Abstract
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.
Highlights
A subject of great interest for a wide variety of applications is how to use a temperature difference to drive fluid flow through a porous medium
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, changing the flux of heat
Summary
A subject of great interest for a wide variety of applications is how to use a temperature difference to drive fluid flow through a porous medium. We are interested in the effect of surface adsorption, and possible long-ranged interactions between the fluid and the porous medium The reason for this interest is recent observations on the importance of this coupling in thermally driven processes, such as membrane distillation.. Jepps et al. proposed a successful model for the free molecular regime, in which they solved deterministic microscopic equations of motion for the isothermal case, with a realistic wall–fluid interaction This method treats the thermodynamic driving force as a deterministic force acting on each individual molecule. The new results are presented in the end, that is, analytical expressions for the flow resistance inside the pore These can be connected with the total resistances including the left and right interfaces to provide models for an experimenter
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