Porosity Calculation of Binary Mixtures of Nonspherical Particles

An investigation has been made of the packing of binary mixtures of either spherical or nonspherical particles. It is shown that this binary packing system can satisfactorily be described by the Westman equation. By use of the concept of "equivalent packing diameter," nonspherical particle packing may be related to spherical particle packing. The porosity of binary mixtures of nonspherical particles can then be predicted by means of a model developed for spherical particles. This approach is verified by the good agreement between the calculated and experimental results.     

Characterization of packing structure of tape cast with non-spherical natural graphite particles

A three-dimensional microstructure of green and pressed tapes cast with graphite particles of non-spherical shape were examined quantitatively on the basis of the distribution of void sizes among the packed particles. The distributions measured over the cross-sections of the tape in three directions were expressed by the theoretical ones deduced for non-spherical particles. Particle shape was characterized by shape indices defined by Fourier analysis of particle outlines measured over the corresponding cross-sections of the green tape. The relationships were totally established between the limiting packing density, characterizing the void size distribution at the same section voidage, and the shape index of particle over the section. As a result, the normalized median void diameter as well as the limiting packing density of the pressed tape was found to increase with the particle shape index, corresponding to wider void size distribution. Therefore, based on developed correlations, the optimization of packing microstructure of the cast tape can be expected to result in high performance battery by using shape-modified graphite particles.     

A fast algorithm for mass transfer on an unstructured grid formed by DEM particles

The Discrete Element Method (DEM) was used to generate a particle packing and transient mass transfer in the particle layer was simulated using a novel algorithm for determining the mass fluxes between DEM particles. This method is intended for simulating diffusion phenomena occurring during the dissolution of swelling polymers as the DEM particles can change size and distort the grid, whilst maintaining sharp boundaries between mesh elements. In this work, the robustness and accuracy of the algorithm was tested by solving a diffusion problem over the DEM mesh and comparing it to an accurate solution obtained by a finite difference (FD) approximation, whose discretisation was 10 times finer than that of the unstructured grid. Parametric studies were conducted where the random packing and the size distribution of the DEM particles were altered and the differences in concentration profiles were compared with the FD reference solution through the use of the mean squared error. Both steady state and transient cases were compared. Two methods to improve the accuracy of the DEM unstructured grid were devised and tested using porosity and tortuosity data. In one case the porosity and tortuosity were obtained from the steady-state simulations and in the other case, local convex hulls were used to calculate porosity. Although both these methods decreased the mean squared error up to a factor of two, they also resulted into increased complexity of the simulation. It was concluded that the use of an effective packing algorithm and a narrow particle size distribution are key to maintaining the accuracy of the DEM-generated unstructured grid method.     

Liquid permeability of packed bed with binary mixture of particles

We investigate the effect of binary sized packing on the permeability of water flow through a column packed with binary mixture of spherical particles. The size ratios λ of large to small particles are chosen to be 1.4 and 2.5. Particle packing density for binary mixture of the particles is larger than that for equal sized particles and shows the maximum around the particle blending ratio at which large particles are densely packed and all the small particles fill the void among the large particles. This behavior is observed in both experimental results and theoretical estimation. The variation pattern of packing density with the blending ratio does not agree with that of permeability. The permeability increases with relative fraction of large particles at the maximum packing. Experimental results for the permeability are compared with three theoretical models. Variation pattern of the permeability with the blending ratio from these theoretical models agrees with that from the experiment. Theses theoretical models are in good agreement each other.     

Vibratory Compaction: II, Compaction of Angular Shapes

Experiments were conducted on compaction of steel grit in elongated cylindrical containers. The packing efficiency of angular shapes is a function of particle shape and absolute size. The derived relation between packing efficiency and particle size is similar to that for spherical systems with the addition of a shape factor. The equations allow calculation of packing fractions of multicomponent systems in terms of diameter ratios only. Application of the findings was made by loading sixteen nuclear fuel specimens by vibratory compaction.     

Modeling of the pressure drop across polydisperse packed beds in cake filtration

Filtration is the separation of solid–liquid mixtures. In this study, we assess the predictive power of Kozeny–Carman model for systems operated at low Reynolds numbers and relatively high pressure drops. We find substantial agreement between the K-C model and experiment only for systems that exhibit tight void size distribution. Dramatic disagreement is observed for particle beds that exhibit wide void size distributions. We propose a modified modeling approach, based on a bimodal void distribution, by introducing two quantities: the fraction of expanded voids and the ratio of void sizes. The simulation results are found to be much more similar to the experimental flow rates than those calculated using the K-C model. The modified model is deemed reliable at predicting the flow behavior, provided that an accurate representation of the void size distribution is available.     

A three-parameter Kozeny–Carman generalized equation for fractal porous media

The Kozeny–Carman equation is a traditional permeability–porosity relationship which has been used in many models of real problems related to flows in porous media. In spite of this, some limitations of this well-known equation has motivated the conception of different versions, specialized for particular applications. In the present article, we deduce a three-parameter Kozeny–Carman equation obtained from a fractal structure involving the specific surface and the tortuosity of the porous medium. Here, a theoretical analysis indicates that the new equation is capable to generalize several models existent in the literature. Besides, parameter estimations fitting experimental data of different materials show that the present model can be used to describe the relationship between permeability and porosity of many materials, such as sandstones, sisal fiber mat and glass fiber fabrics.     

Morphology,structure, and properties of poly(lactic acid) microporous films containing poly(butylene terephthalate) fine fibers fabricated by biaxial stretching

The effects of size and shape, i.e., sphere and fiber, of dispersed poly(butylene terephthalate) (PBT) in poly(lactic acid) (PLA) matrix on the morphology and porous structure of the biaxially stretched films are comparatively investigated. Scanning electron microscope results confirm that the PBT fine fibers can be produced by melt‐stretching following by fast quenching. Rheological characterization reveals the random network structure of PBT fibers. Further, the stretched films composed of spherical PBT particles show the ellipsoidal microvoids due to the interfacial debonding, and the void size relates to the particle size of PBT. However, size of PBT droplets does not influence the void content of the stretched films. The void content considerably increases for equibiaxial deformation as compared with planar deformation, particularly at high draw ratio. Additionally, the stretched films containing fibrous dispersion exhibit the nonaffine behavior and the highest void content of 8%, which is probably due to the localized deformation between fibers. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41415.     

The Filtration of Fibrous Aerosols

Fibrous particles constitute an important class of aerosols that are potential human health hazards. Filters can remove aerosols from the air. The capture of spherical and fibrous aerosols by fibrous filters was investigated in this study. The governing equations of motions for translation and rotation of fibrous particles are derived for airflow over a cylindrical object. Only impaction and interception losses were considered in this study. Transport and deposition of fibrous particles were found to depend on Stokes number, fibrous particle aspect ratio, and ratio of the fibrous particle diameter to the diameter of fibrous filters. Using the Kuwabara flow field, transport and single-fibrous filter capturing efficiency of spherical and fibrous particles were calculated numerically, and these calculations were compared with available data in the literature. The calculated results compared favorably with the results of Yeh and Liu (1974) for spherical particles. Good agreement for losses by interception for both spherical and fibrous particles was observed between our results and those of Lee and Liu (1982). Further experimental data are needed to verify the predicted losses of fibrous aerosols by impaction.     

Structural Property Effect of Nanoparticle Agglomerates on Particle Penetration through Fibrous Filter

Most filtration studies have been conducted with spherical particles; however, many aerosol particles are agglomerates of small primary spheres. Filtration efficiency tests were conducted with silver NP agglomerates, with the agglomerate structure controlled by altering the temperature of a sintering furnace. The mobility diameter and mass of the silver NP agglomerates were measured using a differential mobility analyzer together with an aerosol particle mass analyzer. From these measurements, it was found that the fractal-like dimension, D _fm, varied from 2.07 to 2.95 as the sintering temperatures was increased from ambient to 600°C. The agglomerates were essentially fully coalesced at 600°C allowing direct comparison of the filtration behavior of the agglomerate to that of a sphere with the same mobility diameter. Other agglomerate properties measured include the primary diameter, the agglomerate length and aspect ratio, and the dynamic shape factor.

Agglomerate filtration modeling with no adjustable parameters has been investigated in terms of diffusion, impaction, and interception. The model results agree qualitatively with the experimental results in the particle size range of 50 to 300 nm. The results indicated that the larger interception length of agglomerates is responsible for the smaller penetration through a fibrous filter in comparison to spherical particles with the same mobility diameters.     

Axial dispersion coefficients in packed beds at low reynolds numbers

Peclet numbers describing axial dispersion in gas flow through packed beds of spheres were obtained using a two measurement point, pulse technique in a test section four inches inside diameter and 5.14 feet high. Three packing sizes were investigated, corresponding to tube to particle diameter ratios of 6.4, 17, and 66 In the experiments the contribution of the velocity profile to axial spreading was reduced by using thermal conductivity detectors which responded to dispersion only in the central part of the bed cross-section. In this region of a packed bed the velocity profile is relatively flat. The results point to a particle diameter effect which is more pronounced than has been previously reported. This is in accord with the diffusive mechanism of axial dispersion in a packed bed provided dispersion caused by the velocity profile does not affect the measured pulse response. In the absence of velocity profile effects, the spreading of residence times in void cells is caused primarily by the shedding of the decelerated boundary layers on the downstream side of the particles. At low velocities however, molecular diffusion predominates. Implicit in this discussion is the hypothesis that the uniformity of shape and size of packing particles has an important bearing on the manner in which the Peclet number approaches its limiting value as the gas velocity is increased.     

Studies of the Effects of Particle Size Distribution on the Packing Efficiency of Particles

In the studies of pigment volume effects in paint films, particle packing has been shown to be very important. The effects of particle size distribution on this packing has been known but has received little quantitative consideration. In this paper we consider the packing of real and model continuous distributions of particle sizes. An extension of an algorithm for the calculation of random densest packing is given which applies to continuous distributions. Using a log-normal distribution as a model, the effect of the width of a single distribution on packing is considered. Mixtures of distributions are also considered with the calculation of packing efficiency as a function of mean size ratio and distribution widths. Maxima are shown to occur in the packing efficiency of mixtures of distributions as a function of the volume fractions of the individual distributions. The implications of these packing variations in real systems are then discussed.     

Pressure loss and wall shear stress in flow through confined sphere packings

Randomly structured, confined sphere packings with different porosities are generated and the fluid flow within the porous structure is calculated. These locally resolved fluid flow data – instead of integral parameters – are used to investigate the origins of the pressure loss within a packing. First, an analysis and comparison of averaged local velocities is performed to compare the similarity of the simulation approach with empirical relations by means of the void fraction and the velocity distributions. Next, the pressure losses due to mean values of the simulated, locally resolved wall shear stresses are calculated, and these findings are smaller than the results from the integral approach of Kozeny and Carman. This indicates that the pressure drop, even at low Reynolds numbers, is not solely caused by the wall shear stress; the simulated overall pressure drops exceed the Ergun approach, an effect which is caused by the bounded flow within a capillary. To relate the pressure loss due to these secondary pressure losses, the tortuosity of the fluid flow in the porous structure is introduced and this parameter improves the performance of the pressure drop equation.     

Formation of ultrafine aspirin particles through rapid expansion of supercritical solutions (RESS)

The performance of pharmaceuticals in biological systems can be enhanced by reducing the particle size of pharmaceuticals. Rapid expansion from supercritical solution (RESS) has provided a promising alternative to comminute contaminant-free particles of heat-sensitive materials such as drugs. In this work, aspirin has been successfully precipitated by the RESS technology. The performances of the RESS process under different operating conditions are evaluated through the analysis of the particle characteristics. Our results show that extraction pressure and extraction temperature can significantly affect the morphology and size of the precipitated particles whereas the nozzle diameter and pre-expansion temperature are not observed to apparently influence the RESS particles. The RESS process could produce ultrafine spherical particles (0.1-0.3 μm) of aspirin as reflected by SEM observations.     

硬球链流体在平板和硬球表面分布的密度泛函理论

采用Yethiraj和Woodward的密度泛函理论方法,结合胡英和刘洪来等发展的硬球链流体状态方程,得到了自由连接硬球链流体在平板狭缝中和球形固体颗粒表面附近的密度分布表达式,并计算了在两平行壁所组成的狭缝中和直径大小不同的球形固体颗粒周围硬球链分子的链节密度分布.理论计算结果与作者采用Dickman 和Hall 的方法进行Monte Carlo计算机模拟结果非常吻合.颗粒直径对链状分子的密度分布有一定的影响,随着固体颗粒直径的增加,靠近颗粒表面附近的链节密度降低.     

Packing of Quaternary Mixtures of Fibrous Particles

This paper presents an experimental investigation of packing of quaternary mixtures of fibrous particles of the same diameter but different lengths. The results indicate that the packing density is heavily dependent on the fractional solid volumes and hence the size and shape distributions involved. The packing of fibrous particles appears to be dominated by the shape effect rather than the size effect, and can be satisfactorily predicted by the modified linear packing model.     

3-D simulation of particle filtration in electrospun nanofibrous filters

Virtual 3-D geometries resembling the internal microstructure of electrospun fibrous materials are generated in this work to simulate the pressure drop and collection efficiency of nanofibrous media when challenged with aerosol particles in the size range of 25 to 1000 nm. In particular, we solved the air flow field in the void space between the fibers in a series of 3-D fibrous geometries with a fiber diameter in the range of 100 to 1000 nm and a Solid Volume Fraction (SVF) in the range of 2.5 to 7.5%, using the Fluent CFD code, and simulated the flow of large and fine particles through these media using Lagrangian and Eulerian methods, respectively. Particle collection due to interception and Brownian diffusion, as well as the slip effect at the surface of nanofibers, has been incorporated in the CFD calculations by developing customized C++ subroutines that run in the Fluent environment. Particle collection efficiency and pressure drop of the above fibrous media are calculated and compared with analytical/empirical results from the literature. The numerical simulations presented here are believed to be the most complete and realistic filter modeling published to date. Our simulation technique, unlike previous studies based on oversimplified 2-D geometries, does not need any empirical correction factors, and can be used to directly simulate pressure drop and efficiency of any fibrous media.     

Three-dimensional void space structure of activated carbon packed beds

The three-dimensional void space structure generated by piling active carbon grains has a large impact on the filter operation, through the modification of the transport properties inside the bed. To gain insight into the relation between morphology and transport properties, the three-dimensional void space structure of activated carbon packed beds was studied by X-ray microtomography coupled with image analysis. Image analysis algorithms allowing the determination of the total void fraction, the void size distribution and the radial void fraction profiles were developed. This methodology was used to characterize the void space structure of two filters with the same length but different diameters, 15 and 28 mm. Commercial granular activated carbon with average particle size close to 1 mm was used. The comparison of the void size distributions indicated that void sizes are almost normally distributed around only one maximum for the large filter, while the distribution has a more complex shape in the small filter. The radial void fraction profiles showed an increase of the void fraction from the center of the filter to the wall accompanied with an oscillatory behaviour at the small scale. Power spectrum of radial profiles of the large filter shows a characteristic length matching well with the carbon particle size, indicating that the carbon grains are uniformly packed in the bed. In the small filter, power spectrum suggests an uneven packing of grains. For both filters, the total void fraction measured by image analysis was very close to the value determined ‘physically’ knowing the carbon mass, bulk density and filter dimension.     

A Numerical Study of Structural Change and Anisotropic Permeability in Compressed Carbon Cloth Polymer Electrolyte Fuel Cell Gas Diffusion Layers

The effect of compression on the actual structure and transport properties of the carbon cloth gas diffusion layer (GDL) of a polymer electrolyte fuel cell (PEFC) are studied here. Structural features of GDL samples compressed in the 0.0–100.0 MPa range are encapsulated using polydimethylsiloxane (PDMS) and by employing X‐ray micro‐tomography to reconstruct direct digital 3D models. Pore size distribution (PSD) and porosity data are acquired directly from these models while permeability, degree of anisotropy and tortuosity are determined through lattice Boltzmann (LB) numerical modelling. The structural models reveal that structural change proceeds through a three‐step process, while PSD data suggests a characteristic peak in the pore diameter of 10–14 μm and a decrease in the mean pore diameter from 33 to 12 μm over the range of tested pressures. A mathematical relationship between compression pressure and permeability is determined based on the Kozeny–Carman equation, revealing a one order of magnitude reduction in through‐plane permeability for a two order of magnitude increase in pressure. The results also reveal that the degree of anisotropy peaks in the range of 0.3–10.0 MPa, suggesting that in‐plane permeability can be maximised relative to through‐plane permeability within a material‐specific range of compression pressures.