Statistical Mechanical Theory of Bimolecular Reaction. Derivation of the Arrhenius Law. Characterization of a Catalyst

A statistical mechanical theory is developed for gas-phase bimolecular (binary) reactions: AB ⇌ A + B. Based on the activated-complex hypotheses, and expression for the association rate constant k_a is derived: k_a = k*_{AB* → AB} (QAB*/q_A+B), where k*_{AB* →AB} is the rate constant for the transition from the activated state AB* to the molecular state AB, and qx is the equilibrium occupation probability for state X. The three states (AB, AB*, A + B) are defined by three regions of the energyseparation plane for the relative motion of the reactant pair (A, B). If the interatomic potential has a critical barrier ϵ_c at separation r_c and an attractive well with depth ϵ_b (ϵ_c, ϵ_b > k_BT) computations of the q_AB*/q_{A +B} generate an Arrhenius-Boltzmann factor exp (—ϵ_c/k_BT). The virtual rate constant k*_{AB* →AB} is calculated by assuming that the reactant pair reaching the activated state AB* with the separation r < r_c and the energy E > _c moves on to the molecular state AB only if it loses part of its radial kinetic energy with the aid of third body (catalyst or collision) and is trapped by the potential well. With no catalysts present, this constant is approximately given by k*_{AB* →AB} =πd′²v′ R′⁻³, where v′ is the thermal center-of-mass speed, and d′ and R′ are respectively the collision-sphere radius and the mean distance between AB* and any molecule (A, B, AB or AB*). For binary dissociation, the rate constant k_d is given by k_d = k*_{AB* →A+B} q_AB*/q_AB), which generates exp [—(ϵ_c + ϵ_b)/k_BT]. A catalyst for binary reaction is assumed to act as a mediator, facilitating the energy exchange between the radial and rotational modes of motion. Additionally for association only, it also acts as a confinement agent, preventing the pair from flying away from each other. Connections with the collision theory and the activated complex theory are discussed critically.     

Mass Transfer of the Liquid Phase in a Partially Saturated Porous Medium Under the Action of Low-Frequency Elastic Vibrations

We study the model of a partially saturated porous medium comprising a system of identical parallel cylindrical capillaries filled up with equal droplets. The basic features of the liquid-phase drift and the accompanying sound attenuation and droplet coalescence effects are analyzed in the case of external compression.     

Low-Frequency Molecular Responses in a Liquid upon Recording the Ultrafast Optical Kerr Effect

Optics and Spectroscopy - Low-frequency molecular rotations recorded in a region of 0–150 cm–1 with a high “signal/noise” ratio in the ultrafast optical Kerr effect (OKE),...     

The Kinetics of the Liquid Phase Nucleation in a Stretched FCC Crystal: A Molecular Dynamics Simulation

Physics of the Solid State - The kinetics of a spontaneous formation of liquid phase in a stretched (superheated) Lennard-Jones fcc crystal is studied. Molecular dynamics experiments are used to...     

格子Boltzmann方法模拟双液滴撞击液膜的流动过程

采用单相自由面格子Boltzmann方法中流场计算,自由面条件和表面张力处理方法,研究双液滴撞击液膜的流动过程,实现对垂直间隔的两液滴相继撞击液膜流动过程的模拟.数值结果表明,液滴相继冲击液膜时,液滴间上下距离对液膜状态有很大的影响,液滴间距不同,液膜形状会出现很大差异.数值结果与实验结论定性一致.     

Analysis of Action of Pinch Plasmoids in a Periodic Discharge in a Liquid Flow on Ambient Medium

Technical Physics - A periodic discharge in a liquid flow is an effective tool for modifying the surfaces of metal articles, which is aimed at increasing their durability, hardness, and corrosion...     

Computer Simulation of a 3-D Sensing System with Structured Illumination

A computer simulation system of three-dimensional sensing with structured illumination is presented. It includes the generation of deformed fringe patterns from 3-D shapes and the reconstruction of 3-D shapes, conversely. Some experimental results of the deformed fringe pattern and the reconstructed object shapes are presented. We have also discussed the effect of some major system parameters on the measurement results and considered how to correct these parameters according to the measurement result of the standard plane. Using this simulation system, the major system parameters: environmental conditions, measurement accuracy and algorithm evaluation of the 3-D shape measurement system based on PMP, FTP, SPM, etc., can be researched. © 1997 Elsevier Science Ltd. All rights reserved.     

羟自由基与水杨酸反应机理的初探

探讨羟自由基与水杨酸的反应动力学过程。水杨酸与Fenton反应产生的的羟自由基反应,采用紫外-可见分光光度法（UV）和质谱法（MS）,考察反应物的浓度、反应时间、反应温度、溶剂pH值等对反应产物的浓度以及反应速率的影响。水杨酸与.OH反应生成的紫色产物在波长530nm处有最大UV吸收峰,但仅于pH=4.51的缓冲溶液和水中有吸收峰;且该产物的吸光度值,随着反应物浓度的增加而增加;随反应时间的延长而减少;随着反应温度的升高而减少。反应速率t=5s达到最大值,其后随着反应时间的延长而逐渐降低,1min时达到平衡。通过MS分析,可得到质荷比（m/Z）=153,248,249,288,289,304,328,329,344,345的离子峰。推测羟自由基与水杨酸反应的中间产物是紫色的大分子自由基,而最终产物为二羟基苯甲酸,该反应可能是加成反应和聚合反应同时进行。     

Simulation Study of Shock Reaction on Porous Material

Direct modeling of porous materials under shock is a complex issue. We investigate such a system via the newly developed material-point method. The effects of shock strength and porosity size are the main concerns. For the same porosity, the effects of mean-void-size are checked. It is found that local turbulence mixing and volume dissipation are two important mechanisms for transformation of kinetic energy to heat. When the porosity is very small, the shocked portion may arrive at a dynamical steady state; the voids in the downstream portion reflect back rarefactive waves and result in slight oscillations of mean density and pressure; for the same value of porosity, a larger mean-void-size makes a higher mean temperature. When the porosity becomes large, hydrodynamic quantities vary with time during the whole shock-loading procedure： after the initial stage, the mean density and pressure decrease, but the temperature increases with a higher rate. The distributions of local density, pressure, temperature and particle-velocity are generally non-Gaussian and vary with time. The changing rates depend on the porosity value, mean-void-size and shock strength. The stronger the loaded shock, the stronger the porosity effects. This work provides a supplement to experiments for the very quick procedures and reveals more fundamental mechanisms in energy and momentum transportation.     

Kinetic Simulation of Fractal Aggregation on Liquid Surfaces

A modified fractal growth model based on the deposition, diffusion, and aggregation (DDA) with cluster rotation is presented to simulate two-dimensional fractal aggregation on liquid surfaces. The mobility (including diffusion and rotation) of clusters is related to its mass, which is given by D_m=D₀ s^-γ_D and θ_m=θ₀s^-γ_θ, respectively. We concentrate on revealing the details of the influence of deposition flux F, cluster diffusion factor γ_D and cluster rotation factor γ_θ on the dynamics of fractal aggregation on liquid surfaces. It is shown that the morphologies of clusters and values of cluster density and fractal dimension depend dramatically on the deposition flux and migration factors of clusters.     

Numerical Simulation of Droplets Impacting on a Liquid Film with a Vapor Bubble Growing

A numerical model of multiphase flow is developed to investigate the relative contributions of droplet parameters to spray cooling heat transfer. The 2-D model takes into account the effects of surface tension, gravity and viscosity. The heat and mass exchanges of free surface are defined to study vapor bubble behavior in liquid films. The multiphase flow and heat transfer are discussed for the three droplet parameters： initial droplet position, initial droplet temperature, and droplet impact frequency. The heat transfer mechanisms of the three cases are discussed in detail.     

储层岩石时间域激发极化效应的数学模拟

以储层岩石的串联毛管模型为基础,建立描述含水储层岩石时间域激发极化效应的数学模型.数值模拟储层岩石孔隙中离子的浓差极化效应和双电层形变效应.孔隙中浓差极化控制着激发极化随时间的变化,双电层形变不控制激发极化随时间的变化.浓差极化效应对激发极化极化率的贡献较小,双电层形变效应对激发极化极化率的贡献较大.激发极化充放电过程的快慢,主要取决于固液界面阳离子的吸附能力和岩石的孔隙结构.     

Mathematical Simulation of Heat Transfer in Relaxing Media

Abstract

We find a numerically-analytical solution of a boundary problem for the third-order partial differential equation, which describes the mass and heat transfer in active media.     

垂直排液过程不稳定性的数值模拟

为分析线框排液实验中液膜表面出现的不稳定现象及其成因,针对含有不溶性活性剂的线框液膜排液过程,模拟液膜底部的不稳定现象,分析Marangoni效应、膨胀黏性和扰动波数因素的影响。结果表明：底部扰动在排液开始比较剧烈,而后快速减弱,到排液后期又逐渐增强。排液开始的扰动是由初始扰动引起,而排液后期的扰动与活性剂分布有关。较弱的Marangoni效应可增强表面扰动,而较强的Marangoni效应则减弱底部扰动,使液膜呈刚性,发生表面逆流现象;较高的膨胀黏性减慢液膜排液进程,降低表面速度,且能抑制Marangoni效应引起的逆流现象;波数较大的扰动使液膜在排液初期的扰动变强,但对排液后期的稳定性不产生影响。     

Co-Adsorption of CO in NO-CO Reaction on a Metal Catalytic Surface Studied by Computer Simulation

The effect of co-adsorption of CO molecules in the NO-CO reaction on a metal catalytic surface like Pt（001） is studied by applying the Langmuir-Hinshelwood mechanism using the Monte Carlo simulations. The system is investigated by two approaches of NO adsorption; dissociatively at two empty surface sites and molecularly at a single vacant site. The elementary steps are the same as those in the conventional Ziff-Gulari-Barshad model. With the additional reaction step of co-adsorption, the sustained production of CO2 is obtained, which has never been seen on a square lattice without introducing additional parameters. The most interesting result is the elimination of continuous second order phase transition, i.e. the production of CO2 starts as soon as the partial pressure of CO departs from zero, which is in accordance with the experimental observations. The effect of co-adsorption probability on the phase diagrams has also been studied.     

Mathematical Simulation of a 2D Diode System with a Blade-Shaped Field Emitter

Technical Physics - The electrostatic potential distribution in a 2D diode system with a blade-shaped field emitter on a flat substrate has been calculated. The anode of the system represents a...     

Numerical Modeling and Simulation of a Cholesteric Liquid Crystal Polarizer

A numerical model based on Berreman’s 4 × 4 matrix approach was developed and used for computational simulation of a cholesteric liquid crystal (CLC) polarizer. Explicit expressions of the 4 × 4 propagation matrices for several optical films, which constitute a CLC polarizer, were presented. Numerical simulations for optical properties of a CLC layer, a linear polarizer and a CLC polarizer were executed, and the simulated results were found to be in fairly good agreement with measured results.     

Numerical Simulation of Gravity Waves Excited in the Ocean by Low-Frequency Surface Seismic Waves Based on GPS Recordings

A numerical experiment for reproducing the generation of free gravity waves in the ocean by low-frequency surface seismic waves passing across the bottom is described. The dynamics of the bottom movement is reconstructed based on the real GPS data recorded during the disastrous Tohoku earthquake of March 11, 2011. Results of the numerical simulation show that horizontal movements of underwater slopes play a key role in the generation of free gravity waves.