Analytical Proof That There is no Effect of Confinement or Curvature on the Maxwell-Boltzmann Collision Frequency

作者：Carnio Brett N; Elliott Janet A W^*

来源：Journal of Statistical Physics, 2014, 156(4): 668-685.

DOI：10.1007/s10955-014-1028-5

• Integral
• Maxwell-Boltzmann
• Collision frequency
• Power series

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.

• 出版日期2014-8