Non-equilibrium Thermodynamics of Fast Traveling Waves in a Catalytic Fixed Bed. Emergence of Near-equilibrium Spatiotemporal Dissipative Structure

2018 ◽  
Vol 43 (3) ◽  
pp. 221-235
Author(s):  
Alexander P. Gerasev
Keyword(s):  
Mathematical Model ◽  
Wave Propagation ◽  
Traveling Wave ◽  
Dissipative Structure ◽  
Fixed Bed ◽  
Dissipative Structures ◽  
Catalytic Reactors ◽  
Linear Ordinary Differential Equations ◽  
Physical And Chemical ◽  
Non Equilibrium

AbstractThis work presents the results of the mathematical modeling of the fast traveling wave propagation phenomenon in the fixed-bed catalytic reactors according to a simple (basic) mathematical model with a reversible reaction. Qualitative and quantitative research is used to study the behavior of separatrices’ trajectories of the system’s non-linear ordinary differential equations. Special attention has been paid to the non-equilibrium thermodynamic methods. The entropy balance equation is constructed and analyzed under the assumption of the simple mathematical model of physical and chemical processes. The influence of key physical and chemical parameters on the fast traveling wave properties is studied. The phenomenon of fast traveling wave propagation in the fixed-bed catalytic reactors provides a vivid example of a spatiotemporal dissipative structure in active heterogeneous medium. These dissipative structures are shown to exist near the thermodynamic equilibrium.

Modeling of aerated upflow fixed bed reactors for nitrification

1999 ◽  
Vol 39 (4) ◽  
pp. 85-92 ◽  
Author(s):  
J. Behrendt
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Liquid Phase ◽  
Gas Phase ◽  
Fixed Bed ◽  
Fixed Bed Reactor ◽  
Bulk Liquid ◽  
Initial Value ◽  
Fixed Bed Reactors ◽  
Number Of Cells

A mathematical model for nitrification in an aerated fixed bed reactor has been developed. This model is based on material balances in the bulk liquid, gas phase and in the biofilm area. The fixed bed is divided into a number of cells according to the reduced remixing behaviour. A fixed bed cell consists of 4 compartments: the support, the gas phase, the bulk liquid phase and the stagnant volume containing the biofilm. In the stagnant volume the biological transmutation of the ammonia is located. The transport phenomena are modelled with mass transfer formulations so that the balances could be formulated as an initial value problem. The results of the simulation and experiments are compared.

scholarly journals Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 728
Author(s):  
Yasunori Maekawa ◽  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
Algebraic Characterization ◽  
Symmetric Hyperbolic System ◽  
Full Generality ◽  
Order Linear ◽  
First Order

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

Self-Organisation of the Heat Resistant Steel Structure Following Dynamic Non-Equilibrium Processes

2015 ◽  
Vol 220-221 ◽  
pp. 917-921 ◽  
Author(s):  
Mykola Chausov ◽  
Pavlo Maruschak ◽  
Olegas Prentkovskis ◽  
Andriy Pylypenko ◽  
Valentyn Berezin ◽  
...  
Keyword(s):  
Dissipative Structure ◽  
Steel Structure ◽  
Image Correlation ◽  
Experimental Methodology ◽  
Resistant Steel ◽  
Heat Resistant Steel ◽  
Heat Resistant ◽  
Equilibrium Processes ◽  
Equilibrium Process ◽  
Non Equilibrium

Using an original experimental methodology and software for contactless investigation into strains applying the method of digital image correlation, conditions for DNP realization in the test setup with pre-set rigidity have been found. Strain velocities have been determined to be equal to 2...10 s–1 in the processes of forming and developing a dissipative structure of heat resistant steel under the DNP (dynamic non-equilibrium process).

scholarly journals Suiting Dynamic Models of Fixed-Bed Catalytic Reactors for Computer-Based Applications

Engineering ◽  
2011 ◽  
Vol 03 (07) ◽  
pp. 778-785 ◽  
Author(s):  
Eduardo Coselli Vasco de Toledo ◽  
Edvaldo Rodrigo Morais ◽  
Delba Nisi Cosme Melo ◽  
Adriano Pinto Mariano ◽  
João F. C. A. Meyer ◽  
...  
Keyword(s):  
Dynamic Models ◽  
Fixed Bed ◽  
Catalytic Reactors ◽  
Computer Based

scholarly journals The Concentration of Digoxin Activity after Intravenous in Three Compartments Mathematical Model

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3653-3657
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Digoxin Concentration ◽  
Compartment Model ◽  
System Of Equations ◽  
Transfer Coefficients ◽  
Linear Ordinary Differential Equations ◽  
Concentration Time ◽  
The Laplace Transform ◽  
Three Compartment Model

Present paper is designed to compare the distribution of digoxin in three compartment model administered through an intravenous (i.v). These models under consideration is denoted by a system of non-linear ordinary differential equations. The Eigenvalue and the Laplace transform methods were used to solve the system of equations. Digoxin was administered to five subjects through Intravenous then, the serum digoxin concentrations were measured respectively over a period of 72 hours. The transfer coefficients were obtained from observed digoxin concentrations using method of residuals and the variation of digoxin concentration – time curves plotted using MATLAB.

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