H theorem and kinetic equations for a reacting gas

1973 ◽  
Vol 10 (3) ◽  
pp. 425-431
Author(s):  
Ta-Ming Fang

A previously developed set of kinetic model equations for a chemically-reacting gas is modified. By examining closely the H theorem, a new set of constraints is obtained. These conditions are then used to determine the inelastic collision parameters proposed in the model. The kinetic equations so obtained are able to produce exactly the same rate equations as prescribed by the actual chemical reactions.

2007 ◽  
Vol 7 (23) ◽  
pp. 5989-6023 ◽  
Author(s):  
U. Pöschl ◽  
Y. Rudich ◽  
M. Ammann

Abstract. Aerosols and clouds play central roles in atmospheric chemistry and physics, climate, air pollution, and public health. The mechanistic understanding and predictability of aerosol and cloud properties, interactions, transformations, and effects are, however, still very limited. This is due not only to the limited availability of measurement data, but also to the limited applicability and compatibility of model formalisms used for the analysis, interpretation, and description of heterogeneous and multiphase processes. To support the investigation and elucidation of atmospheric aerosol and cloud surface chemistry and gas-particle interactions, we present a comprehensive kinetic model framework with consistent and unambiguous terminology and universally applicable rate equations and parameters. It enables a detailed description of mass transport and chemical reactions at the gas-particle interface, and it allows linking aerosol and cloud surface processes with gas phase and particle bulk processes in systems with multiple chemical components and competing physicochemical processes. The key elements and essential aspects of the presented framework are: a simple and descriptive double-layer surface model (sorption layer and quasi-static layer); straightforward flux-based mass balance and rate equations; clear separation of mass transport and chemical reactions; well-defined and consistent rate parameters (uptake and accommodation coefficients, reaction and transport rate coefficients); clear distinction between gas phase, gas-surface, and surface-bulk transport (gas phase diffusion, surface and bulk accommodation); clear distinction between gas-surface, surface layer, and surface-bulk reactions (Langmuir-Hinshelwood and Eley-Rideal mechanisms); mechanistic description of concentration and time dependences (transient and steady-state conditions); flexible addition of unlimited numbers of chemical species and physicochemical processes; optional aggregation or resolution of intermediate species, sequential processes, and surface layers; and full compatibility with traditional resistor model formulations. The outlined double-layer surface concept and formalisms represent a minimum of model complexity required for a consistent description of the non-linear concentration and time dependences observed in experimental studies of atmospheric multiphase processes (competitive co-adsorption and surface saturation effects, etc.). Exemplary practical applications and model calculations illustrating the relevance of the above aspects are presented in a companion paper (Ammann and Pöschl, 2007). We expect that the presented model framework will serve as a useful tool and basis for experimental and theoretical studies investigating and describing atmospheric aerosol and cloud surface chemistry and gas-particle interactions. It shall help to end the "Babylonian confusion" that seems to inhibit scientific progress in the understanding of heterogeneous chemical reactions and other multiphase processes in aerosols and clouds. In particular, it shall support the planning and design of laboratory experiments for the elucidation and determination of fundamental kinetic parameters; the establishment, evaluation, and quality assurance of comprehensive and self-consistent collections of rate parameters; and the development of detailed master mechanisms for process models and derivation of simplified but yet realistic parameterizations for atmospheric and climate models.


2005 ◽  
Vol 5 (2) ◽  
pp. 2111-2191 ◽  
Author(s):  
U. Pöschl ◽  
Y. Rudich ◽  
M. Ammann

Abstract. Aerosols and clouds play central roles in atmospheric chemistry and physics, climate, air pollution, and public health. The mechanistic understanding and predictability of aerosol and cloud properties, interactions, transformations, and effects are, however, still very limited. This is due not only to the limited availability of measurement data, but also to the limited applicability and compatibility of model formalisms used for the analysis, interpretation, and description of heterogeneous and multiphase processes. To support the investigation and elucidation of atmospheric aerosol and cloud surface chemistry and gas-particle interactions, we present a comprehensive kinetic model framework with consistent and unambiguous terminology and universally applicable rate equations and parameters. It allows to describe mass transport and chemical reactions at the gas-particle interface and to link aerosol and cloud surface processes with gas phase and particle bulk processes in systems with multiple chemical components and competing physicochemical processes. The key elements and essential aspects of the presented framework are: a simple and descriptive double-layer surface model (sorption layer and quasi-static layer); straightforward flux-based mass balance and rate equations; clear separation of mass transport and chemical reactions; well-defined rate parameters (uptake and accommodation coefficients, reaction and transport rate coefficients); clear distinction between gas phase, gas-surface, and surface-bulk transport (gas phase diffusion correction, surface and bulk accommodation); clear distinction between gas-surface, surface layer, and surface-bulk reactions (Langmuir-Hinshelwood and Eley-Rideal mechanisms); mechanistic description of concentration and time dependencies; flexible inclusion/omission of chemical species and physicochemical processes; flexible convolution/deconvolution of species and processes; and full compatibility with traditional resistor model formulations. Exemplary practical applications and model calculations illustrating the relevance of the above aspects will be presented in a companion paper (Ammann and Pöschl, 2005). We expect that the presented model framework will serve as a useful tool and basis for experimental and theoretical studies investigating and describing atmospheric aerosol and cloud surface chemistry and gas-particle interactions. In particular, it is meant to support the planning and design of laboratory experiments for the elucidation and determination of kinetic parameters; the establishment, evaluation, and quality assurance of comprehensive and self-consistent collections of rate parameters; and the development of detailed master mechanisms for process models and the derivation of simplified but yet realistic parameterizations for atmospheric and climate models.


1985 ◽  
Vol 160 ◽  
pp. 29-45 ◽  
Author(s):  
Yasunari Takano ◽  
Teruaki Akamatsu

This paper analyses effects of chemical reactions on reflected-shock flow fields in shock tubes. The method of linearized characteristics is applied to analyse gasdynamic disturbances due to chemical reactions. The analysis treats cases where combustible gas is highly diluted in inert gas, and assumes that flows are one-dimensional and that upstream flows in front of the reflected-shock waves are in the frozen state. The perturbed gasdynamic properties in the reflected-shock flow fields are shown to be expressible mainly in terms of a heat-release function for combustion process. In particular, simple relations are obtained between the heat-release function and the physical properties at the end wall of a shock tube. As numerical examples of the analysis, the present formulation is applied to calculate gasdynamic properties in the reflected-shock region in a H2–O2–Ar mixture. Procedures are demonstrated for calculation of the heat-release function by numerically integrating rate equations for chemical species. The analytical results are compared with rigorous solutions obtained numerically by use of a finite-difference method. It is shown that the formulation can afford exact solutions in cases where chemical behaviours are not essentially affected by gasdynamic behaviours. When the induction time of the combustion process is reduced to some extent owing to gasdynamic disturbances, some discrepancies appear between analytical results and rigorous solutions. An estimate is made of the induction-time reduction, and a condition is written down for applicability of the analysis.


2010 ◽  
Vol 49 (4) ◽  
pp. 870-879
Author(s):  
F. Calogero ◽  
F. Leyvraz ◽  
M. Sommacal

During the year 1890 the late Prof. Landolt inaugurated his prolonged researches upon the apparent alteration in the total mass of chemically reacting substances. From the time of its inception until it was brought to a conclusion in 1907, the experimental work was freely varied both as regards the conditions and the nature of the chemical reactions involved. The methods and precautions adopted, together with the final results obtained, are to be found embodied and set forth in detail in Landolt’s important memoir, “Über die Erhaltung der Masse hei Chemischen Umsetzungen.”* Before proceeding to deal with my own investigations in this field of research, it may not be inappropriate first very briefly to recall the chief features of Landolt’s work and conclusions.


2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Derya Tekin ◽  
Taner Tekin ◽  
Hakan Kiziltas

AbstractThe degradation of water pollutants with photocatalysts is one of the most studied subjects in the past 20 years. Although considerable studies have been completed in this field, kinetic model studies are still a major inadequacy. In this study, ZnO and Ag/ZnO thin film photocatalysts were synthesized and SEM-EDS, XRD and chronoamperometric measurements were used the characterization of photocatalysts. The network kinetic model was applied the photocatalytic degradation of Orange G using ZnO and Ag/ZnO thin film photocatalysts. The photocatalytic degradation of Orange G was investigated under the different reaction medium (initial dye concentrations, temperature, light intensity). It was found that the network kinetic model is the most appropriate model for the degradation of Orange G dye on the ZnO and Ag/ZnO thin film photocatalysts. The calculated adsorption equilibrium (KB) constant and activation energy of ZnO thin film photocatalyst are 0.0191 and 21.76 kj/mol, respectively. Additionally, the calculated values for Ag/ZnO thin film photocatalyst are 0.035 and 18.32 kj/mol. The general rate equations were determined for each photocatalysts.


1964 ◽  
Vol 7 (12) ◽  
pp. 2012 ◽  
Author(s):  
T. F. Morse

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