Dependence of Compaction Efficiency in Dry Pressing on the Particle Size Distribution

The compact densification with pressing pressure (compaction efficiency) was determined to be sensitive to the particle size distribution. For the three types of alumina powders used in this research, the compaction efficiency increased with increasing particle size. It has been demonstrated that if the compact density versus log (pressure) has a linear relationship for any two types of powders, so do the blends of the two powders. A model is proposed which can predict the compaction efficiency of a binary particle system based on the Furnas particle packing model and consider the packing efficiency as a function of forming pressure. The composition of the binary mixture at which the highest density is obtained under high pressures is also the composition having the largest compaction efficiency. When coarse particles were added to this composition, the compaction efficiency slowly decreased, and when fine particles were added, the compaction efficiency rapidly decreased. For a continuous particle size distribution, the highest compaction efficiency is related to the average value of -log (porefraction).     

提高粉体堆积密度的理论与实验研究

以Andreason理论和可压缩堆积模型为基础,对水煤浆颗粒进行了调质计算和堆积效率计算,通过实验验证了计算结果的准确性,探讨了粒度范围和添加量等因素对堆积效率的影响.结果表明,通过调质可以实现煤粉粒度分布的优化,使其尽可能靠近紧密堆积理论所规定的粒度分布特征;用可压缩堆积模型可以很好地预测粉体颗粒的堆积密度,经过调质后原料的堆积效率提高了6.0％;紧密堆积条件下,增大水煤浆颗粒粒度范围有利于提高其堆积效率;随着调质料的增加,系统堆积效率增大,且逼近紧密堆积条件下的堆积效率;只添加细粉时,堆积效率与原料的粒度组成相关.     

Improved Equation of the Continuous Particle Size Distribution for Dense Packing

The Furnas model describes the discrete particle size distribution for densest packing. Using a model that considers a continuous particle size distribution for the densest packing to be a mixture of infinite Furnas discrete particle size groups, an equation for the cumulative particle size distribution providing the densest packing was derived. Monosize particles with different shapes have a different packing pore fraction. One parameter in the equation is the pore fraction of packed monosize particles; the particle size distribution for achieving densest packing is a function of this pore fraction. A reduced form of this equation is also presented as a working equation. The equation derived here is compared to the modified Andreasen equation for dense packing. An equation and the correlated graph for calculating theoretically the geometric mean particle size and an equation for calculating the specific surface area of the particle size distribution of the improved equation are also derived.     

The effect of particle size distribution on packing density

The packing density of a multi-particle system is found to increase if the particle size distribution is extended. Results are reported for Gaussian and log-normal size distributions using dense random packing of two sands with particle sizes of front <0.07 to 8.0 mm. Packing density is shown to be a function only of size distribution represented by a dimensionless standard deviation, and of particle shape. It is independent of particle size. Packing densities of binary mixtures of continuously distributed systems are found to depend upon the composition of the mixture, the mean-size ratio of the components of the binary, and upon the packing density of the individual components. Maxima occur at compositions of 55 to 75% larger component, and increasing mean-size ratios result in greater packing densities. The “increase in packing density” factor is a useful function for comparing, and setting limits to, packing densities of binary mixtures. The results should allow improved prediction and control of packing densities of many commonly encountered particle systems.     

Packing Density of Composite Powder Mixtures

A model of particle packing in binary composite systems is developed. The effects of both inclusion surfaces and touching inclusions on the packing density are taken into account. To implement the model, a statistical approach is used to determine the number of inclusion contacts as a function of inclusion content. The statistical approach indicates that the average number of inclusion contacts is a linear function of the inclusion volume fraction, a result which agrees very well with independent computer simulations. The model suggests that the packing efficiency, defined by the ratio of the packing density to the ideal packing density (as originally derived by Furnas), is governed by the inclusion volume fraction ( f_i ) and the particle to inclusion size ratio ( r ). Good agreement is obtained between the theory and experimental literature data.     

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.     

A moment model for simulating raindrop scavenging of aerosols

The dynamics of a polydispersed aerosol size distribution, scavenged by precipitation, are numerically studied. The collision efficiency formula proposed by Slinn (Precipitation Scavenging in Atmospheric Sciences and Power Production—1979, Division of Biomedical Environmental Research, US Department of Energy, Washington, DC, USA, 1983, Chapter 11) and the moment method were introduced to represent the particle removal mechanism by raindrops and the aerosol size distribution, respectively. Consequently, the dynamics of the particle size distribution were reduced to a set of ordinary differential equations using the moment approach. A generalized raindrop distribution, including two widely used distributions; the Marshall–Palmer (MP) and Krigian–Mazin (KM) raindrop distributions, was adopted.Our model results have shown that raindrops with smaller diameters, and narrower distributions, collect aerosols more efficiently. Further, it was shown, in the small particle size region that the geometric mean diameter increases, while in the large particle region it decreases. For the two size ranges, the geometric standard deviations decrease with time, and a scavenging gap, the minimum particle removal efficiency region, exists between these particle size ranges.The dynamics of the particle size distributions, the MP and KM raindrop distributions, in the small particle range, show that the effects of the overestimation in the MP distribution were not as great as expected. Also, this study ascertained that the conventional parameterization of the constant collision efficiency introduces significant errors for estimating the particle size distribution dynamics by wet scavenging.     

Yodel: A Yield Stress Model for Suspensions

A model for the yield stress of particulate suspensions is presented that incorporates microstructural parameters taking into account volume fraction of solids, particle size, particle size distribution, maximum packing, percolation threshold, and interparticle forces. The model relates the interparticle forces between particles of dissimilar size and the statistical distribution of particle pairs expected for measured or log-normal size distributions. The model is tested on published data of sub-micron ceramic suspensions and represents the measured data very well, over a wide range of volume fractions of solids. The model shows the variation of the yield stress of particulate suspensions to be inversely proportional to the particle diameter. Not all the parameters in the model could be directly evaluated; thus, two were used as adjustable variables: the maximum packing fraction and the minimum interparticle separation distance. The values for these two adjustable variables provided by the model are in good agreement with separate determinations of these parameters. This indicates that the model and the approximations used in its derivation capture the main parameters that influence the yield stress of particulate suspensions and should help us to better predict changes in the rheological properties of complex suspensions. The model predicts the variation of the yield stress of particulate suspensions to be inversely proportional to the particle diameter, but the experimental results do not show a clear dependence on diameter. This result is consistent with previous evaluations, which have shown significant variations in this dependence, and the reasons behind the yield stress dependence on particle size are discussed in the context of the radius of curvature of particles at contact.     

Numerical simulation and experimental study of the characteristics of packing feature size on liquid flow in a rotating packed bed

Rotating packed bed has high efficiency of gas–liquid mass transfer. So it is significant to investigate fluid motion in rotating packed bed. Numerical simulations of the effects of packing feature size on liquid flow characteristics in a rotating packed bed are reported in this paper. The particle image velocimetry is compared with the numerical simulations to validate the turbulent model. Results show that the liquid exists in the packing zone in the form of droplet and liquid line, and the cavity is droplet. When the radial thickness of the packing is less than 0.101 m, liquid line and droplets appear in the cavity. When rotational speed and radial thickness of the packing increase, the average diameter of the droplets becomes smaller, and the droplet size distribution becomes uniform. As the initial velocity of the liquid increases, the average droplet diameter increases and the uniformity of particle size distribution become worse. The droplet velocity increases with the radial thickness of the packing increasing, and gradually decreases when it reaches the cavity region. The effect of packing thickness is most substantial through linear fitting. The predicted and simulated values are within ±15%. The cumulative volume distribution curves of the experimental and simulated droplets are consistent with the R-R distribution.     

The influence of particle size distribution of some manganese dioxide on practical zinc chloride cell performance

The influence of particle size distribution of manganese dioxide on performance of a zinc chloride cell on continuous discharge and intermittent discharge was studied, using I.C.S. No. 1 (emd), No. 7 (nmd) and No. 12 (cmd). The fine particle nmd showed not only better MnO₂ utilization efficiency but also better cell capacity than the course one, which was considered to be due to the different discharge mechanism of the fine particle nmd from that of the coarse particle nmd. In the case of emd, the fine particle MnO₂ showed better MnO₂ efficiency than the coarse particle one, however, the performance of the fine particle cell was not improved because the fine particle MnO₂ needed more electrolyte than coarse particle MnO₂ did and, as a result, the packing density of the fine particle emd at the maximum MnO₂ utilization efficiency was much lower than that of the coarse particle emd. The influence of particle size distribution of cmd on discharge performance was negligible.     

Filler tolerance of dispersion resins: An analysis of oil absorption and particle size effects

Plastisol rheological characteristics are of prime importance to the formulator and processor. As the formulas become more complicated, interactions can occur between ingredients that have significant effects on rheology. This paper explores aspects of the resin-CaCO₃ filler interaction. Experiments investigating some of the effects of resin-filler interaction on rheological behavior have been performed. The experiments indicate that particle size distributions of the resin and filler, as they relate to packing efficiency, have a significant effect on rheological behavior, especially at high filler concentrations. The effects of particle packing vs. oil absorption are also investigated and discussed.     

Prediction for particle removal efficiency of a reverse jet scrubber

Numerical computation was conducted to predict the collection performance of a reverse jet scrubber for polydisperse particles. The particle size distribution of polydisperse particles was represented by a lognormal function, and the continuous evolution of the particle size distribution in a reverse jet scrubber is taken into account with the first three moment equations. Numerical results were compared with the analytic results using average relative velocity in all zones and experimental results.

In a reverse jet scrubber, the impaction is the main particle collection mechanism because of high relative velocity and short collection time. The particle collection by impaction increases with an increase in particle size, and geometric mean diameter and geometric standard deviation decrease as time goes on. High droplet velocity and gas velocity increase the particle collection efficiency, and the small droplet size also increases the collection efficiency because smaller droplet size provides broader surface area. The packing density is a factor affecting particle collection efficiency in a scrubbing process. The dense packing density also provides large surface area and leads to high collection efficiency.     

Cleaning of fine coals by dense-medium hydrocyclone

The efficiency of separation for fine coal in a 150 mm dia. dense-medium hydrocyclone has been determined. The partition curves have been measured for particles in the size ranges −500 μm +425 μm, −300 μm +250 μm, −150 μm +125 μm and −90 μm +75 μm. The cut point for separation increases with a decrease in particle size and the efficiency of separation decreases as particle size decreases. The cut point of separation varies with medium specific gravity but the efficiency of separation does not. Neither the cut point of separation nor the efficiency of separation is greatly influenced by the cyclone feed rate, provided that overloading does not occur.

The results lead to an accurate predictive model for the calculation of the partition curve as a function of coal particle size and medium specific gravity. The model allows the prediction of the performance of a dense-medium hydrocyclone for the washing of fine coal having arbitrary washability characteristics and particle size distribution. The model is used to demonstrate that a two-stage dense-medium hydrocyclone configuration can significantly improve the cleaning performance for a coal that has good ash-liberation characteristics. However, multi-stage dense-medium hydrocyclones do not offer any real performance advantages for coal that has poor ash-liberation characteristics.     

Model for the Effect of Powder Packing on the Driving Force for Liquid-Phase Sintering

A model for liquid-phase sintering is presented that explicitly considers the effect that the pore size distribution of the sintering compact has on the capillary forces that drive densification. In particular, the effect that liquid redistribution in the pore structure has on the driving force for sintering is considered under the assumption that the liquid can easily move to find a low-energy configuration in the pore structure. It is shown that, for a powder compact that has a narrow pore size distribution, densification exhibits approximately the same time dependencies as those predicted by the Kingery model for liquid-phase sintering. However, systematic changes in the absolute densification rate with the volume fraction of liquid, and the mean and breadth of the pore size distribution, are predicted. With more extreme pore size distributions, such as a bimodal distribution, behavior significantly different from that predicted by Kingery is found. In particular, it is predicted that, without there being a change in sintering mechanism, abrupt changes in densification rate may occur if the peaks in the bimodal distribution are well separated. The model provides a rational basis for interpreting how powder packing and processing steps can influence densification by liquid-phase sintering.     

Development and evaluation of an expression for polydisperse particle scavenging coefficient for the below-cloud scavenging as a function of rain intensity using the moment method

An analytical expression for wet scavenging coefficient for below-cloud scavenging that is function of collision efficiency, raindrop terminal velocity, raindrop size distribution, and particle size distribution is obtained and tested. The parameters of raindrop size distribution are related with rain intensity since rain intensity can be easily measured. Then, the moment method is applied to the expression for scavenging coefficient to derive an analytical expression. Two widely used raindrop size distribution, Marshall-Palmer and lognormal distributions are considered and lognormal particle size distribution is assumed. The derived scavenging coefficient expression is applied to three model environments, urban, rural, and desert to demonstrate its applicability.     

New fast integrated mobility spectrometer for real-time measurement of aerosol size distribution—I: Concept and theory

A new instrument capable of measuring aerosol size distribution with high time and size resolution, and high signal-to-noise ratios is described. The instrument, referred to as Fast Integrated Mobility Spectrometer (FIMS), separates charged particles based on their electrical mobility into different trajectories in a uniform electric field. The particles are then grown into super-micrometer droplets, and their locations on the trajectories are recorded by a fast charge-coupled device (CCD) imaging system. Images captured by the CCD reveal mobility-dependent particle positions and their numbers, which are then used to derive a particle size distribution spectrum. By eliminating the need to scan over a range of voltages, FIMS significantly improves the measurement speed and counting statistics. A theoretical framework has been developed to quantify the measurement range, mobility resolution, and transfer function of FIMS. It is shown that FIMS is capable of measuring aerosol size distributions with high-time and size resolution.     

Theoretical development of a graphical analysis technique to optimize the particle size distribution of pigments in paints and coatings

The new analytical expression introduced in this study shows that a plot of the accumulated volume fraction of pigment particles vs. the square root of particle size should be a straight line for the theoretically preferred particle size distribution. This linear theoretical model was also found to be consistent with the experimentally developed linear model proposed by Kaeuffer. However, Kaeuffer proposed that his straight line went through the origin, but the analytical model developed in this paper has shown that this intercept is not zero. Thus, Kaeuffer’s experimental model is only partially correct. Starting with this new linear model for the theoretically preferred particle size distribution, another simplified analytical expression was also derived to calculate the xth moment average particle size, . The desired xth moment average particle size was found to depend primarily on the physical property to be predicted. Finally, the simplified calculation of the various particle size averages for this same square root particle size distribution should be useful in predicting the maximum packing fraction, maximum impact, and/or the minimum viscosity for pigments in most paint and coating applications. 102 Rue Le Bois, Lafayette, LA 70508.     

Investigation of particle packing in model pharmaceutical powders using X-ray microtomography and discrete element method

This paper outlines a novel technique, based on combination of modern desktop X-ray microtomography, quantitative image processing and computer simulation using the discrete element method (DEM), to investigate randomly packed particles in an attempt to model the process of pharmaceutical tablet manufacture by powder compaction. The systems studied include glass ballotini and spheroidal micronised cellulose (Celphere), all with typical particle sizes between 180 and 300 μm. We demonstrate that X-ray microtomography (XMT) and DEM can reproduce the structure of real packing systems in three-dimensions and have the potential for further investigation of pharmaceutical processes by both modelling and experimental study. This was achieved by generating packing systems using DEM simulations that are consistent with the structural measurements made by XMT on real packed powders via the comparison of their radial distribution functions (RDFs). These results have been validated by direct volume measurements, and scanning electron microscopy (SEM) observations in terms of particle morphologies and size distribution. The result is a significant step forward for the quantitative analysis of model systems for pharmaceutical powders.