The role of fluid turbulence on contact electrification of suspended particles

A probabilistic version of a well-known phenomenological model for contact electrification is used to examine the effect of fluid turbulence on charge development for suspended particles as a function of the particle Stokes number. The distribution of particle collisions and particle charge appear to approach asymptotic states for high values of the Kolmogorov-scale Stokes numbers, exhibiting approximately normal distributions. The influence on particle contact electrification of differences in initial charge carrier density and in particle size are examined.     

Ultrasound and light scattering from a suspension of reversible fractal clusters in shear flow

Shear break-up of reversible fractal clusters is investigated by ultrasound and multiple light scattering in the low shear regime. We consider a dense suspension of Rayleigh scatterers (particles or clusters) with acoustic properties close to those of the surrounding liquid so that the attenuation of the ultrasonic coherent field is weak and multiple scattering is negligible. The concept of variance in local particle volume fraction is used to derive an original expression of the ultrasound scattering cross-section per unit volume for Rayleigh fractal clusters. On the basis of a scaling law for the shear break-up of aggregates, then we derive the shear stress dependence of the ultrasound scattered intensity from a suspension of reversible fractal clusters. In a second part, we present rheo-acoustical experiments to study the shear break-up of hardened red cell aggregates in plane-plane flow geometry and we examine both the self consistent field approximation and the scaling laws used in microrheological models. We further compare the ability of acoustical backscattering and optical reflectometry techniques to estimate the critical disaggregation shear stress and the particle surface adhesive energy. Finally, the microrheological model from Snabre and Mills [#!ref5!#] based on a fractal approach is shown to describe the non Newtonian behavior of a dense distribution of hardened red cell aggregates. Received 12 November 1998 and Received in final form 17 May 1999     

相干瑞利散射海水水下温度测量技术的理论研究

海水水下温度的快速大范围测量是海洋监测的重要内容,在民用和军事领域都有着至关重要的意义,本文提出了采用相干瑞利散射方法测量海水水下温度的新方法:用宽带高速光电探测器接收本振激光和海水后向瑞利散射光相干产生的差频信号,进行傅里叶变换分析获取海水瑞利散射展宽谱,从而反演海水温度,首先从海水的热力学特性出发,对利用瑞利散射谱测量海水水下温度的基本原理进行了理论研究和软件模拟;然后对采用相干探测测量海水瑞利散射谱的测量方法进行了理论分析和软件模拟;在此基础上对瑞利散射海水水下温度测量精度进行了分析,得出当水体瑞利散射频谱半宽度测量精度为1 MHz时,测温精度约为0.35 K。     

湍流对部分相干双曲余弦高斯光束的瑞利区间的影响

推导出了部分相干双曲余弦高斯光束在自由空间和湍流大气中传输瑞利区间的解析公式,并研究了湍流对光束瑞利区间的影响.研究表明,部分相干双曲余弦高斯光束的瑞利区间由湍流强度和光束参数等因数共同确定.湍流使得光束的瑞利区间缩短,并且湍流越强瑞利区间越短.在自由空间中,瑞利区间随光束相干参数 α 、光束参数 β 和高斯束宽 w ₀的增大以及波长 λ 的减小而增大.但是, α,β 和 w ₀越小以及 λ 越大,瑞利区间受湍流的影响越小.并且,当 关键词： 瑞利区间 部分相干双曲余弦高斯光束 大气湍流 自由空间     

转捩射流中涡结构与颗粒扩散的直接模拟

为考察转捩射流中拟序结构的空间演化过程及其对不同Stokes颗粒扩散的影响,采用有限容积方法和分步投影算法对三维气固两相射流进行了直接模拟。其中流体控制方程组的时间积分采用低存储三阶精度的Runge-Kutta格式; 颗粒的跟踪在拉格朗日框架下进行。模拟结果发现,在流场拟序结构由大尺度转化为小尺度的过程中,中、小Stokes数的颗粒能自发地调整它们的扩散方式,分别由非均匀状态向均匀状态以及由均匀状态向非均匀状态转变。     

非Kolmogorov大气湍流对径向部分相干阵列光束瑞利区间和湍流距离的影响

基于广义的Huygens-Fresnel原理和非Kolmogorov谱模型,推导了无线光通信系统中径向分布部分相干高斯-谢尔模型阵列光束在非Kolmogorov大气湍流中传输时瑞利区间z_R和湍流距离z_T的解析表达式,对瑞利区间和湍流距离随湍流参量和光束参量的变化情况进行了数值分析.结果表明:不论是相干还是非相干合成,径向分布部分相干高斯-谢尔模型阵列光束的z_R和z_T均随湍流广义指数α的增大非单调变化,当α=3.11时,z_R和z_T取最小值,此时阵列光束扩展最大;相干合成比非相干合成的光束扩展要小,但其受湍流的影响更大;对于相干合成而言,径向分布半径r0越大,合成光束的z_R和z_T就越大,而非相干合成的z_R和z_T不受r0的影响;不论是相干还是非相干合成,阵列子光束数目对合成光束的z_R和z_T没有影响;当光束相干参量β足够小或波长λ足够大时,大气湍流对阵列光束z_R的影响可以忽略.     

Near-field and far-field spreading of partially coherent annular beams propagating through atmospheric turbulence

Based on the extended Huygens–Fresnel principle, closed-form expressions for the Rayleigh range and the far-field divergence angle of partially coherent annular beams propagating through atmospheric turbulence are derived by using the Wigner distribution function (WDF). Taking the Rayleigh range and the far-field divergence angle as the characteristic parameters of near-field and far-field spreading, respectively, the spreading of partially coherent annular beams both in free space and in turbulence is studied in detail. It is found that the effect of the strength of turbulence and beam parameters (e.g., the spatial correlation length, the waist width, and the wave length) on the beam spreading in the near field is in agreement with that in the far field. However, in turbulence, the effect of the obscure ratio of annular beams on the spreading is different between in the near field and in the far field. Namely, in turbulence the beam spreading in the near field becomes smaller and the beam spreading in the far field becomes larger as the obscure ratio increases. In particular, the effect of turbulence on the Rayleigh range and the far-field divergence angle is nearly unchanged versus the obscure ratio when the spatial correlation length is small. The main results obtained in this paper are explained physically.     

Inertial clustering of particles in high-Reynolds-number turbulence

We report experimental evidence of spatial clustering of dense particles in homogenous, isotropic turbulence at high Reynolds numbers. The dissipation-scale clustering becomes stronger as the Stokes number increases and is found to exhibit similarity with respect to the droplet Stokes number over a range of experimental conditions (particle diameter and turbulent energy dissipation rate). These findings are in qualitative agreement with recent theoretical and computational studies of inertial particle clustering in turbulence. Because of the large Reynolds numbers a broad scaling range of particle clustering due to turbulent mixing is present, and the inertial clustering can clearly be distinguished from that due to mixing of fluid particles.     

Trapping two types of particles using a focused partially coherent elegant Laguerre-Gaussian beam

The radiation forces on a Rayleigh dielectric sphere induced by a focused partially coherent elegant Laguerre-Gaussian (ELG) beam are investigated by using the Rayleigh scattering theory. It is found that a focused partially coherent ELG beam with suitable mode orders can be used to trap a Rayleigh particle whose refractive index is larger or smaller than that of the ambient by varying its initial spatial coherence width. Therefore, one can use one optical-trap system to trap two types of particles with different refractive indices.     

Scattering of sound in a moving viscous microinhomogeneous medium at large Reynolds numbers

A generalization of the Rayleigh law of a low-frequency sound attenuation in a microinhomogeneous medium to the case of scattering particles moving in a viscous liquid at a large Reynolds numbers is proposed. It is shown that, under these conditions, the attenuation may be independent of the scattering by the moving particles themselves but be only determined by the flow caused by these particles, the maximum attenuation being observed in the direction across the particle motion. The corresponding corrections proportional to the first power of the hydrodynamic Mach number are compared with the corrections lying at the basis of the modified Rayleigh law, which was proposed earlier for the potential flow of an ideal liquid around inhomogeneities, and also with the laws of scattering in a moving viscous microinhomogeneous medium at a small Reynolds numbers. As an example of the operation of the generalized law, characteristics of the sound scattering by rain are refined.     

Interaction of solid particles with a tangle of vortex filaments in a viscous fluid

Homogeneous isotropic turbulence consists of coherent filamentary vortex structures superimposed to a more incoherent background. The question which we address is the effect of these structures on the dynamics of small, neutrally buoyant solid particles. Rather than generating the turbulence by direct numerical simulation (DNS) of the Navier-Stokes equations, we use a model of turbulence based entirely on viscous vortex filaments which interact via inertial forces and reconnect with each other. Using this model, we show that solid particles can become trapped around vortex filaments, something difficult to achieve with DNS. Unlike most studies, we have not neglected inviscid inertial effects. By comparing the Stokes, local, and convective components of the particle's acceleration, we also show that the convective part clearly identifies the trapping.     

直接模拟离散颗粒对湍流射流的影响

发展了一种基于双向耦合的直接数值模拟方法,研究了两相湍流射流中离散颗粒对气相射流的影响。流场采用高分辨率的算法直接耦合求解,颗粒相采用拉格朗日方法跟踪。结果表明不同Stokes数的颗粒对射流的影响不同。所有的颗粒都降低了射流速度半宽,但对流向平均速度剖面的影响比较复杂.Stokes数为0.01和50的颗粒降低了横向平均速度,使得湍流强度剖面变的更宽更低;而Stokes数为1的颗粒则增加了横向平均速度,降低了湍流强度。     

Statistics of a coherent lidar signal in a turbulent atmosphere

Absolute and conditional statistical properties of a pulse coherent Doppler lidar signal in a turbulent atmosphere are studied. Upon coherent receiving of optical fields scattered by a large number of particles, the lidar signal is shown to be a nonstationary non-Gaussian random process with Gaussian conditional statistical characteristics. The appearance of non-Gaussian properties of the signal is caused by correlation of turbulent fluctuations of the wind velocity field within the scattering volume. For the considered signal model, which corresponds to the single scattering approximation and is a sum of a large number of random variables, the central limit theorem is found to be untrue due to the statistical dependence of particles’ positions in a turbulent atmosphere. The results of numerical calculations show that, for a homogeneous and isotropic turbulence, the behavior of the signal statistics significantly depends on the size of the scattering volume and on the state of atmospheric turbulence. A Gaussian statistics is observed at small heights; with an increase in height, the non-Gaussian component becomes considerable in fluctuations of the lidar signal.     

Computer simulations for multiple scattering of light rays in systems of opaque particles

A new computer model for multiple light scattering in arbitrary systems of opaque diffusely scattering particles is considered. For ray tracing and scattering in such systems, the geometric optics approximation is used. Semi-infinite media and clusters with spherical and irregular shaped particles are investigated. The irregular particles are approximated with a discrete set of small triangular facets attached to each other. The particle surface is supposed to scatter by the Lambertian indicatrix. Scattering of the first six orders is considered, but the model can be effectively used for calculations of higher orders too. Phase-angle curves of scattering for media and clusters with different packing density are calculated. It is shown that the contributions of scattering orders rapidly diminish as the order grows even for non-absorbing particulate surfaces. Only the first scattering order shows the opposition effect and is rather sensitive to packing density. Higher orders do not show any features near zero phase angle. The contributions of high orders increase slightly, when the packing density increases. The form of particles is important mostly for the second scattering order. For clusters of particles both packing density and number of particles are important for phase function behavior. Clusters consisting of 100 particles show weak phase-angle dependences of high orders of scattering. These dependences become more prominent with increase of number of particles. Phase curves for spherical and cubic clusters are compared. It turns out that the influence of cluster shape is only a minor factor.     

Coherent backscattering of light by complex random media of spherical scatterers: numerical solution

Novel Monte Carlo techniques are described for the computation of reflection coefficient matrices for multiple scattering of light in plane-parallel random media of spherical scatterers. The present multiple scattering theory is composed of coherent backscattering and radiative transfer. In the radiative transfer part, the Stokes parameters of light escaping from the medium are updated at each scattering process in predefined angles of emergence. The scattering directions at each process are randomized using probability densities for the polar and azimuthal scattering angles: the former angle is generated using the single-scattering phase function, whereafter the latter follows from Kepler's equation. For spherical scatterers in the Rayleigh regime, randomization proceeds semi-analytically whereas, beyond that regime, cubic spline presentation of the scattering matrix is used for numerical computations. In the coherent backscattering part, the reciprocity of electromagnetic waves in the backscattering direction allows the renormalization of the reversely propagating waves, whereafter the scattering characteristics are computed in other directions. High orders of scattering (~10 000) can be treated because of the peculiar polarization characteristics of the reverse wave: after a number of scatterings, the polarization state of the reverse wave becomes independent of that of the incident wave, that is, it becomes fully dictated by the scatterings at the end of the reverse path. The coherent backscattering part depends on the single-scattering albedo in a non-monotonous way, the most pronounced signatures showing up for absorbing scatterers. The numerical results compare favourably to the literature results for nonabsorbing spherical scatterers both in and beyond the Rayleigh regime.     

Using simple particle shapes to model the Stokes scattering matrix of ensembles of wavelength-sized particles with complex shapes: possibilities and limitations

We investigate to what extent the full Stokes scattering matrix of an ensemble of wavelength-sized particles with complex shapes can be modeled by employing an ensemble of simple model shapes, such as spheres, spheroids, and circular cylinders. We also examine to what extent such a simple-shape particle model can be used to retrieve meaningful shape information about the complex-shaped particle ensemble. More specifically, we compute the Stokes scattering matrix for ensembles of randomly oriented particles having several polyhedral prism geometries of different sizes and shape parameters. These ensembles serve as proxies for size-shape mixtures of particles containing several different shapes of higher geometrical complexity than the simple-shaped model particles we employ. We find that the phase function of the complex-shaped particle ensemble can be accurately modeled with a size distribution of volume-equivalent spheres. The diagonal elements of the scattering matrix are accurately reproduced with a size-shape mixture of spheroids. A model based on circular cylinders accurately fits the full scattering matrix including the off-diagonal elements. However, the modeling results provide us with only a rough estimate of the effective shape parameter of the complex-shaped particle ensemble to be modeled. They do not allow us to infer detailed information about the shape distribution of the complex-shaped particle ensemble.     

Shadowing effect in clusters of opaque spherical particles

The shadowing effect is studied for clusters of opaque spherical particles. The present modeling allows geometric optics computations of cluster scattering phase functions and shadowing effects with internal accuracy better than 1%. Three types of cluster structures are treated—uniform, ballistic, and hierarchical (physical fractal)—and three types of elementary surface scattering laws are examined—Lambertian, flux-isotropic, and specular. All structures investigated give rise to an opposition effect, that is, a nonlinear brightening toward zero phase angle. The amplitude and width of the opposition effect depend on the cluster parameters. For uniform clusters, the volume fraction and number of particles are the parameters that characterize the shadowing effect. The opposition effect becomes sharper with increasing number of constituent particles and with decreasing particle volume fraction. For ballistic clusters, the only parameter is the number of particles: when it increases, the opposition effect becomes sharper. For hierarchical clusters, the number of cluster structural levels plays a crucial role. With increasing number of cluster levels, the opposition behavior of brightness becomes markedly more nonlinear, mostly due to the decreasing particle volume fraction. It is notable, however, that the opposition effects of the hierarchical clusters and the uniform clusters with the same particle volume fraction differ from each other underscoring the importance of the detailed cluster structure on shadowing. It is shown that, with reasonable accuracy, the cluster scattering phase functions can be factorized as the products of the corresponding single-particle phase function and the so-called shadowing factor almost independently of the elementary surface scattering law. While the opposition effect due to shadowing is presently confirmed, it is typically wider than the opposition effect due to coherent backscattering, an interference mechanism in multiple scattering. The present work helps us to understand, e.g., the opposition effects of the Moon, asteroids, and other atmosphereless celestial bodies.     

Sweep-stick mechanism of heavy particle clustering in fluid turbulence

It is proposed that the inertial range clustering of small heavy particles in fluid turbulence occurs as a result of the sweep-stick mechanism which causes inertial particles to cluster so as to mimic the clusters of points where the fluid acceleration is perpendicular to the direction of highest contraction between neighboring particles. Direct numerical simulations of inertial particles subjected to linear Stokes drag and suspended in homogeneous isotropic turbulence support the validity of the sweep and stick properties on which the sweep-stick mechanism is based, and also support the clustering consequences of this mechanism. It also explains the observed Stokes-number dependence of inertial particle clustering.     

Two types of definitions for Rayleigh range

A comparison of the Rayleigh range between the two types of definitions (defined by the mean-squared beam width and the effective radius of curvature) is studied analytically and numerically, where the propagation of partially coherent beams both in free space and in atmospheric turbulence are considered. It is shown that the two types of the Rayleigh range definitions are consistent in free space. However, in turbulence the Rayleigh range defined by the mean-squared beam width is smaller than that defined by the effective radius of curvature. The main results obtained in this paper are illustrated by numerical calculation examples, where partially coherent Hermite–Gaussian (PCH–G) beams are considered.     

Effective Rayleigh range of partially coherent beams propagating through the turbulent atmosphere

The concept of the Rayleigh range of partially coherent beams is extended from free space to the turbulent atmosphere. The general analytical expression for the effective Rayleigh range of partially coherent beams propagating through the turbulent atmosphere is derived. It is shown that the longer the free-space Rayleigh range is, the more the effective Rayleigh range is affected by turbulence, which is illustrated by numerical calculation examples.