scholarly journals Accurate and efficient computation of the Boltzmann equation for Couette flow: Influence of intermolecular potentials on Knudsen layer function and viscous slip coefficient

2019 ◽  
Vol 378 ◽  
pp. 573-590 ◽  
Author(s):  
Wei Su ◽  
Peng Wang ◽  
Haihu Liu ◽  
Lei Wu
Keyword(s):  
Boltzmann Equation ◽  
Couette Flow ◽  
Knudsen Layer ◽  
Efficient Computation ◽  
Intermolecular Potentials ◽  
Slip Coefficient ◽  
The Boltzmann Equation ◽  
Layer Function

scholarly journals Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couette flow

2006 ◽  
Vol 18 (1) ◽  
pp. 017104 ◽  
Author(s):  
M. A. Gallis ◽  
J. R. Torczynski ◽  
D. J. Rader ◽  
M. Tij ◽  
A. Santos
Keyword(s):  
Boltzmann Equation ◽  
Couette Flow ◽  
The Boltzmann Equation

Nonlinear transport coefficients and plane Couette flow of a viscous, heat-conducting gas between two plates at different temperatures

1987 ◽  
Vol 65 (9) ◽  
pp. 1090-1103 ◽  
Author(s):  
Byung Chan Eu ◽  
Roger E. Khayat ◽  
Gert D. Billing ◽  
Carl Nyeland
Keyword(s):  
Boltzmann Equation ◽  
Couette Flow ◽  
Transport Coefficients ◽  
Heat Conducting ◽  
Hydrodynamic Equations ◽  
Nonlinear Transport ◽  
Plane Couette Flow ◽  
The Boltzmann Equation ◽  
Viscous Heat ◽  
Different Temperatures

By using the example of plane Couette flow between two plates maintained at different temperatures, we present a method of calculating flow profiles for rarefied gases. In the method, generalized hydrodynamic equations are derived from the Boltzmann equation. They are then solved with boundary conditions calculated by taking into consideration the interfacial interaction between the surface and the gas molecule. The nonlinear transport coefficients employed in the generalized hydrodynamic equations are obtained from the Boltzmann equation by means of the modified-moment method. The profiles calculated are in agreement with the Liu–Lees theory as long as the boundary values are in agreement. It is found that the viscous-heating effect has a significant influence on the temperature and velocity profiles. The nonlinearity of transport coefficients also has significant effects on the profiles as the Knudsen and Mach numbers increase.

Velocity profile in the Knudsen layer according to the Boltzmann equation

2008 ◽  
Vol 464 (2096) ◽  
pp. 2015-2035 ◽  
Author(s):  
Charles R Lilley ◽  
John E Sader
Keyword(s):  
Boltzmann Equation ◽  
Power Law ◽  
Solid Surface ◽  
Velocity Gradient ◽  
Hard Spheres ◽  
Knudsen Layer ◽  
Flow Models ◽  
Thermal Accommodation ◽  
Dilute Gas ◽  
The Boltzmann Equation

Flow of a dilute gas near a solid surface exhibits non-continuum effects that are manifested in the Knudsen layer. The non-Newtonian nature of the flow in this region has been the subject of a number of recent studies suggesting that the so-called ‘effective viscosity’ at a solid surface is half that of the standard dynamic viscosity. Using the Boltzmann equation with a diffusely reflecting surface and hard sphere molecules, Lilley & Sader discovered that the flow exhibits a striking power-law dependence on distance from the solid surface where the velocity gradient is singular. Importantly, these findings (i) contradict these recent claims and (ii) are not predicted by existing high-order hydrodynamic flow models. Here, we examine the applicability of these findings to surfaces with arbitrary thermal accommodation and molecules that are more realistic than hard spheres. This study demonstrates that the velocity gradient singularity and power-law dependence arise naturally from the Boltzmann equation, regardless of the degree of thermal accommodation. These results are expected to be of particular value in the development of hydrodynamic models beyond the Boltzmann equation and in the design and characterization of nanoscale flows.

The Boltzmann Equation and the H Theorem (1872–1875)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Transport Phenomena ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

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