Kinetic Study of Small Particles Transport in Rarefied Gas Media.

This work presents a kinetic study of small (micrometer or nanometer scale) particles transport in gas media in a free molecular regime. It is based on a Boltzmann like kinetic theory adapted to treat inelastic collisions through the concept of scattering kernels [1].
The work focus on a generalized treatment of the drag force on a spherical particle due to its motion in a low density gas, with Knudsen number Kn>>1. The approach Is shown to be equally applicable to particle diffusion and electric mobility. It is explicitly considered the influence of soft interaction potential, between the particles and the gas molecules, on the transport, compared to the transport based on rigid sphere potential. An interaction potential relevant for molecule/particle interaction, recently developed by Rudyak and Krasnolutski [2] is used.
Interaction between gas molecules and particles is a rather complex process which changes with particle size and depends on the reflection mode on particle surface which is described by a reflection kernel (transition probability). This requires simplified models for molecule /particle interaction. The best known is the Maxwell model which introduces an accommodation parameter that measures the fraction of molecules diffusively reflected and consider the remaining fraction specularly scattered [3], [4].
The real scattering behavior is still not known and may depend on the particle surface roughness. In this work the transport is analyzed adding to Maxwell model a scattering kernel to describe the perfectly rough particle surface which will scatter the molecules into arbitrary directions while preserving their absolute velocity.
The study made here is then compared to that made by Li and Wang[5] which used Maxwell model for the transport of almost spherical silver and copper oxide nanoparticles, both, in a nitrogen gas.

[1] G. M. Kremer, An Introduction to the Boltzmann Equation and Transport Processes in Gases. Springer, 2010.
[2] V. Ya. Rudyak and Krasnolutski, Dokl. Phys. 47, 758(2002).
[3] J. C. Maxwell, Philos. Trans. R. Soc. London 170, 231-256(1879).
[4] Lucas G. L. F. Pollito, Disserta??o de Mestrado, Instituto Tecnol?gico de Aeron?utica, 2013.
[5] Z. Li and H. Wang, Phys. Rev. E 68, 61207(2003).