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.     

Mean-square displacement of a stochastic oscillator: Linear vs quadratic noise

Using the Langevin equations, we calculated the stationary second-order moment (mean-square displacement) of a stochastic harmonic oscillator subject to an additive random force (Brownian motion in a parabolic potential) and to different types of multiplicative noise (random frequency or random damping or random mass). The latter case describes Brownian motion with adhesion, where the particles of the surrounding medium may adhere to the oscillator for some random time after the collision. Since the mass of the Brownian particle is positive, one has to use quadratic (positive) noise. For all types of multiplicative noise considered, replacing linear noise by quadratic noise leads to an increase in stability.     

The covariant form of the Klein-Kramers equation and the associated moment equations

We provide a covariant, coordinate-free formulation of the many-dimensional Klein-Kramers equation for the phase space distribution of a Brownian particle. We construct a complete set of eigenfunctions of the collision operator adapted to the coordinate system, which involve covariant tensorial Hermite polynomials. The Klein-Kramers equation can then be reformulated as a system of coupled equations for the expansion coefficients with respect to this system. Truncation of this system of moment equations and application of a subsidiary condition yields a covariant generalization of Grad's thirteen-moment equations. As an application we give the explicit form of these equations for spherically symmetric, stationary solutions in spherical coordinates. We briefly comment on possible extensions of our treatment to slightly more complicated cases.     

On the theory of Brownian coagulation

The traditional diffusion approach for calculation of the collision frequency function for coagulation of Brownian particles is critically analyzed and shown to be valid only in the particular case of coalescence of small particles with large ones and inapplicable to calculation of the coalescence rate for particles of comparable sizes. It is shown that coalescence of Brownian particles generally occurs in the kinetic regime (realized under condition of homogeneous spatial distribution of particles), however, the expression for the collision frequency function in the continuum mode of the kinetic regime formally coincides with the standard expression derived in the diffusion regime for the particular case of large and small particles. This explains the validity of the traditional form of the coagulation rate equation in a wide range of parameters, corresponding to the continuum mode. Transition from the continuum to the free molecular mode can be described by the interpolation expression derived within the new analytical approach with fitting parameters that can be specified numerically, avoiding semi-empirical approach of existing models.     

双稳系统的随机能量共振和作功效率

分析了处于双稳系统中的布朗粒子与外界的周期性外力和热随机力的功、热交互作用,建立了基于Langevin方程的随机能量平衡方程.围绕着受周期力、随机力和阻尼力共同作用的Langevin方程,采用动力学和非平衡热力学相结合的方法,从以"力"为立足点转到以"能量"为研究核心,深入分析了布朗粒子沿单一轨线运动时系统与环境之间的能量交换和作功效率,揭示了双稳系统的随机能量共振现象. 关键词： 双稳系统 随机能量共振 作功效率     

Surface deposition and coagulation efficiency of combustion generated nanoparticles in the size range from 1 to 10 nm

The size distribution of the nanoparticles formed in premixed ethylene–air flames and collected thermophoretically on mica cleaved substrates is obtained by atomic force microscopy (AFM). The distribution function extends from 1 to about 5 nm in non-sooting flames and in the soot pre-inception region of the richer flames, while it becomes bimodal and larger particles are formed in the soot inception region of the slightly sooting flames. The distribution is compared with the size distribution of nano-sized organic carbon (NOC) and soot particles, obtained by “in situ” multi-wavelength extinction and light scattering methods. The deposition efficiency is estimated from the differences between these two size distribution functions as a function of the equivalent diameter of the nanoparticles. Furthermore, the coagulation coefficient of particles in flame is obtained from the temporal evolution of the number concentration of the nanoparticles inside the flames. NOC particles, which are rapidly produced in locally rich combustion regions, have peculiar properties since their sticking coefficient both for coagulation and adhesion result to be orders of magnitudes lower than that expected by larger aerosols, like soot particles. The experimental results are interpreted by modelling the van der Waals interactions of the nanoparticles in terms of Lennard-Jones potentials and in the framework of the gas kinetic theory. The estimated adhesion and coagulation efficiencies are in good agreement with those calculated from AFM and optical data. The very low efficiency values observed for the smaller particles could be ascribed to the high energy of these particles due to their Brownian motion, which causes thermal rebound effects prevailing over adhesion mechanisms due to van der Waals forces.     

考虑电离作用的淤泥异向絮凝三维数值模拟

鉴于试验观察淤泥絮凝结构的技术难度,本文尝试以布朗动力学为基础,采用蒙特卡洛方法动态模拟电离作用下颗粒成长为絮团的过程.为结合实际情况,泥沙颗粒初始位置由颗粒粒径和淤泥密度决定,颗粒初始速度按照相应条件下高斯随机分布给定.边界条件用和实际符合较好的循环边界.在模拟数据分析的基础上,讨论并比较了颗粒粒径和淤泥密度对絮凝时间以及絮团开放程度的影响.另一方面,讨论了电离作用后颗粒电荷量对絮团生长的影响.解释了泥沙颗粒表面电荷密度变化对絮凝过程和絮团结构的影响,模拟结果和实际情况较为一致.     

Quasi-Self-Preserving Log-Normal Size Distributions in the Transition Regime

A log-normal model, based on the extended SIMPLER-algorithm utilizing the Modal Aerosol Dynamics Modelling Technique, and a sectional model are compared for Brownian coagulation in the transition regime. The models are in good agreement with respect to the calculated particle size distribution moments. Applying the log-normal model a simple coagulation model consisting of a closed set of five equations is developed that does not require the solution of ordinary diferential equations.     

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.     

Influences of interfacial damage on the effective wave velocity in composites with reinforced particles

The scattering of elastic waves by a spherical particle with imperfect interface and the multiple scattering by many spherical particles with imperfect interface are studied in this paper. First, the scattering of elastic waves by a spherical particle with imperfect interface, i.e. spring interface model, is studied. Then, the multiple scattering by random distributed particles with interfacial damage in a composite material is investigated. The equations to evaluate velocity and attenuation of effective waves defined by statistic averaging are given. Furthermore, based on the established relation between the effective velocity and interfacial constants, a method to evaluate the interfacial damage nondestructively from the ultrasonic measure data is proposed. The numerical simulation is performed for the Sic-Al composites. The effective velocity is computed to show the influences of interface damage. By using the genetic algorithm, the interfacial damage is evaluated from the synthetic experimental data with various levels of error. The numerical results show the feasibility of the method proposed to approximately evaluate the interfacial damage in a composite material with reinforced particles based on ultrasonic data. Supported by the National Natural Science Foundation of China (Grant Nos. 10672019 and 10272003)     

Assembling 100 nm Scale Particles by an Electrostatic Potential Field

The assembly of particles is one of the many methods for the fabrication of organized structures in the range of micro- to nanometer sizes. These structures have potential applications in the electronic, optical and biochemical fields. Recently, many papers have reported the patterning of particles using patterned SAM (self-assembly monolayer) films and micro molding methods. We have been developing a new technique to assemble particles using an electrostatic field. This paper describes a new technique to fabricate two-dimensional microstructures assembled from 100 nm particles. Spherical silica of 900 nm diameter and aluminum of 100 nm diameter were used as the model particles. An electrostatic image was formed on an insulating substrate by drawing a focused electron beam at 10 keV. Both types of particles were deposited on the electrostatic images. In this process, the dielectrophoretic (DEP) force plays an important role in depositing particles on the electrostatic images. The DEP forces for particles in a suspension were calculated using numerical analysis. The result showed that the DEP force above the electrified region on the substrate is larger than disturbing forces, such as Brownian motion.     

Application of the dissipative particle dynamics method to magnetic colloidal dispersions

The validity of the application of the dissipative particle dynamics (DPD) method to ferromagnetic colloidal dispersions has been investigated by conducting DPD simulations for a two–dimensional system. First, the interaction between dissipative and magnetic particles has been idealized as some model potentials, and DPD simulations have been carried out using such model potentials for a two magnetic particle system. In these simulations, attention has been focused on the collision time for the two particles approaching each other and touching from an initially separated position, and such collision time has been evaluated for various cases of mass and diameter of dissipative particles and model parameters, which are included in defining the equation of motion of dissipative particles. Next, a multi–particle system of magnetic particles has been treated, and particle aggregates have been evaluated, together with the pair correlation function along an applied magnetic field direction. Such characteristics of aggregate structures have been compared with the results of Monte Carlo and Brownian dynamics simulations in order to clarify the validity of the application of the DPD method to particle dispersion systems. The present simulation results have clearly shown that DPD simulations with the model interaction potential presented here give rise to physically reasonable aggregate structures under circumstances of strong magnetic particle–particle interactions as well as a strong external magnetic field, since these aggregate structures are in good agreement with those of Monte Carlo and Brownian dynamics simulations.     

A gas of Brownian particles in statistical dynamics

We consider a large number of particles on a one-dimensional latticel Z in interaction with a heat particle; the latter is located on the bond linking the position of the particle to the point to which it jumps. The energy of a single particle is given by a potentialV(x), x∈Z. In the continuum limit, the classical version leads to Brownian motion with drift. A quantum version leads to a local drift velocity which is independent of the applied force. Both these models obey Einstein's relation between drift, diffusion, and applied force. The system obeys the first and second laws of thermodynamics, with the time evolution given by a pair of coupled non linear heat equations, one for the density of the Brownian particles and one for the heat occupation number; the equation for a tagged Brownian particle can be written as a stochastic differential equation.     

Relaxation of the Probability Characteristics of Brownian Motion under the Action of a Non-Delta-Correlated Random Force

We consider the relaxation of the moments of the coordinates of one-dimensional Brownian motion of particles in a symmetric potential profile under the action of a Gaussian, exponentially correlated random force. An analytical-numerical method of analysis based on obtaining and numerically solving a chain of differential equations for joint cumulants of some functions of particle coordinates and a random force is used. A priori constraints on the intensity and correlation time of noise are not imposed. Numerical procedure is checked by comparison with analytical results, which can be found in the limiting cases of delta-correlated and quasistatic random force. The dependence of the relaxation of the average value and variance on the intensity and spectrum of a random force and the character of the initial distribution of particles is elucidated. In particular, the presence of a variance minimum during distribution relaxation is established. The evolution of the model probability distribution of particle coordinates is constructed on the basis of the moment relaxation.     

Spherical particle Brownian motion in viscous medium as non-Markovian random process

The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered.     

Stochastic Kadomtsev-Petviashvili equation

The example of Kadomtsev-Petviashvili equations with a random time-dependent force (stochastic Kadomtsev-Petviashvili equations) is used to show that the theory of Brownian particle motion can be applied to the theory of the stochastic behavior of solitons of model hydrodynamic equations which are completely integrable in the absence of forces and interrelated by the generalized Galilean transformation. The Brownian motion of two-dimensional algebraic solitons of the Kadomtsev-Petviashvili equations with positive dispersion leads to their diffusion broadening similar to the broadening of one-dimensional solitons of other fully integrable hydrodynamic equations. However, for longer times the rate of decay of algebraic solitons is higher because of the degeneracy of the momentum integral for these solitons. The behavior of a periodic chain of algebraic solitons is established under the action of a random force. Tilted plane solitons of the Kadomtsev-Petviashvili equations with negative dispersion vary under the action of a random force similar to the solitons of the Korteweg-de Vries equation. Several of these solitons interact via “virtual solitons” and generate new solitons provided that resonance conditions are satisfied whose dimensions increase as a result of the influence of the random force.     

温库边界对布朗热机性能的影响

研究了单势垒锯齿势中,布朗粒子在外力和空间周期温度场作用下构成的布朗热机的热力学性能.考虑布朗粒子动能变化以及高、低温库之间热漏引起的热流.用Smoluchowski方程描述粒子在黏性介质中的动力学特性,推导出高、低温库的热流以及热机功率和效率的解析表达式.通过数值计算分析势垒高度、外力和温库边界对热机性能的影响.研究表明:由于动能变化和热漏引起的不可逆热流的存在,布朗热机为不可逆热机,热机的功率效率特性为一闭合的关系曲线;势垒边界与温库边界重合时,热机的功率达到最大值;通过改变温库边界的位置,可以在一定范围内提高热机的效率,但同时减小了热机的输出功率.     

基于超二次曲面的颗粒材料缓冲性能离散元分析

自然界或工业中普遍是由非球形颗粒组成的复杂体系,与球形颗粒相比,非球形颗粒间的高离散和咬合互锁可使冲击载荷引起的能量有效衰减实现缓冲作用.基于连续函数包络的超二次曲面单元能准确地描述非球形颗粒的几何形态,并可精确地计算单元间的接触碰撞作用.本文采用离散元方法对冲击载荷作用下非球形颗粒物质的缓冲性能进行数值分析,并与圆柱体冲击的理论结果和球体冲击的实验结果进行对比验证.在此基础之上,进一步研究了筒底作用力在不同颗粒层厚度和形状等因素影响下的变化规律.计算结果表明:不同颗粒形状都存在一个临界厚度H_c.当HH_c时,缓冲率随H的增加而增加;当HH_c时,缓冲率的变化不再显著并趋于稳定值.此外,减小颗粒表面尖锐度和增加或减小圆柱形和长方形颗粒的长宽比都会提高颗粒材料的缓冲效果.     

Behavior of Ultrafine Particles generated from organic vapors by corona ionizers

This paper reports an experimental study on the stability, coagulation and diffusion of molecular clusters and ultrafine particles generated from organic vapors by corona ionizers. Upon leaving the ionizer, particles are made to flow within several types of vessels: depending on the specific geometry of the flow system, clusters either coagulate into large particles or are deposited on the walls. Particles larger than 4nm and molecular clusters penetrate through a wire-screen type diffusion battery, but particles in the size range between 2 and 4nm are collected. Among the organic compounds tested (aromatics, alcohols, ketones and others), only aromatic compounds appear to yield unstable clusters which grow into detectable particles (>2nm) through Brownian coagulation. The other compounds either do not undergo the gas-to-particle conversion process or are too small to be detected. Furthermore, the presence of moisture seems to be of fundamental importance in the particle generation phenomenon. The addition of alcohols to the vapor mixture inhibits particle formation.     

Lattice Boltzmann simulation of the dispersion of aggregated Brownian particles under shear flows

The deformation and breakup processes of a particle-cluster aggregate under shear flows are investigated by the two-phase lattice Boltzmann method. In the simulation the particle is modeled by a hard droplet with large viscosity and strong surface tension. The van der Waals attraction force is taken into account for the interaction between the particles. Also, the Brownian motion is considered for nano-particles. Two important dimensionless parameters are introduced in order to classify calculated results. One is the ratio of fluid force to the maximum inter-particle force, Y, and the other is the Péclet number which is the ratio of the rate of diffusion by a shear flow to the rate of diffusion by Brownian motion. It is found that Y is the key factor in dispersion and that the Brownian motion retards the dispersion.