Scattering Kernel Kinetic Approach of Small Particles Transport in a Free Molecular Regime in Gaseous Media

Abstract

We investigated through the scattering kernel kinetic concept the transport of small particles in gaseous media in a free molecular regime. The scattering kernel is generally used to provide gas-surface interaction boundary conditions for Boltzmann kinetic equation in flow problems (Maxwell, Phil. Trans. R. Soc. 170, 231, 1879; Sharipov, 2001). We developed a general expression for the transport force explicitly in terms of the scattering kernel and of gas molecule velocity distribution function. From the general expression, first, we could use the first-order Chapman-Enskog solution for the distribution function of gas molecules f (r, v, t) which shows three types of transportation mechanisms, or forces, such that F = F D +F T +F S. Where F D is the drag force on the particle due to its relative motion in the gas, F T is the thermophoretic force due to a gradient of temperature in the gas, and F S is due to shear forces on the particle. Second, it is possible to use any of the several scattering kernel models published in the literature. The traditional simple reflection kernels, specular, diffuse, and Maxwell, which comprises particular cases of the generalized force, are limited and do not fully describe the real reflection mode of molecule-particle interaction. So, we used the general (Struchtrup, Phys. Fluids. 25, 112001, 2013) reflection kernel model to study the drag force on small particles. The results were compared with available experimental data. We concluded that it is necessary to explicitly include impact velocity and particle surface rugosity effects which are predicted by the Struchtrup reflection kernel thermal activation model of molecule-particle interaction. Keywords Scattering kernels • Drag force • Small particles • Diffusion 1 Introduction Richard Feynman in December 1959 in his now classic premonitory talk, "There's Plenty of Room at the Bottom-An Invitation to Enter a New Field of Physics," opened the road to nanotechnology. Today we see nanoparticles technology successfully used in a wide range of areas: nanosensors, environmental applications, aerospace engineering, medicine, biotechnology, semiconductors, atmospheric science, material processing, etc. In all these areas, some fundamental particle transport properties such as drag force, diffusion coefficients, electric mobility, thermodiffusion,