Fractal Characterization of Pulverised Materials

This paper describes preliminary work carried out on the applicability of fractal geometry in describing the products of comminution events. A nickel sulphide ore was subjected to two comminution events, impact shattering and ball milling. Fractal analysis was performed on samples of the resulting comminution products. Two differing fractal populations resulted, with the impact sample exhibiting particles having higher boundary fractal dimensions than the milled sample. The fractal dimension of the impact fragments increased with decreasing size, whereas the milled particles displayed a more complex distribution. The under-fractal distributions, of the two populations of fragments, generate straight lines when plotted on Gaussian probability paper. This leads to the possibility of being able to predict the distribution of fragments, in fractal terms, of a particular material when subjected to comminution.     

The velocity measurement of phase objects

Conventional laser velocimeters rely upon small contaminant dust particles to scatter the laser light. A technique is described which requires no contaminant particles but relies upon minute refractive index variations in the fluid. By placing the detector far from the measuring region a set of shadow bands is produced which is convected with the fluid. The velocity is measured by either correlating the light transmitted by two slits or by measuring the frequency of the light transmitted by a grating.     

SEMEDS: an important tool for air pollution bio-monitoring

Plant canopies act as absorbers of air-borne dust particles. Characterization of the dusts present over the leaf surfaces can indicate the nature of contaminant present in the surrounding area and possible sources as well. Dust particulates get adsorbed on both the surfaces of leaves, however more dust particulates get deposited on the upper surface. These dusts contain many inorganic elements, which were analyzed in the present study. For the present investigation, SEMEDS technique used to characterize the dusts adsorbed over the leaf surfaces. Using SEMEDS the samples were analyzed by two types of methods i.e. point analysis and elemental mapping. Both the methods showed the presence of elements like Si, Al, Fe, Mg, and Ca in the dusts adsorbed over the leaf surfaces. Thus, SEMEDS can be used for in situ air pollution monitoring using tree leaves from the area concerned.     

Studies of the collision frequency of ideal gas particles with the surfaces of the objects created using the ballistic deposition technique

This paper is a continuation of our studies of the collision frequency of ideal gas particles with the rough/fractal surfaces. Here, we applied a more realistic surface growth model, i.e. ballistic deposition for creation of fractal objects. We found that the collision frequency with irregular surfaces is the linear function of pressure and this frequency per unit pressure is quite a complicated function of the surface fractal dimension as well as the diameter of colliding particle. The collision frequency with rough surfaces cannot be exactly described by the analytical formula called the Langmuir-Hertz equation. However, we have stated that the deviations of the true collision frequency from the Langmuir-Hertz prediction are not huge and in typical catalytic studies the error introduced by replacing the true frequency by the Langmuir-Hertz prediction can be safely neglected. We have also studied the probability of finding on the surface an atom which has been hit a certain number of times by a gas particle. This probability reveals an interesting behaviour for small gas particles, i.e. it perfectly correlates with the number of directions from which the surface atom is accessible from the gas phase. We have also estimated the evolution of the adsorption energy distribution with the increasing fractal dimension of the surface in the ballistic deposition.     

Particle Growth in an Experimental Dusty Plasma System

The coagulation and growth process of dust particles is investigated through laboratory experiment in a plasma system. A large number of dust particles with different sizes and shapes are formed. The growth process is characterized by the scattering laser intensity and fractal dimension. The comparisons of dust particles and scattering laser intensity obtained at different rf powers are presented. The three-dimensional distribution of dust particles is also given. These results provide an experimental basis for dust growth investigation.     

等离子喷涂层原生性孔隙几何结构的分形及统计特性

孔隙是等离子喷涂涂层原生性结构, 对涂层的耐磨损、耐腐蚀、耐高温等性能具有显著影响, 是涂层参数优化的重要指标之一. 因此, 对涂层孔隙结构特征参数的全面表征对于更加精确地评价涂层质量具有重要意义. 本文将概率统计方法、分形方法与数字图像分析技术相结合, 研究了等离子喷涂涂层原生性孔隙数量、形态、尺寸及其分布等结构特征参数表征方法及孔隙的成形机理. 首先通过改变喷涂功率得到不同孔隙状态的Fe基合金涂层, 随后采用数字图像分析技术对涂层截面孔隙的扫描电子显微形貌图进行处理, 最后通过Weibull统计模型分析了孔隙周长及面积的尺寸分布特征, 并利用基于分形思想的面积-周长幂率研究了孔隙不规则形态的定量表征方法. 在实验过程中, 为了分析涂层孔隙的成形机理, 采用Spraywatch在线监测喷涂粒子的飞行状态. 结果表明: 分形维数能够表征孔隙的不规则形态, 分形维数越大, 孔隙面积越大或边界形态越复杂, 并且其与孔隙的成形机理之间存在良好的映射关系; 孔隙面积及周长的尺寸分布均服从明显的两项Weibull分布特征, 孔隙尺寸较小时, 形状参数β 较大, 而孔隙尺寸较大时, 则反之; 喷涂功率对孔隙尺寸的聚集特点产生不同程度的影响, 随着喷涂功率的增加, 粒子的融化状态逐渐改善, 孔隙的尺寸明显降低; 而当孔隙面积(周长)小于特征值时, 相同尺寸的孔隙概率密度值则越来越接近, 说明孔隙功率的变化对小尺寸孔隙出现的概率影响较小.     

微动条件下材料磨损率的一种计算分析方法

微动现象广泛存在于工程结构中,近年来越来越受到科研工作者的重视.为了对微动磨损进行深入研究,本文根据微动摩擦系统中摩擦副间的特点,针对微动磨损过程,提出不对称双势阱模型,建立了其中粒子的运动方程;利用非平衡统计思想建立了理论模型,得到了计算磨损率的新方法.以金属材料Mg和Fe组成的摩擦副系统为例进行了计算分析,得出磨损率随磨损时间和势阱宽度的变化,进一步分析了载荷正压力变化对磨损率的影响.计算分析结果表明,在其他条件均不变的情况下,材料磨损率随磨损时间的增大而减小,且随着摩擦副系统中势阱宽度和载荷正压力的减小,磨损率也呈减小趋势.最后,通过与试验结果比较,验证了该理论模型的适用性.     

Interactions of charged dust particles in clouds of charges

Two charged dust particles inside a cloud of charges are considered as Debye atoms forming a Debye molecule. Cassini coordinates are used for the numerical solution of the Poisson-Boltzmann equation for the charged cloud. The electric force acting on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the average distance between dust particles should be approximately equal to two Debye radii. Second, attraction takes place when similar charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of total charge of the same polarity, repulsion between the particles takes place at all distances. We apply our results to the experiments with thermoemission plasma and to the experiments with nuclear-pumped plasma.     

Interaction of charged dust particles in clouds of thermodynamically equilibrium charges

The solution of the Poisson-Boltzmann equation for a cloud of charges surrounding two charged dust particles treated as Debye atoms forming a Debye molecule is investigated numerically using Cassini coordinates. The electric force exerted on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the Debye radius (corresponding to the electron density at half the mean distance between the dust particles) must be approximately equal to half the mean distance between the dust particles. Attraction between the dust particles emerges at a distance equal approximately to half the mean distance between the dust particles. Second, attraction takes place when like charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of charge of the same polarity, repulsion between the particles takes place at all distances.     

The effect of particle aggregation on the absorption and emission properties of mono- and polydisperse soot aggregates

This study concerns the effect of soot-particle aggregation on the soot temperature derived from the signal ratio in two-color laser-induced incandescence measurements. The emissivity of aggregated fractal soot particles was calculated using both the commonly used Rayleigh–Debye–Gans fractal-aggregate theory and the generalized Mie-solution method in conjunction with numerically generated fractal aggregates of specified fractal parameters typical of flame-generated soot. The effect of aggregation on soot temperature was first evaluated for monodisperse aggregates of different sizes and for a lognormally distributed aggregate ensemble at given signal ratios between the two wavelengths. Numerical calculations were also conducted to account for the effect of aggregation on both laser heating and thermal emission at the two wavelengths for determining the effective soot temperature of polydisperse soot aggregates. The results show that the effect of aggregation on laser energy absorption is important at low fluences. The effect of aggregation on soot emissivity is relatively unimportant in LII applications to typical laminar diffusion flames at atmospheric pressure, but it can become more important in flames at high pressures due to larger primary particles and wider aggregate distributions associated with enhanced soot loading.     

Directional region control of the thermal fractal diffusion of a space body

We present a directional region control(DRC) model of thermal diffusion fractal growth with active heat diffusion in three-dimensional space. This model can be applied to predict the space body heat fractal growth and study its directional region control. When the nonlinear interference term and the inner heat source term are generalized functions, the relationship between the particle aggregation probability and the interference terms can be obtained using the norm theory. We can then predict the aggregation form of particles in different regions. When the nonlinear interference terms in the model are expressed as a trigonometric function and its composite function, our simulations show that the DRC method of thermal fractal diffusion is effective and has reference value for the directional control of actual fractal growth systems.     

Grayscale projection of finite size fractal clusters

Microscopy techniques are suitable to obtain structural information of colloidal clusters with high resolution, but yield only a two dimensional projection of the objects. When imaging finite size objects with fractal properties, such as clusters of colloidal particles, this projection process has to be taken into account for the calculation of the fractal dimension. In this paper we present a technique to calculate the fractal dimension of finite size clusters with fractal properties using grayscale projections such as images obtained by X-ray microscopy. The grayscales are interpreted as different occupation counts within a projection. It is shown, that the radial distribution of these occupation counts varies with the fractal dimension d of the cluster. Using the radius of maximum occupation probability the fractal dimension up to 2.2 of finite size clusters can be calculated. The theoretical predictions are verified by test calculations employing numerically generated clusters.     

两种带电尘埃颗粒的等离子体鞘层玻姆判据

采用流体方程和尘埃充电自洽模型研究了鞘边含有两种尘埃颗粒的等离子体玻姆判据. 通过拟牛顿法数值模拟了鞘边两种尘埃颗粒的存在对尘埃自身充电以及离子马赫数的影响. 两种尘埃颗粒中含量较少的尘埃颗粒数密度的增加, 导致两种尘埃颗粒表面悬浮势一个降低, 一个升高. 含量较少的尘埃颗粒的数密度越多和半径越小, 都会导致离子马赫数增大. 另外鞘边无论何种尘埃颗粒的速度增加, 鞘边离子马赫数都将减小. 关键词： 等离子体鞘层 尘埃颗粒 玻姆判据     

Analytical model of brittle destruction based on hypothesis of scale similarity

The size distribution of dust particles in thermonuclear (fusion) devices is closely described by a power law, which may be related to the brittle destruction of materials. The hypothesis of scale similarity leads to the conclusion that the size distribution of particles formed as a result of a brittle destruction is described by a power law with the exponent ??? that can range from ?4 to ?1. The model of brittle destruction is described in terms of the fractal geometry, and the distribution exponent is expressed via the fractal dimension of packing. Under additional assumptions, it is possible to refine the ?? value and, vice versa, to determine the type of destruction using the measured size distribution of particles.     

随机分布烟尘团簇粒子辐射特性研究

基于分形理论,采用蒙特卡罗方法对随机分布的烟尘团簇粒子结构进行了仿真模拟,利用离散偶极子近似(discrete dipole approximation, DDA)方法研究了随机分布的烟尘团簇粒子的辐射特性,分析讨论了分形维数、原始微粒粒径和数量以及复折射率对随机分布烟尘团簇粒子辐射特性的影响.研究表明,在给定分形维数的情况下,烟尘团簇粒子的辐射特性取决于原始微粒粒径、数量及复折射率;原始微粒较小的团簇粒子,当分形维数较小时,吸收截面变化不明显,但当分形维数大于2时,吸收截面骤然增大,然而,对于具有比较大的原始微粒粒径、数量及复折射率的烟尘团簇粒子,吸收截面随着分形维数的增大而单调递减;随着分形维数的增大,团簇粒子的散射截面、消光截面及单次散射反照率均单调递增;从整体上来讲,团簇粒子的辐射特性与等效球形粒子的辐射特性存在着比较大的差别,并且这种差别随着分形维数的增大而减小.该工作对研究气溶胶粒子的辐射及气候效应具有重要的科学价值. 关键词： 烟尘团簇粒子 辐射特性 离散偶极子近似方法     

Boundary Fractal Dimensions from Sections of a Particle Profile

The fractal dimension of particles is commonly evaluated from complete particle boundaries. In this work, a study has been made of the self-similar nature of complete and incomplete boundary profiles of a range of morphologically different copper powders. Boundary images were captured from SEM micrographs of particle boundaries at a range of magnifications up to nearly 14000X. An algorithm was developed to compute the fractal dimension of boundary segments. This algorithm was tested against the Koch Island fractal, and was found to give excellent estimates of the fractal dimension. For the particle system studied, the boundary fractal was found to be sensitive to magnification with appreciable drops in value at high magnification. This demonstrates that the particles studied did not have true fractal boundaries and the use of fractal theory to study particle surface roughness must be used with caution.     

Finite size effect of harmonic measure estimation in a DLA model: Variable size of probe particles

A finite size effect in the probing of the harmonic measure in simulation of diffusion-limited aggregation (DLA) growth is investigated. We introduce a variable size of probe particles, to estimate harmonic measure and extract the fractal dimension of DLA clusters taking two limits, of vanishingly small probe particle size and of infinitely large size of a DLA cluster. We generate 1000 DLA clusters consisting of 50 million particles each, using an off-lattice killing-free algorithm developed in the early work. The introduced method leads to unprecedented accuracy in the estimation of the fractal dimension. We discuss the variation of the probability distribution function with the size of probing particles.     

The Effect of Polydispersity in Primary Particle Size on Measurement of the Fractal Dimension of Aggregates

The use of the mass fractal dimension has become a popular method of characterising the structure of aggregates of fine particles. This parameter is often inferred from scattering experiments that exhibit a power law correlation between scattered intensity and the scattering vector. In this paper we demonstrate deviations from this behaviour that occur when the particles making up the aggregate are not monodisperse, even though the aggregate maintains the same fractal structure as observed in the monodisperse case. We have performed light scattering experiments with aggregating colloidal haematite and performed DLCA computer simulations to explain the observed behaviour. The behaviour can influence the determination of the mass fractal dimension, as can other factors such as scattering effects from primary particles.     

New physical concept of the formation of dust crystals

A clear physical model is proposed for phase transitions in a dusty plasma. According to this model, the formation of plasma dust crystals is associated with the nonlinear effect of the collective attraction of dust particles. The nonlinear collective attraction between negatively charged dust particles corresponds to large charges of dust particles used in the available experiments. This concept provides a new physical model of crystallization that is attributable to the capture of dust particles in an attractive potential well rather than to the strong interaction between them. Calculation using this model yields the depth of the attractive potential well and the critical coupling constant in good agreement with the available experimental data.