scholarly journals Study of Growth and Sublimation of Germanium Nitride Using the Concept of Tedmon's Kinetic Model

2020 ◽  
Vol 36 (05) ◽  
pp. 850-854
Author(s):  
Irakli Nakhutsrishvili
Keyword(s):  
Mathematical Model ◽  
Kinetic Model ◽  
Metal Surface ◽  
Kinetic Curve ◽  
Nitride Layer ◽  
Mass Change ◽  
Thermogravimetric Curve

The paper gives a mathematical model of a thermogravimetric curve for the growth of scale on a metal surface with its simultaneous sublimation is presented and considers the case of the growth-sublimation of scale being preceded by the process of gas etching of the monocrystal surface. The obtained equations are used to describe the kinetic curve of the mass change of a germanium sample when a nitride layer is formed on it in a medium of hydrazine vapors.

Potential in microroughness domain of metal surface employed in cathodic protection mode

2021 ◽  
Vol 2021 (3) ◽  
pp. 48-54
Author(s):  
V. Lukovich ◽  
◽  
V. Kartuzov ◽  
Keyword(s):  
Mathematical Model ◽  
Metal Surface ◽  
Cathodic Protection ◽  
Computational Experiment ◽  
Computational Domain ◽  
Protective Potential ◽  
Long Time ◽  
Protection Mode ◽  
Model Equations ◽  
Iterative Procedures

This effort presents the results of investigation of cathodic protection process of a section of the main pipeline, which has been operating in cathodic protection mode for a long time and which insulation has completely exfoliated from metal surface, and a cavity between is filled with water and salt impurities. In this case, a decisive factor is a fact that a metal surface is covered with microroughnesses in the form of protrusions with almost conical shape. The surface is immersed in electrolyte. At the electrolyte-metal interface, a potential difference is formed - a corrosion potential, which creates an unstable equilibrium among the potentials of metal and electrolyte. A mathematical model is designed and implemented into a numerical algorithm and computer program. A computational experiment has been carried out to calculate the potential around microroughness. The model describes a change in potential in this area at incomplete and complete cathodic protection of metal surface. The basis of computational model is a selection of one of metal protrusions of material microheterogeneity and placing it in a cylinder, which diameter coincides with that one of the lower base of this protrusion, and its upper part passes through the apex of the protrusion. Mathematical model equations with corresponding boundary conditions and their discrete implementation are presented. The solution of problems is obtained by iterative procedures based on reference values of protective potential taken from practice. The results of computational experiment are presented in the form of graphs: 1) potential distribution in the field of electrolytes; 2) changes in electrolyte potential at the border with protrusion at different values of polarization potential; 3) changes in polarization resistance in the area (calculated). The geometry of computational domain was also varied, and the values of protective potential were determined to ensure the absence of corrosion. Keywords: corrosion, microroughness, protective potential, plastic current density, electrolyte

The catalytic kinetics and cfd simulation of multi-stage combined removal of acrylonitrile tail gas

2021 ◽  
pp. 115-125
Author(s):  
Zhao Du ◽  
◽  
Qian Liu ◽  
Yuxuan Yang ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Kinetic Model ◽  
Catalytic Reaction ◽  
Cfd Simulation ◽  
Reaction Network ◽  
External Diffusion ◽  
Quantitative Calculation ◽  
Dynamic Factors ◽  
Multi Stage ◽  
Catalytic Kinetics

There is no kinetic data and rate equation that can be used directly for catalytic combustion of acrylonitrile tail gas, which leads to the multi-stage combined catalytic kinetic model of acrylonitrile tail gas collaborative removal. In the actual application process, affected by the internal and external diffusion, this paper proposes the multi-stage combined catalytic kinetic research and CFD simulation analysis of acrylonitrile tail gas collaborative removal. Based on the judgment of multi-stage combined catalytic reaction rules of acrylonitrile tail gas collaborative removal, the multi-stage combined catalytic reaction network of acrylonitrile tail gas collaborative removal is solved by matrix transformation. The possible reaction path in the multi-stage combined catalytic reaction network of acrylonitrile tail gas collaborative removal is solved. For quantitative calculation of product distribution, each step of reaction parameters and dynamic factors are required. According to the mechanism of positive carbon ion reaction, materials were used Studio software and genetic algorithm are used to calculate the dynamic factors and determine the dynamic parameters; the grid automatic generator AutoGrid5 embedded in the Fine/TurboTM software package is used to generate the CFD simulation network, and the iterative algorithm is used to calculate the limit value of the CFD simulation; the S-A model in the CFD simulation platform is used to get the modified value of the dynamic mathematical model, and the dynamic factors and parameters are brought into it to establish the CA mathematical model of multi-stage combined catalytic kinetics for the CO removal of olefine and nitrile tail gas. The experimental results show that, under the same experimental device and parameters, the internal and external diffusion effects of the multi-stage combined catalytic kinetic model of acrylonitrile tail gas collaborative removal are detected. The multi-stage combined catalytic kinetic model of acrylonitrile tail gas collaborative removal in this study uses 10-20 mesh catalyst, and the retention time of acrylonitrile tail gas is less than 4.62 s, the internal and external diffusion will not affect the acrylonitrile tail gas collaborative removal The practical application of the kinetic model for the removal of multi-stage combined catalysis.

Numerical Evaluation of the Effect of a Surface-Active Component on the Convective Mass Transfer During the Metal Surface Melting by the Laser Impulse

2012 ◽  
Vol 7 (3) ◽  
pp. 114-121
Author(s):  
Vladimir Popov ◽  
Oleg Kovalev ◽  
Elena Smirnova ◽  
Yuliya Tsivinskaya
Keyword(s):  
Mathematical Model ◽  
Metal Surface ◽  
Numerical Evaluation ◽  
Active Component ◽  
Pulsed Laser ◽  
Convective Mass Transfer ◽  
Pulsed Laser Radiation ◽  
Surface Active ◽  
Laser Impulse ◽  
Surface Active Component

Under consideration is a mathematical model of the alloying process of the metal surface by the pulsed laser radiation. The dependence of the surface tension on the surface-active impurities in the melt is analyzed. The numerical simulation enabled to determine the possibility of development of flows and distribution of the alloying material into the metal

Mass transfer in heterogeneous system enzyme-substrate; Kinetic model of enzymatic reaction in system of two immiscible liquids

1982 ◽  
Vol 47 (11) ◽  
pp. 3019-3026 ◽  
Author(s):  
František Kaštánek ◽  
Jindřich Zahradník ◽  
Germanico Ocampo
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Kinetic Model ◽  
Interphase Boundary ◽  
Heterogeneous System ◽  
Enzymatic Reaction ◽  
Reaction Rates ◽  
Immiscible Liquids ◽  
Enzyme Substrate

Mathematical model is proposed enabling calculation of enzymatic reaction rates occuring in one phase of a system of two immiscible liquids under conditions of substrate and product transfer over the interphase boundary.

Use of a Mathematical Model to Determine the Fate of Atrazine in Barley (Hordeum vulgare) Plants

Weed Science ◽  
1985 ◽  
Vol 33 (6) ◽  
pp. 906-912 ◽  
Author(s):  
Sylvie Raynaud ◽  
Jean Bastide ◽  
Camille Coste
Keyword(s):  
Mathematical Model ◽  
Hordeum Vulgare ◽  
Kinetic Model ◽  
Second Order ◽  
Order Kinetic ◽  
First Order ◽  
Order Kinetic Model

A model of the pharmacokinetics of atrazine [6-chloro-N-ethyl-N′-(1-methylethyl)-1,3,5-triazine-2,4-diamine] in barley (Hordeum vulgare L. ‘Escourgnon’) plants has been described. Uptake of atrazine conforms to a first-order kinetic model. Roots play a small role as a sink for atrazine. Metabolism of the herbicide conforms to a second-order kinetic model. Using this model, the amount of atrazine in leaves can be evaluated at any time if the concentration of herbicide in solution is known.

Application of a Mathematical Model of Iron-Nitride Layer Growth during Gas Phase Nitriding

1994 ◽  
Vol 163-165 ◽  
pp. 707-712 ◽  
Author(s):  
L. Torchane ◽  
Ph. Bilger ◽  
J. Dulcy ◽  
M. Gantois
Keyword(s):  
Mathematical Model ◽  
Gas Phase ◽  
Nitride Layer ◽  
Layer Growth ◽  
Iron Nitride

scholarly journals Study of a mathematical model of gasoline catalytic reforming by sensitivity analysis methods

2020 ◽  
pp. 440-451
Author(s):  
Л.Ф. Сафиуллина ◽  
К.Ф. Коледина ◽  
И.М. Губайдуллин ◽  
Р.З. Зайнуллин
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Kinetic Model ◽  
Point Of View ◽  
Oil Refining ◽  
Chemical Transformations ◽  
Catalytic Reforming ◽  
Analysis Methods ◽  
Realistic Description ◽  
General Dynamics

Для изучения одного из важнейших процессов нефтепереработки — каталитического риформинга, требуется детализированная кинетическая модель. При разработке кинетической модели возникает сложность в связи с большим количеством компонентов реакционной смеси и большим количеством стадий химических превращений. Альтернативой могут быть сокращенные механизмы реакций, которые применимы для решения задачи и обеспечивают реалистичное описание процесса. В данной работе для анализа кинетической модели и получения сокращенного механизма реакции используются методы анализа чувствительности математической модели. Применение указанной методики позволяет выявить стадии каталитического риформинга бензина, наименее влияющие на общую динамику изменения концентраций значимых веществ реакции. Исследовано влияние исключения данных стадий на кинетику процесса с химической точки зрения. Предложена редуцированная схема каталитического риформинга бензина с исключением данных стадий. Редуцированная схема обеспечивает вполне удовлетворительное согласие как по профилям температуры, так и по профилям концентраций значимых веществ реакции. A detailed kinetic model is required to study one of the most important oil refining processes known as catalytic reforming. The difficulty arises in connection with a large number of components of the reaction mixture and a large number of stages of chemical transformations in developing the kinetic model. An alternative may be reduced reaction mechanisms that are applicable to solve the problem and provide a realistic description of the process. In this paper, to analyze the kinetic model and to obtain an abbreviated reaction mechanism, the sensitivity analysis methods of the mathematical model are used. The least influential stages of catalytic reforming of gasoline, which do not affect the general dynamics of changes in the concentrations of significant reaction substances are identified using this technique. The effect of eliminating these stages on the kinetics of the process from the chemical point of view is analyzed. A reduced scheme for catalytic reforming of gasoline by excluding these stages is proposed. A reduced scheme provides a quite satisfactory agreement both in temperature profiles and in concentration profiles of significant substances.

scholarly journals Ultrafast Dynamic Contrast-Enhanced Breast MRI: Kinetic Curve Assessment Using Empirical Mathematical Model Validated with Histological Microvessel Density

2019 ◽  
Vol 26 (7) ◽  
pp. e141-e149 ◽  
Author(s):  
Naoko Mori ◽  
Hiroyuki Abe ◽  
Shunji Mugikura ◽  
Chiaki Takasawa ◽  
Satoko Sato ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Microvessel Density ◽  
Kinetic Curve ◽  
Breast Mri ◽  
Dynamic Contrast Enhanced ◽  
Ultrafast Dynamic ◽  
Contrast Enhanced

scholarly journals Kinetic Model for Solute Diffusion in Liquid Membrane Systems

2016 ◽  
Vol 13 (2) ◽  
pp. 48-57
Author(s):  
Baghdad Science Journal
Keyword(s):  
Mathematical Model ◽  
Kinetic Model ◽  
Solute Transport ◽  
Liquid Membrane ◽  
Solute Diffusion ◽  
Membrane Systems ◽  
Linear Forms ◽  
Donor Acceptor ◽  
Reversible Processes ◽  
Kinetics Of

In this study, a mathematical model for the kinetics of solute transport in liquid membrane systems (LMSs) has been formulated. This model merged the mechanisms of consecutive and reversible processes with a “semi-derived” diffusion expression, resulting in equations that describe solute concentrations in the three sections (donor, acceptor and membrane). These equations have been refined into linear forms, which are satisfying in the special conditions for simplification obtaining the important kinetic constants of the process experimentally.

scholarly journals The predictive potential of the kinetic model of aging of living systems in demography

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Alexander Alexandrovich Victorov ◽  
Viacheslav Alexandrovich Kholodnov
Keyword(s):  
Mathematical Model ◽  
Kinetic Model ◽  
Biological Species ◽  
Living Systems ◽  
Biological Degradation ◽  
The World ◽  
The Usa ◽  
Development Processes ◽  
The Russian Empire ◽  
And Function

An original mathematical model, previously tested by the authors on other non-demographic objects, is proposed for describing and forecasting demographic systems — the population of the countries of the World using the examples of the USA, China and Russia, as well as the number of mice in the “mouse paradise” experiment of the American scientist John Calhoun. The proposed approach allows us to describe the stages and features of this dynamics: population growth in the USA, growth and possible decrease in the population in China, loss of a part of the population of the Russian Empire and the USSR due to two world wars and the collapse of the USSR, biological degradation of the “mouse paradise” up to its complete extinction. The use of the kinetic model of aging of various types of living systems to predict the development of the number of demographic systems is based on the assumptions that the aging and development processes are related to each other and have the same statistical regularity, reflecting the fractal principle of Nature - the unity of structure and function. The results obtained suggest that a person, a population of the World, humanity and other biological species develop and simultaneously age like each other under the conditions of the always existing syndrome of general adaptation (stress) and according to the same pattern corresponding to the mathematical model proposed here.  

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