Effect of size distribution on the relation between coordination number and void fraction of spheres in a randomly packed bed

Counting the number of contact points on a particle in a packed bed is a time-consuming processes. So, usually, the number of contact points on a particle surface in a randomly packed bed, i.e. the coordination number, is estimated from the void fraction. Many researchers have proposed equations to estimate the coordination number from the void fraction in a packed bed, but all of these equations are obtained for a uniform sized sphere bed. Most actual powder has a wide size distribution, and the effect of the size distribution on the relation between the coordination number and the void fraction is very important. We investigated the effect of the size distribution on the relation using our model and a computer simulation. Based on our results, the coordination number is not changed with the size distribution of the particle bed; however, the void fraction becomes smaller for wider particle size distributions. It means that the value of the coordination number, as estimated by conventional equation for equal spheres from void fraction data, is overestimated for a randomly packed bed of multi-component spheres with wider particle size distributions.     

Determination of heat-transfer coefficient in a bed of spheres by a quasistationary cyclic method

Relations are presented for the amplitude ratio and the phase shift of the temperature of a gas in the periodic heating of a packed bed of spheres. The heat-transfer coefficient in the bed is determined by a cyclic method.     

Experimental and numerical evaluation of the transport behaviour of a moving fuel bed on a forward acting grate

The objective of this study is to evaluate experimentally and numerically the transport behaviour of a moving bed on a forward acting grate. Therefore, the grate was operated with expanded clay and wood chips without combustion. Frequency and amplitude of the grate bars and feed rate were subject to change. Experimental findings showed that large particles have shorter residence times than small particles which is due to segregation on the grate. Additionally, the experiments indicated that increased frequencies of the grate bars lead to reduced residence times whereas the amplitude had no significant effect. The motion of a packed bed e.g., its particles was described numerically by the discrete element method (DEM). Thus, detailed data on all the particle’s paths and velocities are available. These data were used within the mean velocity method (MVM) and the tracking method (TM) to estimate the residence time of a packed bed. Both methods confirmed the dependency of the residence time on particle size, however, better predictions were obtained by the Tracking Method. The mean residence times varies from 40 to 120 min depending on the particle size. B. Peters is an Academic visitor to the Lituanian Energy Institute.     

Measurement of 100 nm and 60 nm Particle Standards by Differential Mobility Analysis

The peak particle size and expanded uncertainties (95 % confidence interval) for two new particle calibration standards are measured as 101.8 nm ± 1.1 nm and 60.39 nm ± 0.63 nm. The particle samples are polystyrene spheres suspended in filtered, deionized water at a mass fraction of about 0.5 %. The size distribution measurements of aerosolized particles are made using a differential mobility analyzer (DMA) system calibrated using SRM^® 1963 (100.7 nm polystyrene spheres). An electrospray aerosol generator was used for generating the 60 nm aerosol to almost eliminate the generation of multiply charged dimers and trimers and to minimize the effect of non-volatile contaminants increasing the particle size. The testing for the homogeneity of the samples and for the presence of multimers using dynamic light scattering is described. The use of the transfer function integral in the calibration of the DMA is shown to reduce the uncertainty in the measurement of the peak particle size compared to the approach based on the peak in the concentration vs. voltage distribution. A modified aerosol/sheath inlet, recirculating sheath flow, a high ratio of sheath flow to the aerosol flow, and accurate pressure, temperature, and voltage measurements have increased the resolution and accuracy of the measurements. A significant consideration in the uncertainty analysis was the correlation between the slip correction of the calibration particle and the measured particle. Including the correlation reduced the expanded uncertainty from approximately 1.8 % of the particle size to about 1.0 %. The effect of non-volatile contaminants in the polystyrene suspensions on the peak particle size and the uncertainty in the size is determined. The full size distributions for both the 60 nm and 100 nm spheres are tabulated and selected mean sizes including the number mean diameter and the dynamic light scattering mean diameter are computed. The use of these particles for calibrating DMAs and for making deposition standards to be used with surface scanning inspection systems is discussed.     

颗粒尺寸对SiC_P预制体孔洞三维特征的影响

通过模压成型和高温烧结制备了不同SiC_P颗粒尺寸(20、50、100和150μm)的预制体,采用高分辨率(~1.0μm)三维X射线断层扫描和三维孔隙网络结构模型,研究了SiC_P颗粒尺寸对预制体孔洞三维特征的影响。结果表明:随着SiC_P颗粒尺寸的增大,淀粉的间隙膨胀作用逐渐减弱,而颗粒堆积间隙逐渐增大。当SiC_P颗粒尺寸由20μm增大到100μm时,截面孔洞形貌更加平齐,面孔隙率均值减小,孔洞体积的空间分布均匀性和连通性都变差,孔洞和喉道的平均尺寸增大,而小尺寸孔喉数量减少,平均孔洞配位数减小;当颗粒尺寸继续增大至150μm时,间隙被更多较小尺寸颗粒填充,且颗粒表面残留网状粘结剂,都大大降低了孔洞体积的空间分布均匀性和连通性,使小尺寸孔喉数量增多,平均孔洞配位数增大。     

A three dimensionally periodic,eleven coordinated,dense packing of symmetry equivalent spheres

Symmetry equivalent equal size spheres can be packed in an array filling 71.87% of space. Each sphere in this packing has eleven neighbors at unit distance. The density of this tetragonal close packing is second only to closest packing with twelve coordination. Anions in numerous compounds, including some which are solid electrolytes, arrange themselves in this pattern. It occurs among others in rutiles, β-BeO, Li₄GeO₄ and CaSO₄.     

Advantages of perfectly ordered 2-D porous pillar arrays over packed bed columns for LC separations: a theoretical analysis

A series of theoretical calculations is presented to quantify the gain in LC separation efficiency that can be expected if the traditionally used packed bed columns were replaced by columns with a perfectly ordered flow-through pore network. It is shown that a perfectly ordered 2-D array of porous cylindrical pillars could yield reduced plate heights as small as h = 0.65 (for k' ' = 0.75) to h = 0.85 (for k' ' = 2) and separation impedances as small as E = 200 (for k' ' = 0.75) to E = 300 (for k' ' = 2) without having to compromise on the porosity (epsilon = 0.4) and the retention capacity of the packed bed of spheres. Fitting the calculated van Deemter plots with Knox's equation especially shows a strong decrease of the A-term contribution, hence confirming that the improved column performance indeed stems from the increased homogeneity of the packing. The presented results, hence, provide a clear quantitative support for Knox's recent argumentation that the use of more uniform beds could greatly enhance the efficiency of pressure-driven LC.     

An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers

The objective of this paper is to identify a numerical method to simulate motion of a packed or fluidized bed of fuel particles in combustion chambers, such as a grate furnace and a rotary kiln. Therefore, the various numerical methods applied in the areas of granular matter and molecular dynamics were reviewed extensively. As a result, a time driven approach was found to be suited for the numerical simulation of particle motion in combustion chambers. Furthermore, this method can also be employed to moving boundaries which are required for the present application e.g. travelling grate. The method works in a Lagrangian frame of reference, which uses the position and orientation of particles as independent variables. These are obtained by time integration of the three-dimensional dynamics equations derived from the classical Newtonian approach for each particle. This includes the keeping track of all forces and momentums acting on each particle at every time step. Viscoelastic contact forces include normal and tangential components with viscoelastic models for energy dissipation and friction. The particle shapes are approximated by spheres and ellipsoids with a varying size and ratio of the semi-axis accounting for the variety of particle geometries in a combustion chamber. For these shapes the overlap of particles during contact is expressed by a polynomial of 4th order in the two-dimensional case and a polynomial of 6th order in the three-dimensional case. A new algorithm to detect two-dimensional elliptical particle contact with sufficient accuracy was developed. It is based on a sequence of coordinate transformations and has demonstrated its reliability in numerous applications. Finally, the method was applied to simulate the motion of spherical and elliptical particles in a rectangular enclosure, on a travelling grate, and in a rotary kiln. Received: 16 November 2001     

无定形态及晶态颗粒堆积结构的三维构建及表征

采用离散元法对等径球在振动条件下堆积形成的无定形结构及晶态结构进行三维构建,并对两种堆积结构的宏观性能如堆积密度及微观性能如配位数、径向分布函数及Voronoi-Delaunay孔尺寸分布进行表征及对比。结果表明:所获得的无定形结构和晶态结构的最大相对堆积密度分别为0.64和0.74,对应的配位数分布的峰值分别为7和12,径向分布函数曲线上,晶态堆积中粒子之间的位置具有长程相关性,同时晶态结构所对应的尺寸分布较无定形结构高且窄,且整体左移。     

超重力反应结晶法制备纳米碳酸钙颗粒研究

以Ca（OH）2悬浊液和CO2气体在起重力反应器（旋转填充床反应器）中进行碳化反应制备纳米立方形碳酸钙为研究对象，实验研究了超重力加速度gr，液体循环量L，气体流量G，Ca（OH）2初始浓度等操作条件对产物粒度及其分布、碳化反应时间的影响。结果表明：利用超重力反应结晶法可以制备出平均粒度为15～40nm、分布较窄的CaCO3，碳化反应时间较传统方法缩短约4～10倍。     

Characterization of the spatial resolution of different high-frequency imaging systems using a novel anechoic-sphere phantom

The spatial resolution of high-frequency ultrasound (HFU, >20 MHz) imaging systems is usually determined using wires perpendicular to the beam. Recently, two tissue-mimicking phantoms (TMPs) were developed to estimate three-dimensional (3-D) resolution. Each TMP consists of nine 1-cm-wide slabs of tissue-mimicking material containing randomly distributed anechoic spheres. All anechoic spheres in one slab have the same dimensions, and their diameter is increased from 0.1 mm in the first slab to 1.09 mm in the last. The scattering background for one set of slabs was fabricated using 3.5-μm glass beads; the second set used 6.4-μm glass beads. The ability of a HFU system to detect these spheres against a speckle background provides a realistic estimation of its 3-D spatial resolution. In the present study, these TMPs were used with HFU systems using single-element transducers, linear arrays, and annular arrays. The TMPs were immersed in water and each slab was scanned using two commercial imaging systems and a custom HFU system based on a 5-element annular array. The annular array had a nominal center frequency of 40 MHz, a focal length of 12 mm, and a total aperture of 6 mm. A synthetic-focusing algorithm was used to form images with an increased depth-of-field. The penetration depth was increased by using a linear-chirp signal spanning 15 to 65 MHz over 4 μs. Results obtained with the custom system were compared with those of the commercial systems (40-MHz probes) in terms of sphere detection, i.e., 3-D spatial resolution, and contrast-to-noise ratio (CNR). Resulting B-mode images indicated that only the linear-array transducer failed to clearly resolve the 0.2-mm spheres, which showed that the 3-D spatial resolution of the single-element and annular-array transducers was superior to that of the linear array. The single-element transducer could only detect these spheres over a narrow 1.5 mm depth-of-field, whereas the annular array was able to detect them to depths of at least 7 mm. For any size of the anechoic spheres, the annular array excited by a chirp-coded signal provided images of the highest contrast, with a maximum CNR of 1.8 at the focus, compared with 1.3 when using impulse excitation and 1.6 with the single-element transducer and linear array. This imaging configuration also provided CNRs above 1.2 over a wide depth range of 8 mm, whereas CNRs would quickly drop below 1 outside the focal zone of the other configurations.     

Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis

The Monte Carlo-based inverse model of diffuse reflectance described in part I of this pair of companion papers was applied to the diffuse reflectance spectra of a set of 17 malignant and 24 normal-benign ex vivo human breast tissue samples. This model allows extraction of physically meaningful tissue parameters, which include the concentration of absorbers and the size and density of scatterers present in tissue. It was assumed that intrinsic absorption could be attributed to oxygenated and deoxygenated hemoglobin and beta-carotene, that scattering could be modeled by spheres of a uniform size distribution, and that the refractive indices of the spheres and the surrounding medium are known. The tissue diffuse reflectance spectra were evaluated over a wavelength range of 400-600 nm. The extracted parameters that showed the statistically most significant differences between malignant and nonmalignant breast tissues were hemoglobin saturation and the mean reduced scattering coefficient. Malignant tissues showed decreased hemoglobin saturation and an increased mean reduced scattering coefficient compared with nonmalignant tissues. A support vector machine classification algorithm was then used to classify a sample as malignant or nonmalignant based on these two extracted parameters and produced a cross-validated sensitivity and specificity of 82% and 92%, respectively.     

Radar target classification method with reduced aspect dependency and improved noise performance using multiple signal classification algorithm

This study introduces a novel aspect and polarisation invariant radar target classification method based on the use of multiple signal classification (MUSIC) algorithm for feature extraction. In the suggested method, for each candidate target at each designated reference aspect, feature matrices called `MUSIC spectrum matrices (MSMs)? are constructed using the target?s scattered data at different late-time intervals. An individual MSM corresponds to a map of a target?s natural resonance-related power distribution over the complex frequency plane under the chosen aspect angle/late-time interval conditions. The collection of these feature matrices is used first to determine the best late-time interval for optimal feature extraction. Then, the MSM of a target, which are computed over the optimal time interval at all reference aspects, are superposed to obtain the `fused MUSIC spectrum matrix (FMSM)'. The FMSM of a target is its main classifier feature in the proposed method as the aspect dependency of an FMSM is highly reduced because of its multi-aspect construction process. The suggested method is demonstrated for both simple and complex target geometries such as conducting spheres, dielectric spheres and small-scale aircraft targets with high accuracy rates even for low SNR values using feature fusion at only a few different reference aspects.     

Analysis of the packing structure of wet spheres by Voronoi–Delaunay tessellation

The structure of a packing of narrowly sized wet spheres with packing density 0.435 is analysed against the well-established random close packing with packing density 0.64 by means of the Voronoi and Delaunay tessellation. The topological and metric properties of Voronoi polyhedra, such as the number of faces, perimeter, area and volume of a polyhedron, the number of edges, perimeter and area of a polyhedron face, have been quantified. Compared to the well established random close packing, the distributions become wider and more asymmetric with a long tail at the higher values. The volume and sphericity of each Delaunay cell have also been quantified. Their distributions are shown to be wider and more asymmetric than those for the random close packing, but the peaks are almost the same. For the wet particle packing, the correlations between Voronoi polyhedron size and shape and between Delaunay cell size and shape are more scattered. The topological and metric results are also shown to be consistent with those obtained for the packing of fine particles, although the dominant forces in forming a packing differ. The results should be useful to the quantitative understanding of the structure of loosely packed particles.     

溴化锂填料吸收器中绝热吸收过程的实验研究

针对传热、传质分离的填料吸收器，设计、加工了一个溴化锂绝热降膜吸收的循环实验装置；实验研究了溴化锂水溶液在填料层上的绝热吸收特性；分析了溶液温度、浓度、降膜雷诺数对吸收效率和传质系数的影响。     

Towards realistic characterisation of chemical reactors: An in-depth analysis of catalytic particle beds produced by sieving

Optimization of large-scale fixed particle bed catalytic reactors requires extensive insight into the multi-scale bed structure, even down to the micrometre scale. Theoretical studies of chemical reactors provide a time- and cost-effective means to supporting the optimisation process. However, they rely on simplified assumptions for the particles, e.g. homogeneous perfect spheres. In practise, the preparation of catalytic particles cannot attain this level of uniformity. Typical preparation techniques, such as sieving, are conducted with the aim of obtaining particle size distributions within a pre-defined range, governed by the sizes of the sieves. However, such methods offer limited control in the actual particle sizes and shapes. This paper evaluates the impact of sieving on the resulting particles and overall structural morphology of catalytic beds. The bed structure is quantified using micro-focus computed tomography (µ-CT), enabling the non-destructive examination and analysis of over 150 thousand particles, in terms of particle size, shape, uniformity, and interparticle porosity. Furthermore, the chemical performance of the resulting beds is compared. The detailed characterisation achieved paves the way for the evolution of more rigorous computational models coupling intricate, localised hydrodynamics with realistic chemical processes. Validation of such models at the lab-scale will accelerate the development of more accurate large-scale models.     

Light scattering and absorption by soot in the presence of sulfate aerosols

The radiative properties of aerosol-soot mixtures, both internal and external, are determined in the visible and near-infrared bands by use of exact indirect mode-matching solutions to electromagnetic-wave scattering from a sphere with an eccentric spherical inclusion and from a cluster of spheres. Spherical sulfate droplets are assumed to represent aerosol particles. Soot particles are represented by volume-equivalent carbon spheres, the size distribution of which is obtained from the number distribution of the primary carbon particles that aggregate into soot grains. The mean gram-specific absorption cross section and the mean albedo of aerosol-soot mixtures are obtained by integration of the corresponding characteristics of composite sulfate-carbon particles over the size range of carbon spheres. Enhanced absorption of light by soot in aerosol-soot mixtures, a result of lensing by sulfate droplets, is highlighted by maps of the electromagnetic field in a sulfate-carbon particle.     

Oil mobility in a saturated water-wetted bed of glass beads

The mobilization of an oil bank in a packed bed of glass beads saturated with an aqueous phase has been studied both theoretically and experimentally. The size of the glass beads was varied in the range between 0.5 and 5mm. Two oils (hexadecane and hexane) with viscosities different for an order of magnitude and densities smaller than that of water have been used. A few more runs have been carried out using perchloroethylene (PCE), with density greater than that of water. The interfacial tension in the aqueous phase was varied in a quite large range (0.38-39.1 dyn/cm) by adding surfactants to the water. The glass assembly made it possible to follow the evolution of the dyed oily phase by the use of a digital camera. A very simple stochastic model for describing the porous structure of the packed bed made it possible to set a criterion for determining the probability of mobilization of ganglia which are produced by the fragmentation of the oil bank. The same model permits also to estimate the probability function of the velocity of a ganglion of an assigned size.     

Facile method for fabricating titania spheres for chromatographic packing

Titania (TiO₂) spheres were fabricated by a solvent evaporation process in which anhydrous ethanol was used as the only solvent. This is a simple and novel route for the fabrication of TiO₂ spheres. The spheres have a narrow particle size distribution and an average diameter of approximately 1.0 µm. The crystal structure of the prepared spheres was improved by high-temperature processing. A possible mechanism for the formation and growth of the spheres is proposed in which titanic acid molecules react with each other through hydroxyl condensation to form primary TiO₂ particles. These aggregate and increase in size by surface reaction, and finally form spheres.