Boltzmann Equation with Power-Law Interparticle Potentials

1969 ◽  
Vol 12 (3) ◽  
pp. 552 ◽  
Author(s):  
C. H. Su
Keyword(s):  
Boltzmann Equation ◽  
Power Law ◽  
Interparticle Potentials

Power-law decreasing in solutions of the Boltzmann equation

1987 ◽  
Vol 120 (5) ◽  
pp. 219-222 ◽  
Author(s):  
D. Zanette ◽  
C.R. Garibotti ◽  
R.O. Barrachina
Keyword(s):  
Boltzmann Equation ◽  
Power Law ◽  
The Boltzmann Equation

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.

Develop Boltzmann equation to simulate non‐Newtonian magneto‐hydrodynamic nanofluid flow using power law magnetic Reynolds number

2020 ◽  
Author(s):  
Quyen Nguyen ◽  
Mehdi Jamali Ghahderijani ◽  
Mehrdad Bahrami ◽  
Ehsan Kamali Ahangar ◽  
Annunziata D'Orazio ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Boltzmann Equation ◽  
Power Law ◽  
Magnetic Reynolds Number ◽  
Nanofluid Flow

Boltzmann Equation Analysis of Electron Swarm Development in Model Gases with Power-Law Elastic Scattering

1992 ◽  
Vol 61 (2) ◽  
pp. 524-529
Author(s):  
Hidenori Itoh ◽  
Masaru Kawaguchi ◽  
Yoshitaka Nakao ◽  
Hiroaki Tagashira
Keyword(s):  
Boltzmann Equation ◽  
Elastic Scattering ◽  
Power Law ◽  
Boltzmann Equation Analysis ◽  
Equation Analysis
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