Concentration dependence of diffusion-controlled processes among stationary reactive sinks

A multiple scattering theory of competition effects in diffusion-controlled reactions are presented. We consider a random array of stationary sinks which react with a density field of another reactant. Using the radiation boundary condition to describe the reaction at the surfaces of the sinks, we treat the modification of the density field due to reaction with sinks exactly. By keeping only the most divergent terms in a given order of scattering and summing them, we obtain the rate constant as a function of the sink concentration in the steady state. We also calculate the concentration-dependent diffusion constant of the density field. Both the rate and diffusion constants have nonanalytic behavior in the sink concentration.Alfred P. Sloan Foundation Fellow 1976–1980; John Simon Guggenheim Memorial Fellow 1979–1980.     

Stationary Nonequilibrium Particle-Number Distribution Density Formed by Particle Sources and Sinks

We analyze an inhomogeneous diffusion equation with the given potential profile and the particle source and sink. The possibility of forming a nonequilibrium but stationary state of the system is discussed. For a time-constant point source, we obtain general formulas determining the nonequilibrium stationary density distributions of the particle number as a function of potential-profile shape. The influence of sources and sinks on the flow structure in a diffusion system is determined. Some examples are considered.     

On the theory of void formation during irradiation

A simple theory of the swelling of materials subjected to high energy particle irradiation is developed. Chemical reaction rate equations are used as a basis. Point defects, interstitials and vacancies, are assumed to be produced randomly throughout the solid. They move by random walk through the material until they cease to exist either by recombination with the opposite type of defect or by incorporation into the crystal at sinks such as dislocations, grain boundaries and voids. The rate equations for interstitials and for vacancies, which are coupled via the recombination term, are solved for steady state conditions under irradiation. Defect concentrations, supersaturations, recombination and total sink annihilation rates are obtained in terms of the production rate, sink annihilation probabilities, jump frequencies and thermal equilibrium concentrations of defects. The swelling rate is derived using sink annihilation probabilities at three principally different types of sinks, i.e. voids, sinks which have a bias with regard to the annihilation of interstitials and vacancies (such as dislocations), and sinks with no bias. The defect annihilation probabilities at void, precipitate, dislocation and grain boundary sinks are estimated by using a cellular model and solving the diffusion equation for geometries approximating that of the cells, e.g. a concentric sphere around a void. The relative effects of different types of sinks, i.e. the microstructure, on the swelling rate is discussed. The swelling rate is integrated to give swelling-time or swelling-dose relations, making some simplifying assumptions about the changes in the sink structure as the irradiation proceeds. It is shown that the relation obtained is rather sensitive to the type of assumptions made.     

Forced convection heat transfer from porous heat sinks placed in partially open cavity: Some case studies

In this present study, the forced convection heat transfer from aluminum foam heat sinks with 10, 20, 40 PPI pore density placed in a discrete form in a partially open cavity were experimentally investigated. Air was used as working fluid. The uniform heat flux was applied to 3 × 3 array of foam heat sinks horizontally mounted in the cavity. The experimental studies were performed for the 3363–9743 range of Reynolds number and the 2.7 x 10⁶ and 7.5 x 10⁶ range of modified Grashof number. The effects of the Reynolds number, the modified Grashof number and the pore density of foam heat sink on the heat transfer were investigated. The results obtained were compared with the results obtained without foam heat sink cases. In addition, the most heated elements within the cavity were identified and solution proposals were presented. In addition, the most heated elements within the cavity were identified and solution proposals were presented.     

形状渐变的颗粒与沉降液的相互作用

工业过程中存在大量的含非球形颗粒的多相流动,研究这类颗粒与流体的相互作用有重要的应用价值。本文选择底面为方形、形状随边长和高度规律变化的长方体颗粒,采用单颗粒沉降法测量了曳力系数,研究了形状变化、材料密度和沉降液黏度的影响。发现曳力系数在整个颗粒Re_p数范围(0.05～6300)内均高于球形颗粒,特别是采用阿基米德数Ar与Re_p数可揭示出所有数据的内在规律,提出了适用于这类长方体颗粒所有形状的统一曳力模型。     

Screening of a moving charge in a nonequilibrium plasma

The problem of screening a moving charged dust particle is analyzed in the model of point sinks. Typical time scales for the formation of a polarization cloud around the moving macroscopic particle are found using the three-dimensional integral transform with respect to the spatial coordinates and the Laplace transform in time. It is shown that the stationary potential of a moving charge has a dipole component dominating at sufficiently large distances. The force exerted on a moving charged macroscopic particle by the electric field of induced charges is calculated. It is shown that, in general, the direction of this force depends on the ratio between the transfer coefficient and the decay rate of plasma particles in the plasma. In the presence of sinks, a dust particle is accelerated by this force if the Langevin recombination rate for ions, β _iL = 4πeμ _i , exceeds the electron-ion recombination rate β _ei . In the absence of sinks or if β _ei > β _iL this force is antiparallel to the dust-particle velocity.     

Diffusion-influenced reactions

We summarize three of our recent results on diffusion-influenced reactions in solutions. All deal with the concentration dependence of the reaction rate when the reactants must first diffuse together before reaction can occur. When one species (the sink species) is not dilute, the rate cannot be obtained by solution of a pair diffusion equation; the correlations among the sinks for the diffusing species must be accounted for. First, we consider fluorescence quenching when the quenchers are not dilute. For charged quenchers and fluorophores we discuss how the solution dielectric constant and ionic strength can strongly influence the deviations from the linear Stern-Volmer behavior (the dilute sink result) which arise due to the sink correlations. Second, we consider heterogeneous catalysis where a reactive species is adsorbed onto a surface and must surface diffuse to reactive sites (the sinks). We find that surface diffusion can be an important factor contributing to the rate of reaction; especially when surface diffusion is rapid relative to the adsorption/desorption rate. Third, we discuss diffusion influenced reactions with sinks which are long ellipsoids. Dilute long ellipsoids provide a large rate enhancement relative to a spherical sink; we show that this rate enhancement survives when nondilute ellipsoids are considered.     

Magneto-transport in the two dimensional Lorentz model

A recently developed theory for the motion of a classical particle in a random array of scatterers is improved and extended to discuss the effects of weak and intermediate magnetic fields. By deriving expressions for the general relaxation kernels it is shown that only the current relaxation kernel is the physical relevant one diverging at the percolation edge. The percolation density and localization length turn out to be independent of the magnetic field. A negative magneto resistance at low scatterer density, a positive magneto resistance at larger density and a non classical Hall coefficient are obtained. For the velocity correlation spectrum a shift of the cyclotron resonance to higher frequency and a new low frequency side peak is predicted.     

Numerical Simulation of Random Close Packings in Particle Deformation from Spheres to Cubes

Variation of packing density in particle deforming from spheres to cubes is studied. A new model is presented to describe particle deformation between different particle shapes. Deformation is simulated by relative motion of component spheres in the sphere assembly model of a particle. Random close packings of particles in deformation form spheres to cubes are simulated with an improved relaxation algorithm. Packings in both 2D and 3D cases are simulated. With the simulations, we find that the packing density increases while the particle sphericity decreases in the deformation. Spheres and cubes give the minimum (0.6404) and maximum (0.7755) of packing density in the deformation respectively. In each deforming step, packings starting from a random configuration and from the final packing of last deforming step are both simulated. The packing density in the latter case is larger than the former in two dimensions, but is smaller in three dimensions. The deformation model can be applied to other particle shapes as well.     

Density measurements of liquids at high pressure: Modifications to the sink/float method by using composite spheres,and application to Fe-10wt%S

Abstract

We describe a new modification of the sink/float method of determining the density of molten materials under high pressure, and apply it to liquid Fe-10wt%hS. The modification is based on the use of composite spheres made of a dense, metallic core and a sapphire or ruby mantle. Composite spheres permit tailored densities for use in a variety of liquid compositions. The inert mantle also prevents chemical reaction with molten metallic samples. The pressure dependence of the density of liquid Fe-10wt%S at 1773 K, determined by bracketing, using composite spheres, is compared with the equation of state of Fe-10wt%S obtained by Sanloup et al. (2000), using X-ray absorption.     

翅片中带有热管的散热器数值模拟和实验研究

CPU温度的持续增高导致了能量分布不均匀,所以高热流密度热控制或大型服务器的冷却处理方式成为研究的热点。文中研究了翅片中带有热管的散热器,对其温度分布进行了数值模拟和实验研究分析,并与物理模型相同散热较好的平板型热管散热器进行了比较。结果表明:翅片中带有热管的散热器不仅可以提高散热器的传热温差,加强了散热底板的均温效果,而且使得翅片散热得到强化,更有效地降低了CPU的中心温度。     

气凝胶单元体模型结构参数与等效热导率研究

本文基于二氧化硅气凝胶的微观结构特点,运用小球构成的立方阵列单元体纳米孔隙模型,结合固相导热和气相传热的尺度效应,计算得到了一定尺寸范围内材料的等效热导率,分析了材料密度、颗粒接触面积、材料比表面积等因素对材料等效热导率的影响。结果表明:存在使气凝胶等效热导率取最小值的最佳密度;在一定的密度范围内,孔隙率一定时,材料的等效热导率随比表面积的增大而减小;颗粒间接触界面直径与固相颗粒直径的比值越大,等效热导率越低,在该比值一定时,气孔的尺寸和分布成为影响模型等效热导率的关键因素。     

Diffusion-controlled reactions among stationary sinks

We summarize results of some of our calculations in diffusion-controlled reaction theory. We derive the transport equation describing a diffusing species which can react with a set of randomly distributed spherical sinks. Both the form of the transport equation and the dependence on sink volume fraction of the reaction rate and the effective diffusion coefficient are discussed.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.Supported in part by the National Science Foundation under Grant No. CHE-78-07849.     

Thermal Performance of Laser Diode Array under Constant Convective Heat Transfer Boundary Condition

Three-dimensional heat transfer model of laser diode array under constant convective heat transfer coefficient boundary condition is established and analytical temperature profiles within its heat sink are obtained by separation of variables. The influences on thermal resistance and maximum temperature variation among emitters from heat sink structure parameters and convective heat transfer coefficient are brought forward. The derived formula enables the thermal optimization of laser diode array.     

金属粒子阵列共振的偏振特性

当金属纳米粒子形成规则分布且阵列周期与单粒子的共振波长近似匹配时, 会形成一种特殊的阵列共振, 这种共振比单粒子的局域表面等离子体共振具有更窄的共振线宽和更高的共振强度. 基于修正的长波近似方法, 讨论了矩形阵列的消光截面与阵列因子和单粒子的极化率之间的关系; 并详细研究了在不同偏振的入射光照射下, 阵列因子随着电偶极子方向的改变而产生的变化, 以及这一效应对阵列共振和消光截面所产生的影响. 结果表明, 大型的方阵是偏振无关的; 在矩形阵列中, 沿着阵列两个轴向的相邻粒子之间的耦合形成了阵列因子的两个极值, 并且分别对应了散射截面的最小值.     

Generalized Landauer formula

The Landauer formula, which relates the conductance G of a 1D elastic scatterer to its transmission coefficient, is derived for arbitrary dimensionality. In the general case G depends on the transmission coefficient and the relations of the transmitted particle density to the density of incident particles.     

Deterministic chaos in the dynamics of charged particles near a magnetic field reversal

The charged particle motion near magnetic field reversals shows a miscellaneous picture, alternating between chaotic and regular trajectories. A general scheme for the different types of solutions in dependence on the initial phase space domain has been obtained as for as the chaotization thresshold and a velocity-space diffusion coefficient in strongly curved fields.     

Generation of thermal donors in silicon: Effect of self-interstitials

The generation of low-temperature thermal donors (TD) in silicon is sensitive to the sample cooling rate (from the anneal to room temperature) and the ambient (air or vacuum). This effect is most clearly pronounced in the case of annealing at 500°C, is noticeable at 480°C, and is practically undetectable at 450°C. The results are interpreted satisfactorily as being due to the TD generation becoming enhanced in the presence of silicon self-interstitial (Si_I) atoms. These atoms are emitted by thermal donors, to be subsequently absorbed by sinks, particularly the sample surface and grown-in microdefects (vacancy voids). When annealing in a vacuum, the surface acts as the main sink. If the anneal is done in air, this sink is passivated as a result of oxidation and/or contamination, with voids becoming the main sinks; as a result, the concentration of Si_I atoms increases substantially and the generation rate is enhanced. Rapid cooling brings about a partial passivation of the voids (as a result of their becoming decorated by rapidly diffusing impurities) and an additional enhancement of the generation rate. The calculated rate curves obtained within this model are well fitted to the experiment.     

Screening of a moving charge in a nonequilibrium plasma

Based on the model of point sinks, we consider the problem on the screening of the charge of a moving macroparticle in a nonequilibrium plasma. The characteristic formation times of the polarization cloud around such a macroparticle have been determined by the method of a three-dimensional integral Fourier transformation in spatial variables and a Laplace transformation in time. The screening effect is shown to be enhanced with increasing macroparticle velocity. We consider the applicability conditions for the model of point sinks and establish that the domain of applicability of the results obtained expands with decreasing gas ionization rate and macroparticle size. We consider the problem of charge screening at low velocities and establish that the stationary potential of the moving charge has a dipole component that becomes dominant at large distances. We show that the direction of the force exerted on the dust particle by the induced charges generally depends on the relationship between the transport and loss coefficients of the plasma particles in a plasma. When the Langevin ion recombination coefficient β _iL = 4πeμ _i exceeds the electron-ion recombination coefficient β _ei , this force will accelerate the dust particles in the presence of sinks. In the absence of sinks or when β _ei > β _iL , this force will be opposite in direction to the dust particle velocity. We also consider the problem on the energy and force of interaction between a moving charged macroparticle and the induced charges.     

A comparative TEM study of the 3D lattice of tellurium nanoclusters fabricated by different techniques in an opal host

An electron-microscope study of synthetic opals containing tellurium introduced into the regular void array either by melt injection or by evaporation from solution is reported. In the first case, a three-dimensional array of tellurium clusters interconnected by bridges was revealed. The clusters retain the same crystallographic orientation as one moves from one cluster to another. This suggests that cooling after inserting tellurium results in its directional crystallization, which is possibly controlled by the interconnecting channels. The second technique of tellurium introduction produces a nonuniform cluster array, with three-dimensional clusters growing not in all voids. The surface of most of the silica spheres is coated by a thin discontinuous layer of tellurium. This structure of the cluster array accounts for the nonlinear current-voltage characteristic of the object as a whole. A possibility of engineering cluster lattices differing in structural parameters has been demonstrated. Fiz. Tverd. Tela (St. Petersburg) 39, 2090–2095 (November 1997)