The kinetics of adsorption on fractals: A numerical experiment

An approach similar to the “random rain” model was used to simulate the formation of a three-dimensional cluster from identical particles. The cluster had a fractal structure with the mean fractal number that increased as the number of constituting “atoms” grew. We simulated adsorption on this cluster and considered the relation between the structure of the cluster and the number of vacant centers on which adsorption could occur. By analogy with the coordination number of an atom, the notion of the coordination number of a fractal particle was introduced. The fractal and coordination numbers were shown to be interrelated. An equation for the kinetics of irreversible adsorption on fractals was suggested.     

Description of primary creep by means of the stochastic model

Feltham's stochastic model is used to describe dislocation hardening during primary creep in metals which contain a three-dimensional irregular network of dislocations. The original stochastic equation is modified so as to fulfil a condition of volume conservation. The modified differential equation is then solved and a time-dependent distribution function of dislocation segment lengths is obtained. Since the creep strain is given by a summation of strain contributions from individual dislocation segments, the time dependence of the creep strain, i.e. the creep curve, can also be obtained.     

An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model

We propose a discretization method of a five-equation model with isobaric closure for the simulation of interfaces between compressible fluids. This numerical solver is a Lagrange–Remap scheme that aims at controlling the numerical diffusion of the interface between both fluids. This method does not involve any interface reconstruction procedure. The solver is equipped with built-in stability and consistency properties and is conservative with respect to mass, momentum, total energy and partial masses. This numerical scheme works with a very broad range of equations of state, including tabulated laws. Properties that ensure a good treatment of the Riemann invariants across the interface are proven. As a consequence, the numerical method does not create spurious pressure oscillations at the interface. We show one-dimensional and two-dimensional classic numerical tests. The results are compared with the approximate solutions obtained with the classic upwind Lagrange–Remap approach, and with experimental and previously published results of a reference test case.     

Studies on kinetics and thermodynamics of ion adsorption reactions by applications of short-lived radioactive tracer isotopes

The short-lived radiotracer isotopes were applied to study the kinetics and thermodynamic feasibility of iodide as well as bromide ion adsorption reactions using industrial-grade resin materials. Free energy of activation (ΔG ^?) and energy of activation (E _a) were calculated by using Arrhenius equation, enthalpy of activation (ΔH ^?), and entropy of activation (ΔS ^?) calculated by using the Eyring-Polanyi equation. These parameters were used to predict the thermodynamic feasibility of the two ion adsorption reactions performed by using Dowex SBR LC and Indion-810 resins. It was observed that during iodide ion adsorption reactions, the values of energy of activation (?18.79 kJ mol^?1), enthalpy of activation (?21.37 kJ mol^?1), free energy of activation (58.13 kJ mol^?1), and entropy of activation (?0.26 kJ K^?1 mol^?1) calculated for Indion-810 resins were lower than the respective values of ?4.28 kJ mol^?1, ?6.87 kJ mol^?1, 64.97 kJ mol^?1, and ?0.23 kJ K^?1 mol^?1 calculated for Dowex SBR LC under similar experimental conditions. Identical trends were observed for the two resins during bromide ion adsorption reactions. The low values of different thermodynamic parameters obtained for Indion-810 resins during both the ion adsorption reactions indicate that the reactions are thermodynamically more feasible using Indion-810 resins as compared to Dowex SBR LC resins. It is expected here that the present nondestructive technique can be extended further for different ions in the solution in order to predict the thermodynamic feasibility of different ion adsorption reactions for the range of resins which are widely used for treatment of industrial waste water effluent.     

Multilayer adsorption by Monte Carlo simulation

Adsorption phenomena are characterized by models that include free parameters trying to reproduce experimental results. In order to understand the relationship between the model parameters and the material properties, the adsorption of small molecules on a crystalline plane surface has been simulated using the bond fluctuation model. A direct comparison between the Guggenheim–Anderson–de Boer (GAB) model for multilayer adsorption and computer simulations allowed us to establish correlations between the adsorption model parameters and the simulated interaction potentials.     

Study of random sequential adsorption by means of the gradient method

By using the gradient method (GM) we study random sequential adsorption (RSA) processes in two dimensions under a gradient constraint that is imposed on the adsorption probability along one axis of the sample. The GM has previously been applied successfully to absorbing phase transitions (both first and second order), and also to the percolation transition. Now, we show that by using the GM the two transitions involved in RSA processes, namely percolation and jamming, can be studied simultaneously by means of the same set of simulations and by using the same theoretical background. For this purpose we theoretically derive the relevant scaling relationships for the RSA of monomers and we tested our analytical results by means of numerical simulations performed upon RSA of both monomers and dimers. We also show that two differently defined interfaces, which run in the direction perpendicular to the axis where the adsorption probability gradient is applied and separate the high-density (large-adsorption probability) and the low-density (low-adsorption probability) regimes, capture the main features of the jamming and percolation transitions, respectively. According to the GM, the scaling behaviour of those interfaces is governed by the roughness exponent α = 1/(1 + ν), where ν is the suitable correlation length exponent. Besides, we present and discuss in a brief overview some achievements of the GM as applied to different physical situations, including a comparison of the critical exponents determined in the present paper with those already published in the literature.     

Study of consecutive processes by means of adsorption calorimetry

Experiments using an isoperibolic (diathermal) adsorption calorimeter show that in some adsorption systems there is an exothermic or endothermic consecutive process following the primary adsorption step. For the simple case of a consecutive process of first order it is possible to derive as well the kinetic as the energetic parameters describing the formation of the intermediate and final adsorption state.     

Studies of adsorption equilibria and kinetics in the systems: Aqueous solution of dyes-mesoporous carbons

Two carbonaceous materials were synthesized by using the method of impregnation of mesoporous silicas obtained by applying the Pluronic copolymers as pore-creating agents. The isotherms of adsorption of methylene blue and methyl orange from aqueous solutions were measured by the static method. The profiles of adsorbate concentration change in time were obtained from the UV-vis spectra. The adsorption isotherms and kinetic dependence were discussed in the terms of theory of adsorption on heterogeneous surfaces.     

The kinetics of field adsorption

In an applied field of ～ 1 V/Å or higher, gas atoms and molecules near the electrode surface can be attracted to the surface and be field adsorbed there. Field adsorption can occur at a temperature much higher than that in ordinary physical adsorption. For example, field adsorption of He and Ne on metal surfaces can occur at a temperature above 100 K. The kinetic of field adsorption on spherical, cylindrical and field ion emitter surfaces are discussed. Methods for measuring the field adsorption energy, the gas supply constant, and other physical parameters using the pulsed-laser time-of-flight atom-probe are described. These parameters are essential for describing the kinetics of field adsorption. We consider field adsorption and desorption of both atomic and molecular gases. In molecular gases, field dissociation of field desorbed species can occur. A proper account of this effect has to be included in the data analysis. A case with two adsorption states at different adsorption sites is also considered. Field adsorption must play an important role in the early stages of cloud formation, and in the adsorption-desorption and catalytical reactions on the surface of interstellar particles, etc.     

Improvement of numerical integration algorithms by means of coordinate transformations

We study the effect of coordinate transformations on numerical integration algorithms and the Richardson extrapolation. Present method is based on Hermitian transformed eigenvalue equations and symmetrical tridiagonal matrices. Received 18 March 2002 / Received in final form 23 May 2002 Published online 24 September 2002     

Studies on adsorption energy distributions computation from adsorption isotherms by the ansatz method

Since the well-known adsorption integral equation (AIE) is an ill-posed problem, calculation of relevant energetic properties from gas and liquid adsorption isotherms on porous solids still remains a challenging field of research. There are two approaches for solving the AIE: (1) the numerical regularization method and (2) the fitting of the experimental adsorption data by functions possessing an analytical solution. Up to now the latter approach has been treated without consideration of the ill-posedness. The inclusion of ill-posedness in the approach leads to its specification which we call the ansatz method. By showing that a certain class of ansatz functions cannot be used for describing the total isotherms, we were urged to consider more general solutions being connected with the Stieltjes integrals. After applying a general inversion formula we can restrict the theoretically possible total isotherms and outline a feasible general ansatz.     

同轴式Reditron的计算机模拟

用二维全电磁模型粒子模拟的方法对同轴式反射电子甑别微波发生器-同轴式Reditron中的虚阴极振荡现象进行了研究。模拟结果表明:当注入电流超过同轴波导中的空间电荷限制电流时,在同轴波导漂移区将会形成虚阴极振荡。在给定的模拟参数下,获得了窄带的TM₀₁模式K波段的高功率微波输出,峰值瞬时输出功率达8.62GW,效率在7~10%之间。     

Direct numerical simulation of diluted combustion by evaporating droplets

Diluted combustion has been studied using DNS in a three-dimensional temporally developing reacting shear-layer with the oxidizer stream laden with evaporating droplets. The gaseous phase is described in the Eulerian frame while the discrete droplet phase is treated in the Lagrangian frame, with strong two-way coupling between the two phases through mass, momentum and energy exchange. Grid-resolution-independent results have been obtained in cases without and with droplets. A comprehensive parametric study has been conducted by varying the initial Stokes number (St₀) and mass loading ratio (MLR₀). Detailed field analysis has been conducted to examine the complex nonlinear interactions among droplet dynamics, evaporation, turbulence and combustion, and so on. Effects of evaporating droplets on averaged flow and combustion quantities have also been presented. In particular, the conditional scalar dissipation rate is found to be enhanced by evaporating droplets, which suggests that they can promote micromixing and combustion under certain conditions, in addition to their roles in combustion suppression. The transport equation for the mixture fraction variance has been analyzed, with a focus on the vaporization-related source terms. Such source terms exhibit more complex local variations in the present shear-flow non-premixed flame configuration, compared with the case in the homogeneous decaying turbulence configuration of Réveillon and Vervisch (2000).     

Concerning the validity of the stochastic approach to chemical kinetics

A simple argument advanced recently in support of the legitimacy of the stochastic formulation of chemical kinetics has been criticized because it seems to require the imminent collision of widely separated molecules. It is argued here that this criticism is unwarranted because it is based on an incorrect use of probabilities. To illustrate the various probabilistic considerations involved, a detailed analysis is presented of a closely related but mathematically simpler problem: the calculation of the collision probability per unit time for a thermally equilibrized one-dimensional gas of point particles.     

Thermodynamics and kinetics of adsorption of atoms and molecules by carbon nanotubes

Thermodynamics and kinetics of adsorption of atoms and molecules by carbon nanotubes are investigated. Expressions are derived that can be used to perform calculations taking into account various external factors and interactions and, therefore, analyze both physical and chemical adsorption processes and determine its thermodynamic parameters. A mathematical model is developed that makes it possible to find parameters of desorption kinetics separately for molecules adsorbed at different locations and reduce possible systematic errors in analysis of experimental results. Theoretical models are validated by analyzing physical and chemical adsorption of hydrogen and physical adsorption of oxygen.     

Exploring the performance of spatial stochastic simulation algorithms

Since the publication of Gillespie’s direct method, diverse methods have been developed to improve the performance of stochastic simulation methods and to enter the spatial realm. In this paper we discuss a spatial τ-leaping variant (Sτ) that extends the basic leap method. Sτ takes reaction and both outgoing and incoming diffusion events into account when calculating a leap candidate. A performance analysis shall reveal details on the achieved success in balancing speed and accuracy in comparison to other methods. However, performance analysis of spatial stochastic algorithms requires significant effort — it is crucial to choose suitable (benchmark) models and to carefully define model and simulation setups that take problem and simulation design spaces into account.