Light scattering: A review of particle characterization applications

This review covers the progress of light scattering applications in the field of particle characterization in the past decade. The review addresses static light scattering (the measurement of scattering intensities due to light–particle interaction at various spatial locations), dynamic light scattering (the measurement of scattering due to light–particle interaction as a function of time), and scattering tracking analysis (the tracking of particle movement through scattering measurement).     

Progress in nanoparticles characterization: Sizing and zeta potential measurement

Characterization of various nanoparticles is on the center stage in nanotechnology development. The subjects for nanoparticles characterization are focused on particle size and particle surface charge determinations. This article summarizes the latest development in particle size analysis using dynamic light scattering and surface charge determination using electrophoretic light scattering for nano-or even sub-nanoparticles in concentrated suspensions.     

Progress in nanoparticles characterization:Sizing and zeta potential measurement

Characterization of various nanoparticles is on the center stage in nanotechnology development. The subjects for nanoparticles characterization are focused on particle size and particle surface charge determinations. This article summarizes the latest development in particle size analysis using dynamic light scattering and surface charge determination using electrophoretic light scattering for nano- or even sub-nanoparticles in concentrated suspensions.     

Effect of nanoparticle concentration on zeta-potential measurement results and reproducibility

The effect of nanoparticle concentration on zeta-potential measurement results at dilute concentrations was evaluated.The values of the zeta-potential for four different types of nanoparticles,Ludox(silica),multi-walled carbon nanotubes(bamboo-shaped and hollow nanotubes)and gold,at various concentrations,were obtained using a laser Doppler electrophoresis instrument.The size of the nanoparticles on dilution was measured using dynamic light scattering(DLS).The results show that there is a concentration range within which the zeta-potential,and particle size,are not affected by nanoparticle concentration.The lower concentration limit for the system to produce consistent results was dependent on the nature of the sample under study and ranged between 10-2 and 10 4wt%.Below this concentration,there was an apparent shift in zeta-potential values to less negative values,which was accompanied by an increase in the particle size.The shift in zeta-potential was attributed to an increase in contribution of the signal from extraneous particulate matter.The increase in particle size was attributed to the nature of the homodyne optical configuration of the instrument.The aim of this study was to elucidate the range in nanopatticle concentration that allows for accurate and reliable measurement of the zeta-potential and DLS data.     

大延伸非均匀介质中地震波全弹性散射理论II-弹性波多次散射理论

推出大延伸非均匀连续介质的弹性波能量传输表达式,并以此为基础建立并发展了相应的弹性动力学能量传递理论.构造了一个基于非均匀薄层或非均匀相屏单次散射迭代法的多次散射模型.该模型既适用于弱散射,也适用于强散驰 既适用于普通散射,也适用于转换散射;尽管高频情况下只考虑普通散射及前向散射.应用该模型计算了弹性多次散射的能通量,处理了散射衰减问题。数值实验的结果表明,短周期地震图上的尾波主要来源于S波散射。     

A derivation of the phase Doppler measurement relations for an arbitrary geometry

The phase Doppler measurement relations are derived based on geometric optics, assuming point detectors and an arbitrary system geometry. A simple calculation method is given for determining the necessary conversion factors in any particular geometry, assuming light scattering by either simple reflection or refraction. The regions of the particle surface participating in the scattering are identified as part of the analysis.     

Resonance scattering characteristics of double-layer spherical particles

Based on the principle of ultrasonic resonance scattering, sound-scattering characteristics of double-layer spherical particles in water were numerically studied in this paper. By solving the equations of the scattering matrix, the scattering coefficient determined by the boundary conditions can be obtained, thus the expression for the sound-scattering function of a single double-layer spherical particle can be derived. To describe the resonance scattering characteristics of a single particle, the reduced scattering cross section and reduced extinction cross section curves were found through numerical calculation. Similarly, the numerically calculated sound attenuation coefficient curves were used to depict the resonance scattering characteristics of monodisperse and polydisperse particles. The results of numerical calculation showed that, for monodisperse particles, the strength of the resonance was mainly related to the particle size and the total number of particles; while for polydisperse particles, it was primarily affected by the particle size, the coverage of the particle size distribution and the particle concentration.     

基于积分方程方法的弹性波多重散射计算

运用积分方程方法计算了含多个随机分布椭圆柱型孔洞的随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。首先,建立了散射位移场满足的积分方程,推导了单个椭圆柱孔洞的散射截面计算公式。接着分析了在含多个随机分布椭圆柱型孔洞的随机非均匀介质中弹性波的多重散射,给出在统计平均意义下的相干波的波速和衰减系数计算公式。然后用Matlab进行了编程,给出了一个数值算例,并将计算结果与波函数展开法进行了比较,分析了随机空隙介质的频散特征及其孔洞椭圆偏心率和材料空隙率的影响。     

弹性波散射与多重散射的T矩阵方法

研究弹性波散射与多重散射的T矩阵方法。首先,基于Helmholtz体内和体外公式推导了对应于圆柱型散射体的T矩阵元素的具体表达式;接着分析了在含多个随机分布圆柱型散射体的随机非均匀介质中弹性波的多重散射并给出在统计平均意义下的相干波的定义以及波速和衰减系数计算公式;最后,针对Ge/Al、Sic/Al复合材料用Matlab进行了编程和数值计算;计算单个柱型散射体的散射截面以及随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。     

SH波绕界面孔的散射

用波函数展开方法研究了SH波绕界面孔的散射问题。由入射、反射和透射波组成的自由波场与孔的散射场叠加成总波场。按照一定方式将两个半平面散射波场延拓于全平面，通过Hankel-Fourier展开方法求得了任意形状孔散射场的级数解。以椭圆形孔为例计算了孔边缘的动应力集中系数。     

Geometrical optics approximation of light scattering by large air bubbles

For large spherical bubbles in water,geometrical optics approximation is considered a better method for calculating light scattering patterns.In this paper,the basic theory of geometrical optics approximation is clarified.The change of phase for bubbles is calculated when total reflection occurs,which is different from particles with relative refractive indices larger than 1.Verification of the method was achieved by assuming a spherical particle and comparing present results to Mie scattering and Debye calculation.Agreement with the Mie theory was excellent in all directions when the dimensionless size parameter is larger than 50.Limitations of the geometrical optics approximation are also discussed.     

层状介质中多个非共面Griffith裂纹的弹性波散射问题研究

本文利用积分变换的方法,研究了层状介质中多个非共面Griffith裂纹的弹性波散射问题,导出了当入射波分别为P(SV)波及SH波时的散射对偶积分方程,并以双覆盖层半空间中的双裂纹为例,对反平面剪切波的散射场进行了求解和较为详尽的分析。最后通过数值计算,得到了许多有关的动力学特性曲线,从而揭示了层状介质中多裂纹弹性波散射问题中的某些内在规律。     

Scattering of nonspherical particles rebounding from a smooth and a rough surface in a high-speed gas-particle flow

Scattering indicatrices of nonspherical particles rebounding from a smooth and a rough surface are obtained by direct Monte Carlo simulations. Particles shaped as ellipsoids of revolution, rectangular prisms, and prisms with truncated vertices are considered. Surface roughness is defined as a two-dimensional profile whose scattering characteristics are close to those of real roughness induced by abrasive erosion of the surface in a high-speed gas-particle flow. Impact interaction of an individual particle with the surface is considered in a three-dimensional formulation. The scattering indicatrices of reflected particles are found to depend substantially on the particle shape in the case of rebound from a smooth surface and to be almost independent of the particle shape if the particles rebound from a rough surface. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 79–88, March–April, 2008.     

A technical study on the Spraytec performances: influence of multiple light scattering and multi-modal drop-size distribution measurements

The present paper reports an experimental investigation on the performance of the Spraytec, the recent particle sizer commercialized by Malvern Instruments, Malvern, UK. As with the previous Malvern particle sizers, the Spraytec provides a volume-based drop-size distribution from the analysis of a diffraction pattern resulting from the interaction between a spray and a laser beam. This work focuses on the behavior of the Spraytec in two different situations. First, the influence of multiple scattering caused by the measurement of large and spatially inhomogeneous sprays is investigated. Second, a test of multi-modal drop-size distribution measurement is conducted. Contrary to the previous Malvern instrument, Spraytec's mathematical inversion procedure includes a patented multiple-scattering algorithm that allows measurements of very high concentrated sprays. This algorithm is tested here for large and inhomogeneous sprays for which multiple light scattering affects the measurement. The results show that the Spraytec algorithm cannot satisfactorily correct the measurements in this specific situation. It was also observed that the use of this algorithm is prohibited in the absence of multiple light scattering. In the second part of the study, a test of multi-modal drop-size distribution measurement is conducted. For the investigated situations it was found that the Malvern Spraytec is reliable in measuring such spray drop-size distributions.     

Numerical robustness of single-layer method with Fourier basis for multiple obstacle acoustic scattering in homogeneous media

We investigate efficient methods to simulate the multiple scattering of obstacles in homogeneous media. With a large number of small obstacles on a large domain, optimized pieces of software based on spatial discretization such as Finite Element Method (FEM) or Finite Difference lose their robustness. As an alternative, we work with an integral equation method, which uses single-layer potentials and truncation of Fourier series to describe the approximate scattered field. In the theoretical part of the paper, we describe in detail the linear systems generated by the method for impenetrable obstacles, accompanied by a well-posedness study. For the numerical performance study, we limit ourselves to the case of circular obstacles. We first compare and validate our codes with the highly optimized FEM-based software Montjoie. Secondly, we investigate the efficiency of different solver types (direct and iterative of type GMRES) in solving the dense linear system generated by the method. We observe the robustness of direct solvers over iterative ones for closely-spaced obstacles, and that of GMRES with Lower–Upper Symmetric Gauss–Seidel and Symmetric Gauss–Seidel preconditioners for far-apart obstacles.     

NUMERICAL ANALYZITION OF NANO-PARTICLE FOLLOWING FEATURES FOR RAYLEIGH SCATTERING VELOCITY MEASUREMENT TEST IN LOW DENSITY WIND TUNNEL

在低密度风洞试验流场中,加入少量纳米粒子,可以增强瑞利散射测速试验的散射光强度.纳米粒子能否适应流场气流速度变化是测量结果准确性的关键.为了研究瑞利散射测速实验中测量到的纳米粒子的速度能否反映流场当地气流速度,采用基于直接模拟蒙特卡罗方法的稀薄两相流双向耦合算法,对低密度风洞流场中纳米粒子在大梯度流场中的跟随性进行了数值研究.仿真了10 nm,50 nm和100 nm TiO₂三种尺寸的纳米粒子分别在M6和M12低密度风洞返回舱高超声速绕流流场中的运动特性.仿真结果显示,不同尺寸的纳米粒子在不同的流场稀薄度条件下的跟随性不同,纳米粒子尺寸越小,跟随性越好.在稀薄度较低的M6流场中,10 nm粒子跟随性很好,与瑞利散射测量结果比较接近,粒径50 nm以上的粒子跟随性较差,而在稀薄度较高的M12流场中,10 nm粒子的跟随性也变差,表明通过瑞利散射测量到的纳米粒子速度和流场中气体速度有一定差距,不能准确反映流场当地速度.     

蒙特卡洛方法数值研究大气颗粒物动力学效应和辐射传输性质

爆发性增强的雾天,空气污染严重能见度低,这与大气边界层湍流性质、悬浮颗粒的动力学及散射性质密切相关.文中基于颗粒群平衡方程和Mie理论,采取加权蒙特卡洛方法,自行开发了Fortran程序.文中计算所得的颗粒尺度分布函数、颗粒散射性质与实验值、理论解一致,验证了数值模型和方法的正确性.此外,数值研究了雾爆发性增强阶段雾滴谱拓宽、能见度降低的机理,讨论湍流输运和颗粒局部聚集效应下颗粒间的碰并过程,并耦合颗粒散射性质,数值分析雾发展中湍流耗散率对颗粒对径向相对速度、系统透过率的影响;以及颗粒对径向相对速度与系统透过率、颗粒尺度的关系.研究结果表明:随着湍流耗散率的增大,颗粒的径向相对速度呈现先缓慢而后快速增大的变化趋势.1000s时刻,湍流的耗散率为1.0×10-2m2/s3,颗粒径向相对速度(无量纲)为0.0969;对于0.6μm的可见光,雾环境颗粒系统的透过率为0.47.此外,雾发展中雾滴易与气溶胶碰并,系统的散射性质与水组成的雾滴系统不同,天气的能见度明显降低.      

Scattering far field solution of SH-wave by movable rigid cylindrical interface inclusion

The Green's function is used to solve the scattering far field solution of SH-wave by a movable rigid cylindrical interface inclusion in a linear elastic body. First, a suitable Green's function is developed, which is the fundamental displacement solution of an elastic half space with a movable rigid half-cylindrical inclusion impacted by out-of-plane harmonic line source loaded at any point of its horizontal surface. By using the Green's function, a series of Fredholm integral equations of the first kind which determine the scattering far field can be set up. Then the paper gives the expressions on the far field including the displacement mode of scattering wave and the solution of scattering cross-section. Finally, some examples and numerical results are discussed to analyze the influence of the combination of different media parameters on the answer of far field.     

颗粒群碰撞搜索及CFD-DEM耦合分域求解的推进算法研究

在采用计算流体力学-离散元耦合方法(computational fluiddynamics-discrete element method, CFD-DEM)进行固液两相耦合分析时, 颗粒计算时间步的选取直接影响到耦合计算精度和计算效率. 为此, 本文选取每个目标颗粒为研究对象, 引入插值函数计算时间步的运动位移, 构建可变空间搜索网格; 通过筛选可能碰撞颗粒建立搜索列表, 采用逆向搜索方式判断碰撞颗粒, 从而提出一种改进的DEM方法(modified discreteelement method, MDEM). 该算法在颗粒群与流体耦合计算中, 颗粒计算初始时间步选取不受颗粒碰撞时间限制, 通过自动调整和修正实现大步长, 由颗粒和流体耦合条件实时更新流体计算时间步, 使颗粒计算时间步选取过小导致计算效率低、选取过大导致颗粒碰撞漏判的问题得以解决, 为颗粒与流体耦合的数值模拟提供了行之有效的计算方法. 通过两个颗粒和多个颗粒的数值模拟, 得到的颗粒间碰撞力、碰撞位置及次数, 与理论计算结果的相对误差均低于2%, 与传统的DEM碰撞搜索算法相比, 在选取的3种计算时间步均不会影响计算精度, 且有较高的计算效率. 通过多个颗粒与流体的耦合数值模拟, 采用传统的CFD-DEM方法, 只有颗粒计算时间步选取10$^{-6}$ s或更小才能得到精确解, 而采用本文方法取10$^{-4}$ s也能够得到精确解, 避免了颗粒碰撞随时间步增大而出现的漏判问题, 且计算耗时降低了16.7%.