Derivation of the Transport Equation for Multicomponent Diffusion through Capillaries in the Transition Region between Gas‐Diffusion and Knudsen‐Diffusion

Abstract

AbstractThe transport equation for multicomponent diffusion through a very long capillary in the transition region is derived using Boltzmann's H‐function. In discussing this function for a mixture of ideal gases enclosed in a cylinder having a finite ratio of cylinder surface and volume it is shown that‐the free enthalpy dissipation for isothermal diffusion in the absence of external forces contains two terms: the dissipation in the interior of the cylinder volume and at the surface. Using Onsager's principle of least dissipation of energy one obtains the transport equation mentioned above. It is, however, only valid for very long capillaries. In shorter tubes “end correction” will influence the transport process.