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- Title
Analytical Proof That There is no Effect of Confinement or Curvature on the Maxwell-Boltzmann Collision Frequency.
- Authors
Carnio, Brett; Elliott, Janet
- Abstract
The number of Maxwell-Boltzmann particles that hit a flat wall in infinite space per unit area per unit time is a well-known result. As new applications are arising in micro and nanotechnologies there are a number of situations in which a rarefied gas interacts with either a flat or curved surface in a small confined geometry. Thus, it is necessary to prove that the Maxwell-Boltzmann collision frequency result holds even if a container's dimensions are on the order of nanometers and also that this result is valid for both a finite container with flat walls (a rectangular container) and a finite container with a curved wall (a cylindrical container). An analytical proof confirms that the Maxwell-Boltzmann collision frequencies for either a finite rectangular container or a finite cylindrical container are both equal to the well-known result obtained for a flat wall in infinite space. A major aspect of this paper is the introduction of a mathematical technique to solve the arising infinite sum of integrals whose integrands depend on the Maxwell-Boltzmann velocity distribution.
- Subjects
CURVATURE; MAXWELL-Boltzmann function; MATHEMATICAL proofs; INFINITE series (Mathematics); NANOTECHNOLOGY
- Publication
Journal of Statistical Physics, 2014, Vol 156, Issue 4, p668
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-014-1028-5