Representation of a tube of radius with periodic partitions separated by distance . Each partition has a circular aperture of radius in its center.
Tortuosity , Eq. (6), as a function of the radii ratio at three values of the interpartition distance, , 2, and 5 from top to bottom. The tortuosity decreases and approaches unity as the interpartition distance increases and grows as the size of the aperture decreases.
Theoretically predicted time dependence of the relaxation function at three values of the dimensionless partition permeability, , , 1, and 5 from top to bottom. The curves are obtained by numerically inverting the Laplace transform in Eq. (11). The relaxation accelerates as the permeability increases.
The mean squared displacement as a function of time at two values of the radii ratio, [panel (a)] and [panel (b)]. Curves are theoretically predicted dependences obtained by numerically inverting the Laplace transform in Eq. (14). Symbols are the results obtained in Brownian dynamics simulations at (squares), (circles), and (stars). In simulations the results were obtained by averaging over trajectories. The relative error of these results does not exceed 2%. One can see excellent agreement between theoretical and simulation results for all sets of the tube parameters except one, and .
Ratios of the effective diffusion coefficients found in Brownian dynamics simulations to their theoretically predicted counterparts, Eqs. (5) and (6). Majority of the simulation results was obtained by averaging over trajectories. The results marked by the asterisk were obtained by averaging over trajectories. The relative errors of the former and latter do not exceed 2% and 4%, respectively.
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