Absorption and Scattering of Light by Highly Concentrated Two‐phase Flows

The spray cone emerging during an extended metal atomization process (called spray forming) has been investigated in order to quantify the influence of highly concentrated multiphase flows on phase‐Doppler‐anemometry (PDA) measurements. Using this non‐intrusive, optical measurement technique not only the local particle size and velocity distributions of the spray can be obtained but also additional information about the mass flux in the multiphase flow. Since standard phase‐Doppler systems can be easily applied to low concentrated particle systems (spherical particles with smooth surfaces and an optical transparent continuous phase taken for granted) the application of this measurement technique to highly concentrated multiphase flows is more complex. Both the laser light propagating from the PDA device to the probe volume and the scattered one going backward to the PDA receiving system are disturbed by passing the highly concentrated multiphase flow. The resulting significant loss in signal quality especially concerns the measurement of the smaller particles of the spray because of their reduced silhouette (in comparison with the bigger ones). Thus, the detection of the smallest particles becomes partially impossible leading to measurement of a distorted diameter distribution of the entire particle collective. In this study the distortions of the measured distributions dependent on the particle number concentration as well as on the path length of the laser light are discussed.     

On the Sizing Accuracy of Laser Optical Particle Counters

The performance of a narrow-angle and a wide-angle, forward scattering laser aerosol spectrometer has been studied as a function of particle size and refractive index. The results have been compared with theoretical calculations based on light scattering theory. The results indicate that for the narrow-angle instrument, the scattered-light intensity is not a monotonic function of particle size for transparent particles (a monotonic relationship is required for unambiguous particle size measurement) above 0.7 μm. The instrument is therefore limited in its useful range to size distribution measurement between 0.2 μm – its lower particle size limit – and 0.7 μm for transparent particles. In the case of the wide-angle instrument, the instrument output is a monotonic function of particle size for transparent particles, but the output is severely attenuated for light absorbing particles above 0.3 μm. The instrument, therefore, cannot be used for accurate size measurements above 0.3 μm for light absorbing particles.     

驻波声场中单分散细颗粒的相互作用特性

利用外加声场促进悬浮在气相中的细颗粒发生相互作用,进而引起颗粒的碰撞和凝并,使得颗粒平均粒径增大、数目浓度降低,是控制细颗粒排放的重要技术途径.为探究驻波声场中单分散细颗粒的相互作用,建立包含曳力、重力、声尾流效应的颗粒相互作用模型,采用四阶经典龙格-库塔算法和二阶隐式亚当斯插值算法对模型进行求解.将数值模拟得到的颗粒声波夹带速度和相互作用过程与相应的解析解和实验结果进行对比,验证模型的准确性.进而研究颗粒初始条件和直径对相互作用特性的影响.结果表明,初始时刻颗粒中心连线越接近声波波动方向、颗粒位置越接近波腹点,颗粒间的声尾流效应就越强,颗粒发生碰撞所需要的时间就越短.研究还发现,颗粒直径对颗粒相互作用的影响取决于初始时刻颗粒中心连线偏离声波波动方向的程度.当偏离较小时,颗粒直径越大,颗粒发生碰撞所需要的时间越短;当偏离很大时,直径较小的颗粒能够发生碰撞,而直径较大的颗粒则无法发生碰撞.     

Weak-localization effect for light backscattered by surfaces with a complex structure

Results of laboratory measurements of the weak-localization effect for light scattered by surfaces with different characteristics are presented. The measurements were made in a range of phase angles of 0.2°–3.5°. The aim of the measurements was to study the influence of the choice of surface material (metal, dielectric), the size of particles of the scattering surface, their packing density, the reflectivity of a sample, and the wavelength of incident radiation on the effect. For the measurements, both nonpolarized and linearly polarized light was used. Powders of dielectric materials were found to enhance the weak-localization effect with increasing particle size, but the effect weakened starting with a certain size of the order of wavelength. The pressing of powders of dielectric transparent materials enhanced the opposition effect. This was most pronounced for samples with small-sized particles. The phase dependence of brightness became wider and more linear with decreasing reflectivity of the surface. A qualitative difference in the behavior of the phase dependence for the ratio of cross-and copolarized components was observed. For metals and metal-like materials, the ratio increased with decreasing phase angle. Dielectrics were found to have an opposite dependence.     

Particle Sizes of Fumed Oxides: A New Approach Using PCS Signals

Fumed oxides produced in gas‐phase processes, such as silicas and aluminum oxide, consist of a cluster of aggregated primary particles. The aggregate size of these particles is an important variable in many applications. However, current procedures for measuring particle sizes all assume that the particles have a spherical shape and are thus not truly capable of determining aggregate size. The results of such particle size measurements are consequently called “equivalent spherical diameter” (ESD), but these results vary from method to method. This publication shows that it is feasible to use the number of primary particles per aggregate, rather than the ESD, as a measure for the particle size of clusters of this type. The method is based on dynamic light scattering (photon correlation spectroscopy, PCS), which has proven itself in the analysis of fumed oxides. A numerical simulation based on random, computer‐generated model aggregates is used to modify the well‐known Stokes‐Einstein equation so that the number of primary particles can be determined.     

Stochastic modeling of evaporating sprays within a consistent hybrid joint PDF framework

In the present study, a framework for modeling two-phase evaporating flow is presented, which employs an Eulerian–Lagrangian–Lagrangian approach. For the continuous phase, a joint velocity-composition probability density function (PDF) method is used. Opposed to other approaches, such PDF methods require no modeling for turbulent convection and chemical source terms. For the dispersed phase, the PDF of velocity, diameter, temperature, seen gas velocity and seen gas composition is calculated. This provides a unified formulation, which allows to consistently address the different modeling issues associated with such a system. Because of the high dimensionality, particle methods are employed to solve the PDF transport equations. To further enhance computational efficiency, a local particle time-stepping algorithm is implemented and a particle time-averaging technique is employed to reduce statistical and bias errors. In comparison to previous studies, a significantly smaller number of droplet particles per grid cell can be employed for the computations, which rely on two-way coupling between the droplet and gas phases. The framework was validated using established experimental data and a good overall agreement can be observed.     

Detection of Deposited Particles from the Backside of a Glass Plate

Microcontamination of product surfaces by deposited particles is an important problem in clean technologies. A most sensitive product to contamination by particles is a wafer during chip production. Therefore, methods for monitoring particle deposition on wafer surfaces have been developed in the last decade. A wafer with an unstructured and reflecting surface is inserted into the process equipment. After some time, depending on the process, this wafer is removed from the process equipment and is analysed with respect to the number of deposited particles using a wafer scanner. However, in situ particle detection in a process chamber is not possible with this technique. This would be possible if, instead of a monitor wafer, a transparent glass plate is mounted, e.g. in the housing of the process equipment. Then the illuminating and scattered light detection equipment can be mounted outside the process equipment. Since both the illuminating laser beam and the scattered light have to be transmitted through the glass plate, losses will occur, which will reduce the lower limit of detection with respect to particle size. In this article we estimate the detection possibilities theoretically and experimentally. A simple model based on Mie and vector scattering theory has been developed to describe the light-scattering behavior of a single spherical particle on a glass plate with random surface irregularities. The scattered light of individual particles of four particle sizes (1.03, 1.6, 2.92 and 4.23 μm) on the same glass surface and from the uncontaminated area of the glass plate was measured for unpolarized and normally incident light. The values of the scattered light from this model were compared with the experimental results. The comparison shows a reasonable agreement of the angular distribution of the scattered light. The developed model is used to predict the lower limit of detection for particles on a transparent surface. The theoretical estimations show that it should be possible to detect particles of a diameter down to 0.2 μm with the described measurement technique.     

The influence of particle distribution and interphase on the thermal expansion coefficient of particulate composites by the use of a new model

In this work, the thermal expansion coefficient (CTE) of a composite containing spherical particles surrounded by an inhomogeneous interphase embedded in an isotropic matrix is evaluated by means of a new model. The thermomechanical properties of the interphase are formulated as continuous radial functions. It is assumed that this third phase developed between the polymeric matrix and the filler particles contains both areas of absorption interaction in polymer surface layers onto filler particles as well as areas of mechanical imperfections. It can be said that the concept of boundary interphase is a useful tool to describe quantitatively the adhesion efficiency between matrix and particles and that there is an effect of this phase on the thermomechanical properties of the composite. The thickness and volume fraction of this phase were determined from heat capacity measurements for various filler contents. On the other hand, it is assumed that the particle arrangement (distribution) which can be considered as an influence of neighboring inclusions and their interaction should affect the thermomechanical constants of the composite. The theoretical predictions were compared with experimental results as well as with theoretical values from expressions obtained from other workers and they were found to be in satisfactory agreement.     

An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows

A three-dimensional, incompressible, multiphase particle-in-cell method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to an Eulerian grid and then mapping back computed stress tensors to particle positions. A subgrid particle, normal stress model for discrete particles which is robust and eliminates the need for an implicit calculation of the particle normal stress on the grid is presented. Interpolation operators and their properties are defined which provide compact support, are conservative, and provide fast solution for a large particle population. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. Particles are implicitly coupled to the fluid phase, and the fluid momentum and pressure equations are implicitly solved, which gives a robust solution.     

The Phase-Doppler Method Applied to Very Small Particles

Using a computer model based on Lorenz-Mie and generalized Lorenz-Mie theory, various optical confiugurations of a phase-Doppler system were analysed with regard to their suitability for diameter measurements in the sub-micron range. The major concern in this size range is multi-valuedness of the phase-diameter characteristic, the relatively small signal-to-noise ratio obtained with the very low scattered intensity and the small value of the phase difference to be measured. It is shown numerically and by experiment that for particles in a free stream the multi-valuedness and the shot noise need not prohibit measurements in the sub-micron size range. The major source of phase error results from light scattered form objects or material other than the particle inside the measuring volume. Using an optical set-up with nearly counter-propagating incident beams and a large angle between the detectors, measurements were obtained for particle diameters down to 200 nm, and it is estimated that with some improvements in receiver optics measurement down to 100 nm will be possible.     

Phase-Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity

The principle of the dual burst technique (DBT) based on phase-Doppler anemometry (PDA) is proposed for simultaneous particle refractive index, size and velocity measurements. This technique used the trajectory effects in PDA systems to separate the two contributions of the different scattering processes. In the case of forward scattering and refracting particles, it is shown that from the phase of the reflected contribution, the particle diameter can be deduced, whereas from the refracted contribution the particle refractive index and velocity can be obtained. Furthermore, the intensity ratio of these two scattering processes can be used for absorption measurements. Simulations based on generalized Lorenz-Mie theory and experimental tests using monodispersed droplets of different refractive indices and absorption coefficients have validated this technique.     

Phase transitions for a continuous system of classical particles in a box

A continuous classical system involving an infinite number of distinguishable particles is analyzed along the same lines as its quantum analogue, considered in [1]. A commutativeC*-algebra is set up on the phase space of the system, and a representation-dependent definition of equilibrium involving the static KMS condition is given. For a special class of interactions the set of equilibrium states is realized as a convex Borel set whose extremal states are characterized by solutions to a system of integral equations. By analyzing these integral equations, we prove the absence of phase transitions for high temperature and construct a phase transition for low temperature. The construction also provides an example of a translation-invariant state whose decomposition at infinity yields states that are not translation-invariant. Thus we have an example in the classical situation of continuous symmetry breaking.This article is a part of the author's doctoral thesis, which was submitted to the mathematics department at Duke University     

Digital Holography for Instantaneous Spray Diagnostics on a Plane

We present a measurement technique that is capable of simultaneously determining sizes and positions of multiple transparent droplets in a plane from scattered light features. The technique is largely independent of particle intensity and mutual obscuration. Reflected and refracted light from the droplets in a pulsed laser sheet is recorded holographically to yield the smallest possible probe volume and the largest possible number density. Larger droplets are best analyzed at the image plane; in this case, the droplets appear as two spots (glare points), whose separation is proportional to the droplet diameter. Smaller droplets are easier to analyze at an out‐of‐focus plane, where their images appear as fringe patterns whose spatial frequency is related to droplet size. Photographic techniques allow only one of these planes to be chosen and are therefore not suitable for multidisperse sprays. Optical holography allows to analyze arbitrary depths, but often suffers from low sensitivity and long analysis times. With digital holography, the spray images are captured digitally by a CCD camera and reconstructed numerically; as in optical holography, the particle reconstruction plane can be freely chosen a posteriori to optimize the measurement. We discuss the issues raised by the transition from holographic film to a CCD sensor as the recording medium, and demonstrate the capabilities of the digital technique.     

对利用动态光散射法测量颗粒粒径和液体黏度的改进

光散射技术通过测量悬浮液中布朗运动颗粒的平移扩散系数,得到颗粒流体力学直径或液体黏度.本文由单参数模型入手,建立了低颗粒浓度下,单颗粒平移扩散系数与颗粒集体平移扩散系数和颗粒浓度之间的线性依存关系并将其引入光散射法中,从而对现有的测量方法进行了改进.改进后的测量方法可实现纳米尺度球型颗粒标称直径的测量和液体黏度的绝对法测量.以聚苯乙烯颗粒+水和二氧化硅颗粒+乙醇两个分散系为参考样本,通过实验,验证了改进后方法的可行性.此外,还针对上述两个分散系,实验探讨了温度和颗粒浓度对颗粒集体平移扩散系数的影响规律,发现聚苯乙烯颗粒+水分散系中,颗粒间相互作用表现为引力;二氧化硅颗粒+乙醇分散系中,颗粒间相互作用表现为斥力.讨论了颗粒集体平移扩散系数随颗粒浓度变化规律与第二渗透维里系数的关系.     

The kinetics of homogeneous nucleation of silver nanoparticles stabilized by polymers

The formation of Ag nanoparticles synthesized by homogeneous nucleation, stabilized by polymers (PVA and PVP) was monitored by UV–Vis spectrophotometry and transmission electron microscopy. Our aim was to differentiate between the two main phases of particle formation, i.e. nucleation and growth and to characterize their rates with the help of appropriate kinetic equations. Time resolved spectrophotometric measurements revealed that particle formation is an autocatalytic process: a slow, continuous nucleation phase (3–5 min) is followed by a rapid, autocatalytic growth phase where the maximal particle size is 5–7 nm. By freezing the reaction mixture, the process of particle growth can be followed from 5 to 40 min on TEM pictures. The first order rate constants were calculated and they are strongly depend on the polymer concentration. If the growing particles are attached by PEI to the surface of a solid support, the formation of silver nanoparticles can also be followed by atomic force microscopy (AFM) and we can control the particle growth on mica surface. The cross section analysis of the pictures show, that the particle growing process can be also monitored at solid–liquid interface.     

Theoretical studies on particle shape classification based on simultaneous small forward angle light scattering and aerodynamic sizing

Particle shape contributes to understanding the physical and chemical processes of the atmosphere and better ascertaining the origins and chemical compositions of the particles. The particle shape can be classified by the aspect ratio,which can be estimated through the asymmetry factor measured with angularly resolved light scattering. An experimental method of obtaining the asymmetry factor based on simultaneous small forward angle light scattering and aerodynamic size measurements is described briefly. The near forward scattering intensity signals of three detectors in the azimuthal angles at 120?offset are calculated using the methods of T-matrix and discrete dipole approximation. Prolate spheroid particles with different aspect ratios are used as the shape models with the assumption that the symmetry axis is parallel to the flow axis and perpendicular to the incident light. The relations between the asymmetry factor and the optical size and aerodynamic size at various equivalent sizes, refractive indices, and mass densities are discussed in this paper. The numerically calculated results indicate that an elongated particle may be classified at diameter larger than 1.0 μm, and may not be distinguished from a sphere at diameter less than 0.5 μm. It is estimated that the lowest detected aspect ratio is around 1.5:1 in consideration of the experimental errors.     

Aerosol light absorption and its measurement: A review

Light absorption by aerosols contributes to solar radiative forcing through absorption of solar radiation and heating of the absorbing aerosol layer. Besides the direct radiative effect, the heating can evaporate clouds and change the atmospheric dynamics. Aerosol light absorption in the atmosphere is dominated by black carbon (BC) with additional, significant contributions from the still poorly understood brown carbon and from mineral dust. Sources of these absorbing aerosols include biomass burning and other combustion processes and dust entrainment.For particles much smaller than the wavelength of incident light, absorption is proportional to the particle volume and mass. Absorption can be calculated with Mie theory for spherical particles and with more complicated numerical methods for other particle shapes.The quantitative measurement of aerosol light absorption is still a challenge. Simple, commonly used filter measurements are prone to measurement artifacts due to particle concentration and modification of particle and filter morphology upon particle deposition, optical interaction of deposited particles and filter medium, and poor angular integration of light scattered by deposited particles. In situ methods measure particle absorption with the particles in their natural suspended state and therefore are not prone to effects related to particle deposition and concentration on filters. Photoacoustic and refractive index-based measurements rely on the heating of particles during light absorption, which, for power-modulated light sources, causes an acoustic signal and modulation of the refractive index in the air surrounding the particles that can be quantified with a microphone and an interferometer, respectively. These methods may suffer from some interference due to light-induced particle evaporation. Laser-induced incandescence also monitors particle heating upon absorption, but heats absorbing particles to much higher temperatures to quantify BC mass from the thermal radiation emitted by the heated particles. Extinction-minus-scattering techniques have limited sensitivity for measuring aerosol light absorption unless the very long absorption paths of cavity ring-down techniques are used. Systematic errors can be dominated by truncation errors in the scattering measurement for large particles or by subtraction errors for high single scattering albedo particles. Remote sensing techniques are essential for global monitoring of aerosol light absorption. While local column-integrated measurements of aerosol light absorption with sun and sky radiometers are routinely done, global satellite measurements are so far largely limited to determining a semi-quantitative UV absorption index.     

光源的偏振态对动态光散射颗粒测量结果的影响

研究了在动态光散射纳米颗粒测量中,光源的偏振态对测量结果的影响。采用了粒径为100nm、体积浓度为0.5%的标准颗粒作为样品,使He-Ne激光通过起偏器得到0°～180°方向的偏振光,测量了散射光强、偏振度和粒径测量值的变化,计算了相应的粒径均值偏差和标准差,并将这一结果与无偏振He-Ne激光入射进行了比较。结果表明,当入射光为线偏振光时,偏振方向垂直于散射面时测量效果最好;另一方面,由于颗粒系散射迭加造成的散射光偏振度降低,使线偏振光源与无偏振光源产生的散射光偏振度无明显差别,证明在测量中可以使用无偏振He-Ne激光代替。     

数字显微全息重建图像的景深扩展研究

显微物镜的景深问题限制数字显微全息在大纵深视场中的应用. 本文充分利用数值重建的特点, 采取低频和高频系数子图上的最大亮度梯度的局部方差作为聚焦判据, 在小波分解域内对显微全息重建图像的景深扩展问题进行了研究. 对倾斜的连续物体碳纤维进行三维重建, 分析了重建距离与直径测量误差的关系. 以超声波雾化器生成的微液滴颗粒场为例, 对离散颗粒场的重建图像进行了景深扩展. 利用基于广义洛伦兹-米散射理论的模型分别模拟1-15 μm 的非透明与透明离散颗粒的显微全息图, 分析了该方法重建的颗粒场的纵深定位误差与夫琅禾费系数的关系, 对比了非透明与透明颗粒纵深定位误差的异同点. 实验和模拟结果显示出该方法对于连续物体和离散颗粒场的显微全息重建图像的景深扩展能力, 且能由此准确重建物体信息.     

Trajectory Ambiguities in Phase Doppler Systems: Study of a near forward and a near-backward geometry

Generalized Lorenz-Mie theory for the scattering of arbitrarily shaped beams by spherical particles has been applied to two standard phase Doppler layouts, employing receiving units at 30° and 150° off-axis locations. It is shown that the particle trajectory effects may lead to inaccurate size measurements for the near-forward receiver and may make the near-backward measurements totally misleading when a large particle size range (1:40) needs to be covered. Only limited improvements can be achieved by using two phase-shift signals from a single receiving unit for discrimination. The errors associated with the trajectories are also detrimental to the concentration measurements based on the existing criteria. However, an extended optical system employing two identical receiving units, located symmetrically about the plane of the laser beams, provides a robust solution to the trajectory ambiguity. It can be used to measure correctly the particle size and the particle location in the measuring volume. The difficulties associated with estimating the effective size of the measuring volume as a function of the particle diameter (in order to determine the true size distribution and the particle number density) may also be resolved by employing an extended system. Hence, despite a higher cost, this arrangement is attractive, at least for obtaining some benchmark simultaneous measurements of sizes and velocities in two-phase particulate flows.