Energy transfer through a dissociated diatomic gas in Couette flow

1958 ◽  
Vol 4 (5) ◽  
pp. 441-465 ◽  
Author(s):  
John F. Clarke
Keyword(s):  
Energy Transfer ◽  
Gas Phase ◽  
Couette Flow ◽  
Chemical Reaction ◽  
Chemical Equilibrium ◽  
Reaction Rate ◽  
Surface Reaction ◽  
Rate Equations ◽  
Equilibrium Flow ◽  
Diatomic Gas

The transfer of energy through a dissociated diatomic gas in Couette flow is considered, taking oxygen as a numerical example. The two extremes of chemical equilibrium flow and chemically frozen flow are dealt with in detail, and it is shown that the surface reaction rate is of prime importance in the latter case. The chemical rate equations in the gas phase are used to estimate the probable chemical state of the gas mixture, this being deduced from the ratio of a characteristic chemical reaction time to a characteristic time for atom diffusion across the layer. The influence of the surface reaction appears to spread outwards through the flow from the wall as gas-phase chemical reaction times decrease. For practical values of the surface reaction rate on a metallic wall, the energy transfer rate may be significantly lower in chemically frozen flow than in chemical equilibrium flow under otherwise similar circumstances.Similar phenomena to those discussed will arise in the more complicated case of boundary layer flows, so that a treatment of the simpler type of shear layer represented by Couette flow may be of some value in assessing the relative importance of the various parameters.

A polycentric growth model of gallium arsenide epitaxial layers from the gas phase with simultaneous diffusion, adsorption and chemical reaction

1988 ◽  
Vol 53 (12) ◽  
pp. 2995-3013
Author(s):  
Emerich Erdös ◽  
Jindřich Leitner ◽  
Petr Voňka ◽  
Josef Stejskal ◽  
Přemysl Klíma
Keyword(s):  
Growth Rate ◽  
Gallium Arsenide ◽  
Epitaxial Growth ◽  
Gas Phase ◽  
Surface Reaction ◽  
Quantitative Description ◽  
The Other ◽  
Rate Equations ◽  
Impact Interaction ◽  
Partial Pressures

For a quantitative description of the epitaxial growth rate of gallium arsenide, two models are proposed including two rate controlling steps, namely the diffusion of components in the gas phase and the surface reaction. In the models considered, the surface reaction involves a reaction triple - or quadruple centre. In both models three mechanisms are considered which differ one from the other by different adsorption - and impact interaction of reacting particles. In every of the six cases, the pertinent rate equations were derived, and the models have been confronted with the experimentally found dependences of the growth rate on partial pressures of components in the feed. The results are discussed with regard to the plausibility of individual mechanisms and of both models, and also with respect to their applicability and the direction of further investigations.

scholarly journals Modified Rate Law for Bimolecular Reactions: Applicable to Surface as well as Non-surface Reactions

2021 ◽  
Vol 37 (6) ◽  
pp. 1429-1433
Author(s):  
Gami Girishkumar Bhagavanbhai ◽  
Rawesh Kumar
Keyword(s):  
Reaction Rate ◽  
Surface Reaction ◽  
Catalyst Surface ◽  
Chemical Species ◽  
Bimolecular Reaction ◽  
Rate Equations ◽  
Bimolecular Reactions ◽  
Rate Law ◽  
Langmuir Adsorption ◽  
Adsorption Desorption

The rate equations in kinematics are expressed through basic laws under surface reaction as well as non-surface reaction. Rate law is center theme of non-surface reaction whereas Langmuir adsorption isotherms are basis of surface reaction rate expressions. A modified rate equation for bimolecular reaction is presented which considers both catalyst surface affairs as well as fraction of successful collision of different reactant for cracking and forming bonds. The modified rate law for bimolecular reaction for surface as well as non-surface reaction is stated as “Rate of a reaction is directly proportional to concentration as well as catalyst surface affair of each reactant” as r = k ΩA[A] ΩB[B] where catalyst surface affair of ith species is defined as Ωi = Ki/(1+Ki[i] + Kj[j] + …). Here, Ki is the equilibrium constant of “i” species for adsorption-desorption processes over catalyst. i, j,… indicates the different adsorbed chemical species at uniform catalyst sites and the same [i], [j], … indicates the concentration of different adsorbed chemical species at uniform catalyst sites.

scholarly journals A New Method for Determining the Nanocrystallite Size Distribution in Systems Where Chemical Reaction between Solid and a Gas Phase Occurs

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Rafał Pelka ◽  
Walerian Arabczyk
Keyword(s):  
Gas Phase ◽  
Chemical Reaction ◽  
Nanocrystalline Materials ◽  
Reaction Rate ◽  
Solid Phase ◽  
Nanocrystallite Size ◽  
Rate Limiting Step ◽  
Crystallite Sizes ◽  
Chemical Reaction Rate ◽  
Rate Limiting

The proposed method, based on measuring the chemical reaction rate in solid phase, is, therefore, limited to such systems where reaction between nanocrystalline materials and a gas phase occurs. Additionally, assumptions of the model of reaction between nanocrystalline materials and a gas phase, where the surface chemical reaction rate is the rate limiting step, are used. As an example of such a reaction, nitriding (with ammonia) of the prereduced industrial iron catalysts for ammonia synthesis of different average crystallite sizes was used. To measure the reaction rate, the differential reactor equipped with systems for thermogravimetric measurements and analysis of the chemical composition of the gas phase was used. The crystallites mass and size distributions for the analyzed samples of catalyst were determined.

A TRAJECTORY-FOLLOWING METHOD FOR SOLVING THE STEADY STATE OF CHEMICAL REACTION RATE EQUATIONS

2009 ◽  
Vol 08 (supp01) ◽  
pp. 1025-1044 ◽  
Author(s):  
XIN-LONG LUO
Keyword(s):  
Steady State ◽  
Convergence Analysis ◽  
Chemical Reaction ◽  
Reaction Rate ◽  
Computing Time ◽  
Rate Equations ◽  
Time Step ◽  
Euler Formula ◽  
Chemical Reaction Rate ◽  
Trajectory Following

This article gives a trajectory-following method for the steady state of chemical reaction rate equations. In order to avoid wasting unnecessary computing time during the steady-state phase and get roughly accurate solutions during the transient-state phase, this method is realized via adopting the semi-implicit Euler formula as the stepping direction and adaptively adjusting the time-step size by an analogous trust-region technique. Under some standard assumptions, its global convergence analysis and local superlinear convergence analysis are also given. Finally, some numerical experiments of this method, in comparison with the traditional optimization methods and ordinary differential equation methods, are reported. The numerical results show that this trajectory-following method is a promising solution for this class of problems.

scholarly journals The mechanism of the hydrogen-oxygen reaction V. The reaction in vessels coated with alkali iodides

1946 ◽  
Vol 186 (1007) ◽  
pp. 469-472 ◽  
Keyword(s):  
Gas Phase ◽  
Reaction Rate ◽  
Surface Reaction ◽  
Indirect Evidence ◽  
Alkali Halides ◽  
Normal Reaction ◽  
Mode Of Operation ◽  
Reduced Rate ◽  
Halide Salts ◽  
Mechanism Of The Reaction

Previous work on the hydrogen-oxygen combination in vessels coated with alkali halides showed that with the iodides the temperature dependence of the reaction rate is abnormal. In iodide-coated vessels the whole mechanism of the reaction is now shown to be different: the greatly reduced rate is independent of [H 2 ], proportional to a + b [O 2 ] and independent of added nitrogen, all in sharp contrast with what is found in chloride-coated vessels. The normal reaction is thought to be completely suppressed by minute amounts of iodine liber­ated into the gas phase, a residual surface reaction being measured. The chemical actions which must be assumed to occur between the iodide and the gases provide indirect evidence for the probable mode of operation of the other halide salts in controlling the hydrogen-oxygen combination.

scholarly journals A method of measuring the velocity of very rapid chemical reactions

1923 ◽  
Vol 104 (726) ◽  
pp. 376-394 ◽  
Keyword(s):  
Gas Phase ◽  
Chemical Reactions ◽  
Chemical Reaction ◽  
Chemical Equilibrium ◽  
Stable Condition ◽  
Chemical System ◽  
Unstable State ◽  
Unstable Condition ◽  
Time Required ◽  
Short Time

In devising methods for determining the velocity of any chemical reaction there are two experimental problems which invariably arise : (1) To arrange that the chemical system under investigation be made initially unstable in a period of time that is negligibly short in comparison with that taken by the chemical reaction. (2) To record from time to time the stages reached by the system (during its passage from the initial unstable state to the final stable condition wherein the several reacting substances are in chemical equilibrium) by means of methods which take a negligibly short time in comparison with that taken by the chemical reaction. A perusal of the literature shows that previous investigators have, in the main, restricted themselves to the study of slow reactions, such as may require many minutes or even hours to reach completion. In such cases, both requirements which we have mentioned can be easily met. For the production of the initially unstable condition can be achieved without difficulty by merely mixing the several reacting substances together in proportions far removed from those which prevail when equilibrium has been attained. The time required by the mixing operation can be reduced to a few seconds, and can therefore be neglected when dealing with a process which may last many minutes or even hours. The slow reactions possess a further attraction, in that the procedure for estimating the concentrations of the several reactants at different stages during the progress of the reaction need not be a hurried one. This permits the use of a wide variety of methods, e. g ., polarimetry as in the study of the inversion of sucrose, ordinary titration as in the saponification of esters, and separation of one of the constituents as a gas phase as in the decomposition of diazo-acetic ester by water, i. e ., N 2 . CHCOOC 2 H 5 +H 2 O→OHCH 2 . COOC 2 H 5 +N 2 (gas phase).

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