Self-diffusion of fluids in narrow cylindrical pores

Abstract

Fluids under stochastic dynamics in narrow cylindrical pores exhibit a dynamical transition from single-file diffusion (SFD) to Fickian bulk diffusion. For long time, the mean square displacement will change as the pore size increases, with a transition from SFD, ∼t1/2, to Fickian, ∼t, while the diffusion coefficient (Dxx) increases from zero. We present a theory of this important process in terms of a hopping time, τhop, leading to Dxx∝(τhop)−1/2 which is verified with simulation. While the crossover is to be expected, the simple form is a priori unanticipated and is likely to be universal.