Motion of carbon nanotubes in the temperature gradient field

The motion of carbon nanotubes in the process of thermophoresis is calculated using the model of an ideal gas with the monokinetic approximation of R. Clausius. The proposed scheme of a simple calculation of thermophoresis is based on the theorem of the momentum change for the nanoparticle-molecule system in the $\lambda$-layer. The calculation involves the partition into eight temperature layers the size of which is equal to the free path lenth, and the nanotube is placed in six layers. In the vicinity of a nanotube, the temperature variation is assumed to be linear. In determining the effects of molecules on the tube, the scheme of compensated impacts is applied. This substantially simplifies calculating the process of the momentum exchange between particles and molecules. Thus, all real double collisions were modeled by triple ones causing no Brownian motions. Under the assumption of the specular reflection of molecules, the final result is a mere sum of interactions between counter-moving pairs and nanotube. It is shown that the speed of thermophoresis of carbon nanotubes does no depend on their sizes within the values of the Knudsen number ($10< \mathrm{Kn} <100$) and depends only on the number of atoms in molecules of the gas environment and on the temperature gradient in it.