Analysis of models of single-file diffusion.

Theoretical models of single-file transport in a homogeneous channel are considered. Three levels of channel populations were specified for which different approximations could be used. The results of these approximations are in good agreement with the results of a computer experiment (Aityan and Portnov 1986). At low populations, the pair correlation functions were negligibly small and allowed the use of linear approximation for unidirectional fluxes and populations. The value of the pair correlation function and the respective approximation for fluxes was obtained by the two-particles random-walk technique. At extremely high populations, the "divider" technique was proposed to describe the single-file transport. The divider technique allowed to explain the exponential shape of the pair correlation function FABn, n + 1 profile at extremely high populations. At medium populations the finite difference superposition approximation was valid.

Computer simulation of single-file transport.

A stochastic model of single-file transport was developed as the Markov process in continuous time technique. The model was constructed using an EC-1060 computer. Unidirectional fluxes were investigated and populations of channels were correlated with flux fluctuations. The profiles of channel populations were shown to have nonlinear shapes even with the transport of nonelectrolyte (the classical diffusion approach gives linear profiles). The relationship between the paired correlation function F(AB) and the concentration of transported particles was examined. The F(AB) profile was shown to become flattened (or exponential for asymmetrical cases) at high concentrations. The concentration dependence jA/jA0 ratio were analyzed, where jA is a single-file unidirectional flux, jA0 is unidirectional flux for the case of free diffusion. An interesting "stack" phenomenon was observed for abnormal time correlations of single-file fluxes.