Kinetics of oxidation of deoxybenzoin by chromic acid

The kinetics of the oxidation of deoxybenzoin by chromic acid in 95% (vol/vol) aqueous acetic acid has been investigated. The reaction rate is first order with respect to the oxidant as well as to the organic substrate. The reaction rate decreases in the presence of added Mn (II) ions. The presence of complexing agents like succinic acid, piperidine, etc. decreases the rate. The thermodynamic parameters for the oxidation have been computed. A mechanism proceeding through an enol intermediate has been suggested.     

Studies in the formation of heterocyclic rings containing nitrogen

The mode of formation of keto-hexahydro-s-triazines has been studied by conducting the reaction in two stages. The experiments revealed that the condensation with aromatic aldehydes is more complex, and the mechanism is not clear, although in the case of aliphatic aldehydes the step-wise formation of hexahydro-s-triazines has been reported.     

The step-wise adsorption of nitrogen on carbon black

Adsorption measurements have been carried out for nitrogen on the commercial carbon blacks Spheron 6 and Vulcan. The adsorption on Spheron 6 is step-wise in the pressure range 0 to 45 mm. (fraction of surface covered approximately 10^?5), and on Vulcan to at least 0.16 mm. Calorimetric measurements of differential heats of adsorption on Spheron 6 have shown that they vary with the amount of surface covered being greatest at low coverages and decreasing toward the heats of liquefaction as a limit. 1,2 This indicates that the surface of such materials contains various types of adsorption sites, having different heats of adsorption, and suggests that sufficiently refined measurements would show a step-wise adsorption isotherm. This paper reports the results of experimental studies of the adsorption of nitrogen on the carbon blacks Spheron 6 and Vulcan in the pressure range 0.00 to 75 mm., and at 0° and 100° C.     

Kinetics of the thallic ion oxidation of olefins

The kinetics of oxidation of chalkone (phenyl styryl ketone) and cinnamaldehyde by T1 (III) acetate in aqueous acetic acid is of the first order in olefin and first order with respect to the oxidant. The parameters of the transition state theory have been computed. The rate of the reaction is strongly accelerated by increasing acid concentration. The reaction rate is also retarded by added sodium chloride and sodium acetate. The results have been interpreted in the light of the ionic mechanism considering T1 (OAc)₃ to be the active oxidant in aqueous acetic acid.     

Kinetics of oxidation of thiohydantoin and rhodanine with vanadium (V)

The oxidation of thiohydantoin and rhodanine by quinquivalent vanadium ion is first order with respect to both vanadium ion and the organic substrate. The rate of oxidation increases with increase in concentration of hydrogen ions. The energy, entropy and free energy of activation have been evaluated. Formation of an intermediate complex between the organic substrate and vanadium (V) is not indicated by kinetic evidence. Some possible steps in the reaction have been proposed.     

Chaotic mixing simulations

Numerical simulations of high Reynolds number flows in the unit driven cavity have been performed. The system is shown to become unsteady at Re=8125 and chaotic at Re=17,000. In between this range the system switches between periodic and quasi-periodic states with step-wise changes in period. A passive concentration field and passive tracer particles are introduced into the flow at its asymptotic state to show the effects of chaos on mixing.     

Kinetic studies in ester hydrolysis

The influence of added salts on the reaction rate for the hydrolysis of dibasic esters has been reported using diethyl sebacate in 50% dioxanwater solution. The cations alone are found to determine the slowing effect and at comparable ionic strengths the order is Li>Na>K>Ba. Both stages are affected similarly and confirms the view indicated in earlier parts that we are having a purely ion-dipole type of reaction. This has been shown in the present study by using the Amis equation for the first stage and the Laidler-Landskroner equation for the second stage of the reaction. A possible segregation of water in the primary hydration shell of the cation is noticeable in the reaction.     

Comparisons between thermodynamic and one-dimensional combustion models of spark-ignition engines

A one-dimensional combustion model, employing a constant eddy diffusivity and a one-step chemical reaction, has been developed and applied to study the flame propagation in a spark-ignition engine. Calculations have been made at 1600 and 4200 rev min⁻¹ under fuel rich conditions and compared with available engine pressure data. One- and two-zone thermodynamic models have also been developed and applied to study the combustion process in the engine. The thermodynamic models have been compared with the one-dimensional model results and comparisons include the average mixture temperature, the temperatures of the burned and unburned gases and the flame surface area. These comparisons indicate that the one-dimensional model predictions are very sensitive to the eddy diffusivity and reaction rate data. The two-zone thermodynamic model predicts, first, a monotonically increasing flame surface area with time and, then, a monotonically decreasing surface area, whereas the one-dimensional model always predicts a monotonically increasing flame surface area. The average mixture temperature predicted by the one-zone thermodynamic model is higher than those of the two-zone and one-dimensional models during the compression stroke, while that of the one-dimensional model is higher than the temperatures predicted by the one- and two-zone models during the expansion stroke. The one-dmensional model predicts an accelerating flame even when the front approaches the cold cylinder wall. This yields a faster fuel consumption rate than those predicted by the one- and two-zone thermodynamic models which predict smoother burned fuel mass profiles.     

Kinetics of Thallium (III) oxidation of aromatic ketones

The kinetics of oxidation of acetophenone and six substituted acetophenones by Thallium (III) acetate have been studied in 95% (v/v) aqueous acetic acid. The reaction is first order with respect to the oxidant as well as the organic substrate and acid catalysed. The probable nature of Tl (III) species in aqueous acetic acid has been indicated. The rate data fitted well with Brown’sσ ⁺ values withρ ⁺ = ?0.70. A mechanism for the Tl (III) oxidation of aromatic ketones has been proposed.     

Vinyl polymerization

Polymerization of Acrylamide initiated by cobaltic ions in aqueous solution at 15° C. and 20° C. in HClO₄ and H₂SO₄ media have been studied. Kinetics have been followed by determining the rate of cobaltic ion disappearance as well as monomer disappearance with variations in cobaltic, monomer and hydrogen ion concentrations, temperature, ionic strength, etc. Besides polymer reaction it has been observed that side reactions like water oxidation and monomer oxidation also contribute to rate of cobaltic ion disappearance. Certain anomalous results in H₂SO₄ medium have been observed. A reaction scheme involving CoOH²⁺ and Co³⁺ as initiators in HClO₄ and H₂SO₄ media respectively and mixed termination—mutual and linear—has been suggested. Certain rate parameters involving rate constants for initiation, propagation, termination and the corresponding activation energies have been evaluated.     

Solvent influences in the alkaline hydrolysis of esters in aqueous ethanol

The rate data for the alkaline hydrolysis of a number of monoesters, diesters and lactones have been obtained in varying compositions of aqueous ethanol. The application of the Amis and Laidler-Landskroener equations to the data yields reasonable values for the parameters representing the radius of the transition state for the hydrolysis confirming the ion-dipole nature of the reaction. An attempt to explain the rate data on the basis of the solvation requirements of the transition state has been made.     

高等数学竞赛的相关策划

针对全国每年的大学生数学竞赛以及江苏省每两年一次的高等数学竞赛，为了提高竞赛成绩，对教材及教学方法进行了改革，策划了八项措施，并付之于实践中，取得了优异成绩。在近五届的数学竞赛中，一等奖的获奖率65％，远高于全省平均获奖率10％。     

Combined higher order finite volume and finite element scheme for double porosity and non-linear adsorption of transport problem in porous media

In this work, a dual porosity model of reactive solute transport in porous media is presented. This model consists of a nonlinear-degenerate advection-diffusion equation including equilibrium adsorption to the reaction combined with a first-order equation for the non-equilibrium adsorption interaction processes. The numerical scheme for solving this model involves a combined high order finite volume and finite element scheme for approximation of the advection-diffusion part and relaxation-regularized algorithm for nonlinearity-degeneracy. The combined finite volume-finite element scheme is based on a new formulation developed by Eymard et al. (2010) [10]. This formulation treats the advection and diffusion separately. The advection is approximated by a second-order local maximum principle preserving cell-vertex finite volume scheme that has been recently proposed whereas the diffusion is approximated by a finite element method. The result is a conservative, accurate and very flexible algorithm which allows the use of different mesh types such as unstructured meshes and is able to solve difficult problems. Robustness and accuracy of the method have been evaluated, particularly error analysis and the rate of convergence, by comparing the analytical and numerical solutions for first and second order upwind approaches. We also illustrate the performance of the discretization scheme through a variety of practical numerical examples. The discrete maximum principle has been proved.     

Effects of chemical reaction and radiation on an unsteady MHD flow past an accelerated infinite vertical plate with variable temperature and mass transfer

This paper deals with the study of the effects of first order chemical reaction and radiation on an unsteady MHD flow of an incompressible viscous electrically conducting fluid past an accelerated infinite vertical plate with variable temperature and mass transfer. The resulting approximate dimensionless system of governing partial differential equations are integrated in closed form by the Laplace transform technique A uniform magnetic field is assumed to be applied transversely to the direction of the flow. Rosseland model of radiation has been chosen in the investigation, the expressions for the velocity field, temperature field and concentration field and skin-friction in the direction of the flow, coefficient of heat transfer and mass flux at the plate have been obtained in non-dimensional form and these are illustrated graphically for various physical parameters involved in the study. Investigation reveals that the fluid velocity is decelerated in the region adjacent to the plate, due to the effect of first order chemical reaction and the rate of heat transfer (from plate to the fluid) decreases due to the absorption of thermal radiation. The results obtained in this work are consistent with physical situation of the problem.     

Exact solutions of potentiostatic current transients for a corrosion reaction under mixed charge transfer and diffusion control

An analytical solution has been obtained for the current response transients to a potentiostatic step for a corrosion reaction where a planar metal electrode is immersed in an acidic electrolyte. This solution can be used to provide values of important kinetic parameters of the reaction such as corrosion current and Tafel slopes. The model is derived for conditions of mixed charge transfer and diffusion control and includes the metal ion deposition partial reaction. A Nernstian diffusion model is used, where anodic and cathodic species diffuse in a finite diffusive layer. A numerical solution has previously been published [1], but it is believed that this is the first time an analytical solution has been presented. Transients obtained by including both the metal dissolution and metal-ion deposition (back) reactions, are compared to those obtained by neglecting the metalion deposition reaction. It is shown that neglecting the back reaction can cause significant errors especially when large cathodic potential steps are applied and as the corrosion current approaches the limiting current density of the cathodic reaction.     

阶梯激励合约下代理人行为与合约激励效果

基于委托代理理论研究了阶梯激励合约下的代理人行为,并从委托人角度探讨了最优合约设计的问题。在一般市场需求分布和代理人效用函数下,代理人的效用可能是其努力水平的双峰函数,且存在一个阈值使得当合约绩效奖励超过该阈值时,代理人的努力水平“跳跃式”增加。通过比较阶梯激励合约与其他两类激励合约发现,当代理人是风险厌恶型且代理人的产出完全依赖于其努力水平,委托人总是更偏好阶梯激励合约。     

Gas absorption with first order chemical reaction in a laminar falling film over a reacting solid wall

In the present work, a general case of gas absorption with first order irreversible chemical reaction in a liquid film, for laminar flow over a solid wall, has been analyzed theoretically. First order chemical reaction between the diffused solute and the wall is also considered. Laplace transform followed by power series method has been applied to solve the governing equations. Thereafter, the obtained analytical solution of the developed general model has been successfully verified by an explicit numerical scheme. The general model has also been reduced to six simplified cases, tackled by previous workers and an excellent agreement in the solutions is observed. Moreover, the results are validated by the experimental data available in the literature. The obtained concentration profiles in both the phases have been used to find the absorption rates and enhancement factor.     

Numerical prediction of recirculation flows with free convection encountered in gas-agitated reactors

Flows in a gas-agitated reactor have been predicted by a finite difference procedure. The free-convection phenomena in the gas-liquid mixtures have been accounted for by the calculation of a void fraction determined from the gas flow rate. Computations have been performed for two different situations: first, with the allowance of slip between gas and liquid phases, and second, without any slip. Reasonable agreement has been achieved between the measurements.     

Über ein Charakteristiken-Differenzenverfahren zur Berechnung laminarer Grenzschichten

Summary The difference method ofLuckert-Hartree-Iglisch for the continuation of a boundary layer with a given pressure distribution is applied to an example to study various aspects of the method such as its adaptibility to automatic computers and the possibility of reducing the numerical work by suitable transformation of the variables. The method shows the step-wise dependence of the solution on the prescribed pressure distribution more directly than, e.g., power series expansions of the Blasius-Howarth type.      

Aplicación de un algoritmo evolutivo para la optimización del modelado computacional de la pirólisis de materiales

The pyrolysis models undergoes a fast development due to the enhancement of both the computational power and the new test used to characterize the behaviour of materials under thermal stresses, which were widely used in the field of the chemical engineering to obtain the reaction rates. Thus, these models allow us to characterize either the transient heat of material (thermal inertia) or the complete chemical scheme of mass loss processes (kinetic triplet). The pyrolysis model needs a several number of parameters what does the optimization of a suitable set of parameters a difficult task. Two kinds of materials have been investigated; the first one was a real material which mass loss process was characterized as “one-step” reaction and the second one as a “two-steps” process. Further, it has been analyzed the influence of some algorithm features (initial population number, parameter range, crossover influence) in the optimization time and also in the accuracy of results.