with data that include differences in both the particle sizes and densities and sedimentation in both the viscous region and the transitions region, between viscous and turbulent (inertial flow). The new analysis can be used for any ratio of particle sizes even when the particle sizes are relatively close. It has been successfully tested beyond the viscous region and with variations in particle density as well as particle size. Although one previous analysis has been successful in predicting most earlier binary data with particles of different size, the new analysis is believed to be better supported by physical principles and thus more reliably extrapolated to different conditions.     

Radial porosity distribution in cylindrical beds packed with spheres

Experimental determinations of radial porosity for cylindrical beds packed with spheres are reported. The data indicate that, for a wide range of bed and sphere sizes, porosity varies significantly and regularly near the container wall. For uniformly sized spheres, the oscillations in porosity can be detected up to a distance of about 5 particle diameters from the wall. For mixtures of spheres of two sizes, regular oscillations are detected only up to 2 or 3 diameters from the wall and for three sizes the effect of the wall is observed only within a distance of 1 particle diameter.     

PREDICTION OF A GAS-PARTICLE TURBULENT JET WITH THE FLUCTUATION-SPECTRUM-RANDOM-TRAJECTORY MODEL

A numerical treatment for determining the particle velocity and the trajectories in a two-phase flow is described herein and this new fluctuation-spectrum-random-trajectory (FSRT) model is proposed to account for the turbulent diffusion of particles. It is predicted for the flow of a turbulent axisymmetric gaseous jet laden with spherical solid particles of nonuniform size. The particle velocity and the concentration field are obtained by the revised volume average method. The predictions are compared with experiment.     

A one-dimensional plug-flow model of a counter-current spray drying tower

A one-dimensional numerical model for a detergent slurry drying process in a counter-current spray drying tower is developed for the prediction of the gas and droplet/particle temperature profiles within the tower. The model accommodates droplets/particles over a range of sizes. A semi-empirical slurry droplet drying model is integrated with a counter-current tower simulation based on mass, energy and particulate phase momentum balances in order to calculate the drying rate and the particle residence time within the tower. The coupled first order ordinary differential equations for the two phases are solved numerically using the iterative shooting method in an algorithm developed within MATLAB. The predictions of the numerical model are compared with industrial pilot plant data. The results are found to vary significantly with the specified size distribution of the droplets. Despite the simplicity of the model in ignoring the coalescence, agglomeration, wall deposition and re-entrainment, the model gives reasonable agreement with the experimental data.     

Kinetics of photocatalytic degradationof methylene blue over TiO2 particles in aqueous suspensions

The kinetics of photodegradation of methylene blue over UV light illuminated titania particles in aque-ous suspensions has been studied with different initial methylene blue concentrations and TiO_2 particle sizes.Thedegradation rate increases with the decrease of initial concentration and particle size.A quasi-experienced modelfor photodegradation rate is derived based mainly on the coinstantaneous effects of different initial concentrationsand partic1e sizes.The mathematica1 re1ationships of model parameters with initia1 concentration and particle sizeare given.The model results of the photodegradation rate of methylene blue are coincident with the experimentaldata.     

Wind tunnel study and numerical simulation of dust particle resuspension from indoor surfaces in turbulent flows

Particle resuspension from flooring is an important source of air pollution in the indoor environment. In this work, resuspension of monolayer, polydisperse, irregularly shaped dust particles from various types of floorings was studied via a series of wind tunnel experiments. The range of free-stream velocity needed for resuspension of dust particles was evaluated as a function of particle size and material of particles and surfaces. In addition, a Monte Carlo simulation for predicting the resuspension of dust particles was developed. The resuspension model took into account the effects of particle irregularity, particle surface roughness, and flow characteristics. The dust particle resuspension from different floorings for several particle sizes was evaluated. The model predictions for resuspension fractions were compared with the experimental data and good agreement was observed. The study provided information on the role of airflow velocity on irregular dust particle resuspension from common floorings.     

Polymer powders mixing part II: Multi-component mixing dynamics using RGB color analysis

In this work, the mixing quality of a multi-component blend of particles is determined using Multivariate Image Analysis of RGB images combined with the Grey Level Co-occurrence Matrix (GLCM) texture analysis. The mixing dynamics and flow behavior are studied in terms of mixing homogeneity and time to achieve equilibrium for binary, ternary and quaternary mixtures of equal size particles. The parameters studied are rotational speed, filling ratio, initial powder composition and particle sizes. Using the experimental data in the rolling regime, a second order model is proposed to predict the mixing curve as a function of time.     

Measurement of coal particle size and shape with concentrated coal-water mixtures

The behavior of concentrated coal-water mixtures having narrow particle size ssfractions of coal was investigated. The pulverized coal was fractionated into six distinct particle size ranges, i.e. -70+80, -80+120, -120+140,-140+200, -200+400 and -400 mesh sizes by using a series of sieves. Settling rates were determined as functions of solids concentration for suspensions in water of coal particles to establish the measurement of particle size and shape factor and to assess concentration effect upon the observed hindered settling rates. The settling rates were modelled using the Richardson-Zaki model with the exponent n variable to account for the nonspherical shape of the coal particles. The data was also correlated with the Michaels-Bolger model which explicitly account for the excess water which is dragged down along with the particles undergoing sedimentation. In addition, coal particles and suspensions were characterized by coal analysis, heating value, solid heat capacity and thermal conductivity, densities, maximum packing concentrations and pore size distributions.     

Ultrasonic technique to determine particle size and concentration in slurry systems

Acoustic velocity measurements have been used to estimate particle size and concentration in liquid-solid (LS) and gas-liquid-solid (GLS) systems. The slurries of 34 and particles and their binary mixtures in distilled water are tested in concentration range 2-10 vol% in batch operations. In GLS systems, the superficial gas velocity is varied from 0.03 to 0.10 m/s. The presence of gas bubbles affected the acoustic velocity measurements significantly. A data filtration procedure is developed to minimize the effect of gas phase and estimate variations in gas-free liquid-solid region. The filtered data are used to predict concentration using calibration equations and theoretical velocity prediction models of LS systems. The estimated concentrations are comparable with sedimentation-dispersion model predictions in GLS system. This technique is also used to predict average particle size and composition in binary mixtures of particles.     

Effects of particle size on microstructure and mechanical strength of a fly ash based ceramic membrane

Recycling fly ash for ceramic membrane fabrication not only reduces solid waste discharge, but also decreases the membrane cost. Now, fly ash is becoming a promising substitute material for ceramic membrane preparation. A significant difference between fly ashes from different plants is the particle size, which makes performances of fly ash membranes unpredictable. The novelty of this work is to clarify the effects of the particle size of fly ash on ceramic membranes, thereby giving practical suggestions on fly ash selection for ceramic membrane preparation. Ceramic membranes were fabricated with different sizes of fly ashes. Effects of particle size on porosity, pore size, microstructure, mechanical strength and gas permeability of the membrane were investigated. Results indicate that a broader particle size distribution of fly ash leads to a denser structure of membrane with a lower porosity. Pore size and gas permeability of membrane increase while bending strength decreases with the particle size increasing. Bending strength of a fly ash membrane is largely determined by large particles in the fly ash because the large particles lead to cracks in the membrane. This work provides experimental bases for developing high performance ceramic membranes from fly ash.     

TURBULENCE CLOSURE MODELING OF TWO-PHASE FLOWS

A second order turbulence closure model is developed for the numerical prediction of isothermal non-reacting, two-phase turbulent shear flows. This model is based on the two-equation (k - ?) model but treats the continuous (gas) phase and (solid) particulate phase as separate interacting continua. The presence of the particles will increase the dissipation rate in the gas phase and additional terms based on the particle size and loading are added to the traditional k and ? equations. The model is tested by making predictions of the spreading rate and velocity decay in the developing region of the two-phase axisymmetric jet. The predictions agree favorably with available experimental data in this region.     

Calculation of the hindered settling velocity of a bimodal mixture of solid particles of arbitrary shape in a Newtonian fluid

A method for calculating the settling velocity of a bimodal mixture of particles of arbitrary shape is proposed. The method uses the concept of effective particle diameter, which characterizes the particle shape, volume, and midsection area. The method takes into account the contact interaction between particles of different sizes due to their collisions. The calculation results are compared with experimental data on settling of bimodal mixtures of limestone particles of arbitrary shape.     

Experimental testing of the hydrodynamic collision model of fine particle flotation

Flotation rates of glass beads and of latex particles have been measured as a function of particle size using very small bubbles. With glass beads the observed rate versus size relationship agreed quite well with the prediction of a simple hydrodynamic collision model, but that found with latex particles did not. It is suggested that electrical forces may have to be taken into account when the particles have a significant zeta potential. With both types of particle, the relationship between flotation rates measured at two different bubble sizes is consistent with the model's predictions.     

Predicting the effective thermal conductivity of polydispersed beds of softwood bark and softwood char

In this paper, the effective thermal conductivity (ETC) of softwood bark and softwood char particle beds which are highly polydispersed has been studied theoretically and experimentally. Use of the linear packing theory and unit cell model of heat conduction enabled to express ETC of polydisperded beds as a function of particle size distribution. Each of the softwood bark and softwood char samples were sieved into seven fractions. The initial porosity and binary packing size ratio of the particles have been characterized as a function of mean sieve size. ETC of polydispersed beds of bark and char has been predicted as a function of particle size distribution. Model predictions were in good agreement with the experimental measurements. The proposed approach can be used to predict the ETC of any size distribution of softwood bark and softwood char beds without measuring the in situ bed porosity.