The behavior of a vapor-gas mixture in the continuum limit: Asymptotic analysis based on the Boltzmann equation

2001 ◽  
Author(s):  
Kazuo Aoki
Keyword(s):  
Boltzmann Equation ◽  
Asymptotic Analysis ◽  
Continuum Limit ◽  
Gas Mixture ◽  
The Boltzmann Equation ◽  
The Continuum

scholarly journals Inversion of the transverse force on a spinning sphere moving in a rarefied gas

2021 ◽  
Vol 933 ◽  
Author(s):  
Satoshi Taguchi ◽  
Tetsuro Tsuji
Keyword(s):  
Boltzmann Equation ◽  
Knudsen Number ◽  
Rarefied Gas ◽  
Mean Free Path ◽  
Transverse Force ◽  
Surface Velocity ◽  
Translational Velocity ◽  
The Boltzmann Equation ◽  
Wide Range ◽  
The Continuum

The flow around a spinning sphere moving in a rarefied gas is considered in the following situation: (i) the translational velocity of the sphere is small (i.e. the Mach number is small); (ii) the Knudsen number, the ratio of the molecular mean free path to the sphere radius, is of the order of unity (the case with small Knudsen numbers is also discussed); and (iii) the ratio between the equatorial surface velocity and the translational velocity of the sphere is of the order of unity. The behaviour of the gas, particularly the transverse force acting on the sphere, is investigated through an asymptotic analysis of the Boltzmann equation for small Mach numbers. It is shown that the transverse force is expressed as $\boldsymbol{F}_L = {\rm \pi}\rho a^3 (\boldsymbol{\varOmega} \times \boldsymbol{v}) \bar{h}_L$ , where $\rho$ is the density of the surrounding gas, a is the radius of the sphere, $\boldsymbol {\varOmega }$ is its angular velocity, $\boldsymbol {v}$ is its velocity and $\bar {h}_L$ is a numerical factor that depends on the Knudsen number. Then, $\bar {h}_L$ is obtained numerically based on the Bhatnagar–Gross–Krook model of the Boltzmann equation for a wide range of Knudsen number. It is shown that $\bar {h}_L$ varies with the Knudsen number monotonically from 1 (the continuum limit) to $-\tfrac {2}{3}$ (the free molecular limit), vanishing at an intermediate Knudsen number. The present analysis is intended to clarify the transition of the transverse force, which is previously known to have different signs in the continuum and the free molecular limits.

Solution of the Boltzmann equation for a reacting gas mixture

1993 ◽  
Vol 342 (1665) ◽  
pp. 413-438 ◽  
Keyword(s):  
Activation Energy ◽  
Boltzmann Equation ◽  
Cross Sections ◽  
Bimolecular Reaction ◽  
Model Parameters ◽  
Gas Mixture ◽  
Hard Sphere Model ◽  
Heat Of Reaction ◽  
Exothermic Reactions ◽  
The Boltzmann Equation

A spatially homogeneous gas mixture consisting of structureless molecules of kind A, B, C, D is considered in which the reversible bimolecular reaction A+B ^ C+D occurs. The Boltzmann equation describing this model gas is solved numerically by using the multigroup method. The collision cross sections correspond to the reactive hard sphere model. Parameters are the heat of reaction, the activation energy and the steric factor. Emphasis in the presentation of the results is laid on highly exothermic reactions with large activation energy, in which case the gas undergoes a thermal explosion. It is found that the corrections of the chemical rate constants due to translational non-equilibrium effects are noticeable. The result is a shortening of the reaction period by up to 25%.

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