Johnson's SB Distribution Function as Applied in the Mathematical Representation of Particle Size Distributions. Part 2: Application of numerical results

The validity of the numerical results obtained in Part 1 is examined via some typical examples. The results indicate that the numerical results can be applied to the particle size distribution transformation within the practically tolerated error. On this basis an equation was derived to calculate analytically the mean diameters of a powder. The verification and application of this equation are demonstrated by a typical example. It is shown that the Hatch-Choate relationship used in the transformation of particle size distributions expressed by the log-normal distribution is only a special (extreme) case of the present numerical results. Although the numerical simulation cannot always provide a consistent transformation, this approach can greatly facilitate the application of the S_B distribution function in powder technology by simplifying the transformation between particle size distributions and the calculation of mean diameters.     

Monte Carlo simulation of particle aggregation and gelation: I. Growth,structure and size distribution of the clusters

The application of a statistical method, the local polynomial regression method, (LPRM), based on a nonparametric estimation of the regression function to determine the critical micelle concentration (cmc) is presented. The method is extremely flexible because it does not impose any parametric model on the subjacent structure of the data but rather allows the data to speak for themselves. Good concordance of cmc values with those obtained by other methods was found for systems in which the variation of a measured physical property with concentration showed an abrupt change. When this variation was slow, discrepancies between the values obtained by LPRM and others methods were found.Received: 2 October 2003, Published online: 25 March 2004PACS: 02.50.-r Probability theory, stochastic processes, and statistics - 82.70.-y Disperse systems; complex fluids     

Calculating the soot particle size distribution function in turbulent diffusion flames using a sectional method

Soot formation in a turbulent jet diffusion flame is modeled using an unsteady flamelet approach in post-process. In the present work, we apply a detailed kinetic soot model with a sectional method, and study the evolution of the particle size distribution. Detailed information on the evolution of the soot particle size distribution function is acquired. It is found that the particle size distribution function is bimodal throughout the flame. The transition from the small to large particle size distributions is strongly influenced by surface growth and oxidation reactions. We find that large particles are most likely to be emitted from the flame.     

Ultrasonic determination of the particle size distribution in water-based magnetic liquid

Magnetic liquids are stable colloidal suspensions of nano-sized magnetic particles in a carrier liquid medium. In the present paper the determination of the particle size distribution function using ultrasonic spectroscopy is described. The ultrasonic spectra of water-based magnetic fluid measured in the 3.5-50 MHz frequency range are analyzed using formulas for the velocity and absorption of sound in dispersion media obtained by Vinogradov. The results of the ultrasonic studies are compared with the particles size distribution function evaluated from the processing of the magnetic susceptibility data.     

Monte Carlo simulation of electron avalanches and avalanche size distributions in methane

The simulation of electron avalanches and avalanche size distributions in methane is presented in this paper. A model for electron transport under the influence of a constant electric field based on the Monte Carlo method is described in detail. The model is verified and then used to simulate the avalanche development, to calculate the number of electrons in the avalanche (avalanche size), and to determine the avalanche size distribution. The simulated avalanche size distributions in methane are compared with the experimental results, and a good agreement is observed. The influence of inter‐electrode distance, pressure, and reduced electric field on the shape of the avalanche size distribution is discussed. The assumption from the literature that for a constant reduced electric field the shape of the reduced avalanche size distribution is independent of the mean size of the avalanche is confirmed for a wide range of experimental conditions. The simulations have shown that avalanche size distributions depend only on the reduced electric field, confirming the similarity principle.     

光纤微机电系统压力传感器的理论分析和数值模拟

设计了一种基于微机电系统(MEMS)的光纤压力传感器,证明了光纤MEMS压力传感器在工作状态下可以由法布里_珀罗腔的理论模型解释。推导出了在光纤MEMS压力传感器中硅横膈膜的压力与干涉光强的关系表达式,并对光纤MEMS压力传感器的模型进行了数值模拟,初步确定了在传感器的制作过程中各个物理量的取值。其中腔体半径为300μm、腔体深度为1.42μm、硅横膈膜厚度为23μm,为光纤MEMS压力传感器的加工和制作提供了理论基础。     

Modification of the large particle method applied in numerical solution of problems of microwave electronics

The method of large particles, which is applied in one-dimensional numerical simulation of processes in electron devices, such as traveling-wave tubes, is suggested. With the number of large particles fixed, the amount of computation remains virtually the same, while the accuracy attained under strong nonlinearity rises significantly.     

Theoretical analysis and numerical simulation of acoustic waves in gas hydrate-bearing sediments

Based on Carcione-Leclaire model,the time-splitting high-order staggered-grid finite-difference algorithm is proposed and constructed for understanding wave propagation mechanisms in gas hydrate-bearing sediments.Three compressional waves and two shear waves,as well as their energy distributions are investigated in detail.In particular,the influences of the friction coefficient between solid grains and gas hydrate and the viscosity of pore fluid on wave propagation are analyzed.The results show that our proposed numerical simulation algorithm proposed in this paper can effectively solve the problem of stiffness in the velocity-stress equations and suppress the grid dispersion,resulting in higher accuracy compared with the result of the Fourier pseudospectral method used by Carcione.The excitation mechanisms of the five wave modes are clearly revealed by the results of simulations.Besides,it is pointed that,the wave diffusion of the second kind of compressional and shear waves is influenced by the friction coefficient between solid grains and gas hydrate,while the diffusion of the third compressional wave is controlled by the fluid viscosity.Finally,two fluid-solid(gas-hydrate formation)models are constructed to study the mode conversion of various waves.The results show that the reflection,transmission,and transformation of various waves occur on the interface,forming a very complicated wave field,and the energy distribution of various converted waves in different phases is different.It is demonstrated from our studies that,the unconventional waves,such as the second and third kinds of compressional waves may be converted into conventional waves on an interface.These propagation mechanisms provide a concrete wave attenuation explanation in inhomogeneous media.     

Effect of particle size distribution and dynamics on the performance of two-dimensional packing

Extensive computer simulation is used to revisit and to generalize two classical problems: (i) the random car-parking dynamics of A. Rényi and (ii) the irreversible random sequential adsorption (RSA) of parallel squares of same size on a planar substrate of area L². In this paper, differently from the classical RSA, the squares obey the size distribution n(a)=n(1)a^−τ, where a=1,2,3,… is the area of the squares. Using this scaling distribution and three classes of packing dynamics we study the final packing fraction of particles, ?(τ,L), and in particular its thermodynamic limit L→∞. We show that the efficiency to attain a high/low packing density of particles on the substrate is strongly dependent on the value of the exponent τ and on the characteristics of the dynamics.     

Monte Carlo simulation of particle aggregation and gelation: II. Pair correlation function and structure factor

Diffusion-limited cluster aggregation and gelation are studied using lattice and off-lattice Monte Carlo simulations. The pair correlation function g(r) and the structure factor S(q) of the particle gels were investigated as a function of the volume fraction ( ) and time. At volume fractions below , the gel structure is fractal on small length scales with . g(r) shows a weak minimum at the correlation length ( ), before reaching the average concentration at large length scales. The cut-off function of g(r) varies during the aggregation process, but at a given , where is the gel time, it is a universal function of . At high volume fractions, the structure is dominated by excluded-volume interactions, while at low volume fractions, it is determined by the connectivity.Received: 27 April 2004, Published online: 26 October 2004PACS: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 02.70.Uu Applications of Monte Carlo methods     

Fusion reactions in plasmas as probe of the high-momentum tail of particle distributions

In fusion reactions, the Coulomb barrier selects particles from the high-momentum part of the distribution. Therefore, small variations of the high-momentum tail of the velocity distribution can produce strong effects on fusion rates. In plasmas several potential mechanisms exist that can produce deviations from the standard Maxwell-Boltzmann distribution. Quantum broadening of the energy-momentum dispersion relation of the plasma quasi-particles modifies the high-momentum tail and could explain the fusion-rate enhancement observed in low-energy nuclear reaction experiments.     

Particle counting and numerical models: Effect of instrumental size resolution and particle shapes on optical cross-sections

The effect of instrumental size resolution measurements on numerical calculations of optical cross-sections is investigated. The particle counting instruments considered are a FSSP-300, a large scattering angle probe instrument similar to a ASASP-X, and, an aerodynamical system ELPI instrument. The scattering and hemispheric backscattering cross-sections, C_sca and C_bk, are calculated on the basis that the full width of the instrumental size bin should be considered in modeling. An average process is applied on these quantities over the full size bin of the instrument; they are then compared to their usual estimation on the single mean diameter D_p per channel. The effect of particle shape is investigated with ellipsoids and spheres. Results show sensitivity of the optical cross-sections to the shape of the particles as well as position of the mean geometrical diameter D_p of the channels within the interferences modes of the scattering efficiencies. The value of the width of the size bins, d log D, of each channel is crucial in the results. This comparison gives a useful estimation of error important in optical particle counting instruments based on inversion process of optical quantities. In addition, accuracy of size distribution measurements is found not to be representative of accuracy in the calculations of optical cross-sections.     

A Theoretical and Experimental Study of the Total Light Scattering Technique for particle size analysis

The total light scattering method for particle size measurement has a series of outstanding features, e.g. very simple instrumental arrangement, no serious requirements for its optical, photodetecting and electronic systems and its ease of use. Nevertheless, some problems still remain unsolved which should be dealt with to improve its further applications. An improvement has been made in this work. Comprehensive theoretical studies showed that this method is applicable to particle size analysis in the range 0.1–10 μm, i.e. for those particles whose diameter lies between the lower limit of the diffraction method and the upper limit of photon correlation spectroscopic (PCS) technique. Experimental studies with different monodisperse polystyrene latex spheres as standard reference material give good agreement with their nominal values.     

Retrieval of spheroidal particle size distribution using the approximate method in spectral extinction technique

Retrieval of spheroidal particle size distribution using an approximate method in spectral extinction technique is proposed. The combined approximate method, which is the combination of Mie method and generalized eikonal approximation (GEA) method, is used as an alternative to the rigorous solutions to calculate the averaging extinction efficiency of spheroid. Based on the averaging extinction efficiency, the accuracy and limitations of the retrieval are then investigated. Moreover, the validity range and effect of the refractive index are also examined. The Johnson's S_B function in this paper is used as a versatile function to fit the commonly used particle size distribution functions in the dependent model. Simulations and experimental results show that the combined approximate method can be successfully applied to retrieval of spheroidal particle size distribution. In certain constraint conditions, the retrieval results demonstrate the high reliability and stability of the method. By using the combined approximate method, the complexity and computation time of the retrieval are significantly reduced, which is more suitable for quick and easy measurement. The method can also be used as a replacement when the rigorous solutions suffer computationally intractable difficulties.     

Operator representation of the wave function for a charged particle in an external field and its applications

A consistent derivation of the operator form for the solution of the wave equation for a charged particle in an arbitrary external electromagnetic field is presented. The expressions obtained can be used for solving any problems in quantum electrodynamics in external fields in the framework of the semiclassical operator method. The peculiarities of the application of this method are demonstrated for the small-angle elastic scattering of a high-energy photon in an arbitrary localized electric field. The problem is solved for the first time without presuming the central symmetry of the external field potential.