On chemical relaxation modes in homogeneous chemical systems

1988 ◽  
Vol 66 (11) ◽  
pp. 2768-2776
Author(s):  
F. Palomares ◽  
J. Veguillas ◽  
M. A. Diaz
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Theoretical Description ◽  
Kinetic Theory Of Gases ◽  
Relaxation Mode ◽  
Chemical Systems ◽  
Phenomenological Equations ◽  
Chemical Relaxation ◽  
Relaxation Modes ◽  
Homogeneous Chemical

We study the compatibility between the linearized phenomenological equations of an homogeneous chemical gaseous system, and the theoretical ones obtained with the aid of the kinetic theory of gases. Our discussion is based on the concept of chemical relaxation mode. The theoretical description is provided by a reactive Boltzmann equation for each component of the system. Then, we show the conditions under which the linearized phenomenological equations can be reproduced.

scholarly journals On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2382
Author(s):  
Andrey Saveliev
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Magnetic Fields ◽  
Kinetic Theory ◽  
Charged Particles ◽  
Kinetic Theory Of Gases ◽  
The Boltzmann Equation ◽  
Ideal Magnetohydrodynamics ◽  
Complex Valued

In this work, we revisit Boltzmann’s distribution function, which, together with the Boltzmann equation, forms the basis for the kinetic theory of gases and solutions to problems in hydrodynamics. We show that magnetic fields may be included as an intrinsic constituent of the distribution function by theoretically motivating, deriving and analyzing its complex-valued version in its most general form. We then validate these considerations by using it to derive the equations of ideal magnetohydrodynamics, thus showing that our method, based on Boltzmann’s formalism, is suitable to describe the dynamics of charged particles in magnetic fields.

On the Theory of Determining the Transport Characteristics of Gas Mixtures

2020 ◽  
Vol 992 ◽  
pp. 823-827
Author(s):  
I.V. Anisimova ◽  
A.V. Ignat'ev
Keyword(s):  
Mass Transfer ◽  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Potential Energy ◽  
Uniform Convergence ◽  
Transport Coefficient ◽  
Collision Term ◽  
Kinetic Theory Of Gases ◽  
The Boltzmann Equation ◽  
Improper Integrals

The paper considers the identification of properties of real gases and creation of nanomaterials on the basis of molecular and kinetic theory of gases, namely the Boltzmann equation. The collision term of the Boltzmann equation is used in the algorithm for the identification of transport properties of media. The article analyses the uniform convergence of improper integrals in the collision term of the Boltzmann equation depending on the conditions for the connection between the kinetic and potential energy of interacting molecules. This analysis allows to soundly identify the transport coefficient in macro equations of heat and mass transfer.

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

Some notes on a volume fraction mixture theory and a comparison with the kinetic theory of gases

1991 ◽  
Vol 29 (5) ◽  
pp. 561-573 ◽  
Author(s):  
A.C. Hansen ◽  
R.L. Crane ◽  
M.H. Damson ◽  
R.P. Donovan ◽  
D.T. Horning ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Volume Fraction ◽  
Mixture Theory ◽  
Kinetic Theory Of Gases ◽  
Fraction Mixture

The Royal Society’s first rejection of the kinetic theory of gases (1821), John Herapath versus Humphry Davy

1963 ◽  
Vol 18 (2) ◽  
pp. 161-180 ◽  
Keyword(s):  
Kinetic Theory ◽  
Royal Society ◽  
Kinetic Theory Of Gases ◽  
Early Nineteenth Century ◽  
Important Distinction ◽  
Mathematical Inquiry ◽  
History Of ◽  
Humphry Davy ◽  
Apparent Similarity ◽  
Caloric Theory

On 24 May 1820 a manuscript entitled ‘A Mathematical Inquiry into the Causes, Laws and Principal Phenomena of Heat, Gases, Gravitation, etc.’ was submitted to Davies Gilbert for publication in the Philosophical Transactions of the Royal Society . The author was John Herapath (1790-1868), and his article included a comprehensive (if somewhat faulty) exposition of the kinetic theory of gases. Sir Humphry Davy, who assumed the Presidency of the Royal Society on 30 November 1820, became primarily responsible for the fate of the article and wrote several letters to Herapath concerning it. After it became clear that there was considerable opposition to its publication by the Royal Society, Herapath withdrew the article and sent it instead to the Annals of Philosophy , where it appeared in 1821 (1). Herapath’s theory received little notice from scientists until thirty-five years later, when the kinetic theory was revived by Joule, Krönig, Clausius, and Maxwell. The incident is significant in the history of physical science because it illustrates an important distinction between the two doctrines concerning the nature of heat—the kinetic and the vibration theories—a distinction which is often forgotten because of the apparent similarity of both doctrines as contrasted with the caloric theory. It also throws some light on the character of early nineteenth century British science, both in and out of the Royal Society.

Boundary-value problems in the kinetic theory of gases. Part 2. Thermal creep

1971 ◽  
Vol 45 (4) ◽  
pp. 759-768 ◽  
Author(s):  
M. M. R. Williams
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Kinetic Theory ◽  
Effective Thermal Conductivity ◽  
Half Space ◽  
Thermal Creep ◽  
Kinetic Theory Of Gases ◽  
Boundary Wall ◽  
Creep Velocity

The effect of a temperature gradient in a gas inclined at an angle to a boundary wall has been investigated. For an infinite half-space of gas it is found that, in addition to the conventional temperature slip problem, the component of the temperature gradient parallel to the wall induces a net mass flow known as thermal creep. We show that the temperature slip and thermal creep effects can be decoupled and treated quite separately.Expressions are obtained for the creep velocity and heat flux, both far from and at the boundary; it is noted that thermal creep tends to reduce the effective thermal conductivity of the medium.

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