Instantaneous Reaction Rate Research Articles

Nitrogen Mineralization Potential of Arid and Semiarid Soils of Morocco

An accurate estimate of N mineralized from soil organic matter during the growing season is required to make correct N fertilizer recommendations for crops. In Morocco, very little information regarding the N-supplying power of soils is available. These studies were conducted to determine N-mineralization potential (No) and rate constant (k) values, N flux, and instantaneous rate of reaction for soils of the Chaouia region of Morocco. Fourteen soils were selected and net mineralizable N during 16 wk of incubation at optimum moisture and temperature was determined for each soil. Exponential and hyperbolic models were used to describe net mineralization, and No and k values for each soil were determined using nonlinear least-squares regression. Values using the exponential model ranged from 120 to 241 mg N kg−1 of soil for No and 0.06 to 0.274 week−1 for k. The values ranged from 164 to 391 mg N kg−1 of soil for No and 0.024 to 0.212 week−1 for k, using the hyperbolic model. The lowest average No values for different soils were shown to occur in Palexerolls, which are shallow soils approximately 35 cm deep that have received very low N input. Calculations using the exponential and hyperbolic models indicated the active fraction of total N in these soils varied from 7 to 22% and 10 to 36%, respectively. This study supported earlier reports that a single exponential model as well as a hyperbolic model can be used to estimate reliable No and k values in soils if a nonlinear least-squares fitting technique is used.

Flame extinction in a temporally developing mixing layer

Nonequilibrium effects leading to the local quenching of a diffusion flame were investigated by examining the evolution of large-scale structures in a two-dimensional temporally developing mixing layer. Pseudospectral calculations of a temperature-dependent, nonpremixed, constant-density, reacting shear layer indicate that the primary important parameter to be considered for flame extinction is the local instantaneous scalar dissipation rate, conditioned at the scalar stoichiometric value (Xst). At locations where this value is increased beyond a critical value (Xq), the local temperature decreases and the instantaneous reaction rate drops to zero. This is consistent with the results of perturbation methods employing large activation energy asymptotics for the study of flame extinction in nonpremixed flames.

Sulfuric acid aerosol formation by the reaction of HO radicals with SO2

In order to investigate sulfuric acid formation by the reaction of HO radicals with SO2, photoirradiation experiments were carried out by means of a 4‐m3 chamber, in which humidified air containing SO2, CH3ONO, n‐C4H10 and NO with concentrations in ppm range was exposed to simulated solar radiation at 303 ± 1K and under atmospheric pressures. The HO radicals were generated by a photolysis of CH3ONO and their concentration was estimated from the decay rate of n‐C4H10 concentration. The amount of SO2 lost by the reaction was evaluated through time integration of the instantaneous reaction rate k 1 [HO] [SO2] by using the rate constant k 1 = 1.22 × 10‐12 cm3 molecule‐1 s‐1 which we reported previously for the HO + SO2 reaction. The yield of sulfuric acid was determined, on the other hand, by the filter collection and the subsequent ion chromatographic analysis of the aerosol product. From the agreement between the yield and the reactant loss, the accuracy of the k 1 value was proved and simultaneously the st...

The 'double' Michaelis-Menten equation: estimation of parameters.

When the concentration dependence of an enzymic reaction or a transport process can be described by the sum of two Michaelis-Menten terms, reliable data that relate reaction rate and substrate concentration can be obtained even when as much as 70 per cent of substrate was consumed during the assay. Each data pair consists of the average reaction rate during an assay and the concentration where the instantaneous reaction rate was equal to the average rate. Although that concentration cannot be computed exactly (as it depends on the four kinetic parameters), it may be computed in a good approximation as if the reaction followed the simple Michaelis-Menten relationship. The relative error in the approximated concentration for 1 less than or equal to K2/K1 less than or equal to 10(5) and 10(-2) less than or equal to V2/V1 less than or equal to 10(2) did not exceed 5 per cent up to 50 per cent of substrate consumption, and did not exceed 10 per cent up to 70 per cent of substrate consumption.

The Structure of Diffusion Flames

Abstract The theory for the mixing and chemical reaction of two streams of fluid is developed for unsteady laminar and for turbulent flow. Only one conserved scalar is required to fully describe the mixing and various reaction models are considered including the Burke-Schumann flame sheet and shifting equilibrium. A new expression is derived for the instantaneous reaction rate of any species Wi = –pD(▿ξ)2Yi/dξ2 where ξ is a conserved scalar. New insight is obtained into the structure of the instantaneous reaction zone for both laminar and turbulent flames. Diagnostic parameters are presented for determining when various models are applicable and for what properties.

A model of unmixedness for turbulent reacting flows

The phenomenon of unmixedness caused by turbulent fluctuations leading to a situation in which the instantaneous value of fuel or oxidizer concentration and, therefore, the instantaneous chemical reaction rate vanish, is investigated. A qualitative and quantitative analysis is presented, with the goal of developing a simple model making possible the evaluation of the decrease in overall reaction rates, without incurring a serious penalty in computer time and memory. Such a model, adequate for both parabolic and elliptic flow fields, is proposed and it is shown that the assumptions made lead to a mixing length type relation connecting the local value of the r.m.s. fluctuating concentration of a given species to the local gradient of its mean concentration and to the length-scale of the turbulent motion. Different cases are distinguished according to the possible combinations of turbulence level and mean concentration gradient. The computational procedure is described for the general case of N R elementary, reversible, simultaneous reactions, involving N S species. Results obtained using the proposed model are compared with experimental data, showing satisfactory agreement.

Nonisothermal Chemical Kinetics

IN a recent article1, MacCallum and Tanner suggest that the traditional homogeneous reaction rate expression is applicable only to isothermal processes, and that an additional term should be added when the temperature varies over the course of the reaction. This suggestion has several disturbing features. It implies, contrary to logic, that the instantaneous reaction rate depends not only on the present state of the system (the frequency of collisions and relative energies and orientations of all of the system molecules) but also—through dT/dt—on previous and future states. The proposed correction is impossible to calculate, because in a real system temperature cannot be varied holding time constant, and therefore the factor (∂C/∂T)t is devoid of physical meaning; moreover, even for the hypothetical case of a step-function change in temperature, the instantaneous change in concentration must be 0, which eliminates the correction. A particularly far-reaching implication of the suggestion is that essentially all of the nonisothermal reactor modelling and analysis that has taken place over the past 80 years has been fundamentally unsound, by virtue of having been based on equation (1).

Current Distribution in Nonequilibrium J×B Devices

The interdependent problems of determining the current density field and the electron temperature and number density profiles in nonequilibrium J×B devices are formulated realistically, and solved numerically. The two-dimensional formulation includes the important effects of thermal and concentration diffusion, thermal and velocity boundary layers, and finite reaction rates on the electrical behavior of crossed-field devices, and allows each effect to be studied separately. As a result, this study predicts and interprets the asymmetry of the current distribution that has often been reported in experimental studies. Computations in potassium-seeded nitrogen plasmas have shown that streamwise nonuniformities can be very pronounced both in the core and in the electrode boundary regions of high-current density devices. In the limiting case of instantaneous reaction rates (ionization equilibrium at the electron temperature) and instantaneous energy relaxation, current lines in the core display a striking increase in slope throughout the narrow region between the insulator segments, where they become almost perpendicular to the flow direction and much denser than in the remaining part of the core. Under these conditions, there is no evidence of current ``shorting'' through the boundary layer, although the Te distribution is such that high-luminosity regions appear over the electrodes, particularly over the cathode. The general and flexible methods developed in this study allow realistic evaluation of suggested designs under various operating conditions.

Constant pressure-differential gas apparatus for kinetic studies of gas-solid reactions

An apparatus which includes essentially a Rotameter for the measurement of small rates of flow of gas is designed to enable instantaneous reaction rates of gas-solid reactions to be obtained continuously.

Design of experiments on the kinetics of the water‐gas shift reaction

AbstractExperiments on the continuous catalytic water‐gas shift reaction have been carried out making full use of the principles of statistical design to elucidate the reaction mechanism. Instantaneous reaction rates were determined for sixteen different combinations of the five variables: partial pressures of carbon monoxide, hydrogen, carbon dioxide, and temperature. Nitrogen gas was used as an inert diluent to make up the total pressure to 1 atm. From the analysis of variance of these sixteen runs it can be shown that the Temkin mechanism for the water‐gas shift reaction cannot represent the data within the experimental accuracy. A tentative alternative mechanism which is consistent with the data obtained is presented. The work shows that while it is possible to obtain useful empirical kinetic data from small, well‐planned experiments, both highly precise experimental data and very careful statistical treatment are required. When these are available, a very marked reduction in the amount of experimental work can be effected.

Chemical reactions catalysed on a tube wall

The progress of a reaction catalysed on a tube wall is analysed for an assigned radial pattern of axial velocity. A procedure is given for mathematically transforming an observed axial profile of cross-section average reactant concentrations into a plot of the instantaneous reaction rate vs. the wall concentration at which the reaction is proceeding. It is also shown how to calculate the average conversion at any contact time for an arbitrary reaction rate function.

A Photoelectric Investigation of the Cool Flame of Ether

A method is described, in which the light from a cool flame under the form of a static, uniform glow is measured as a function of time by means of a multiplier photo-tube and a single-sweep cathode-ray oscillograph. The circuit embodies an a.c.—d.c. amplifier and a slow sweep. Cool flames of diethylether-oxygen mixtures in a Pyrex cylinder 4.6 cm in diameter have been studied under the following range of conditions: 180–250°C, 0–150 mm and 5–95 percent ether. The pulsating glow, which lasts about 1 second, shows two and sometimes more maxima. The generally accepted lower pressure limits appear as regions of feeble but smoothly decreasing intensities. Under the conditions of our experiments, the temperature coefficient is negligible. Both intensity and integral emission increase regularly with the concentrations of the reactants and are maximum at 50 percent ether by volume, the variations being roughly symmetrical with respect to the partial pressures of either component. Variations of pressure and composition cause regular but considerable changes in the shapes of the oscillograms. Light and pressure pulses follow each other closely, suggesting that the latter are of mainly thermal origin and that the light intensities reflect the instantaneous reaction rates. The glow lasts longer in the wider vessels. In the presence of the reaction products, it either fails to appear or emits the normal amount of light. A preliminary analysis of the quantitative data is given and possible interpretations, in terms of oxidation mechanisms, are discussed.