Transport of a two-component mixture in one-dimensional channels

Abstract

The transport of a two-component gas mixture in subnanometer channels is investigated theoretically for an arbitrary filling of channels. Special attention is paid to consistent inclusion of density effects, which are associated both with the interaction and with a finite size of particles. The analysis is carried out using the hard-sphere model, in which the interaction is manifested as the effective (dynamic) attraction of particles, leading to their correlation. The adsorption isotherm is calculated and the ground state of the mixture in one-dimensional channels is investigated. It is shown, using the density functional method, that the two-component mixture in channels with increasing degree of filling is transformed into a spatially inhomogeneous state. This gives rise to short-lived clusters with size and lifetime increasing with the degree of channel filling. The description of transport in subnanometer channels is reduced in this case to the description of diffusion in a spatially inhomogeneous high-density one-dimensional system. The transport of particles in a medium with short-lived clusters occurs as a collective effect of the barrier-free transfer of density excitation. It is shown that, for high fill factors, the two-component mixture acquires a new property: clusters with a definite size are stabilized in channels due to effective attraction emerging between particles. The lifetime of formed clusters increases exponentially in accordance with the Arrhenius law; at a low temperature, channels with such clusters might be blocked to transport of particles of the mixture. The dependences of fluxes on the mixture composition (degree of filling) and pressure obtained theoretically are in good agreement with the experimentally observed regularities.