Particle flow through a hydrophobic nanopore: Effect of long-ranged wall-fluid repulsion on transport coefficients

An analytical model for transport of rarefied non-isothermal gas in a cylinder with repulsive wall-gas interaction is developed, solving the stationary, collisionless Boltzmann equation. The results are compared to the well-known results of ordinary Knudsen diffusion, and the effect of the repulsive wall interaction is presented as correction factors to the Knudsen results. Detailed physical interpretations of the correction factors are given, showing how the wall interaction inhibits the particle flow through the cylinder, and how the energy carried per particle is affected, thus changing the flux of heat. It was shown that the flow mobility and the thermal conductivity of the gas are generally smaller in the presence of such interactions and that the heat of transfer can even change sign under certain conditions. By the latter statement, we mean that the heat flux under isothermal conditions, or equivalently, the particle flux driven by a temperature gradient, can switch direction due to the particle-wall repulsion.