Single-file diffusion in a multilayered channel

We demonstrate that strongly repelling Brownian particles confined in two-dimensional microchannels with multiple layers show single-file diffusion. At long times the mean-square displacement (MSD) is proportional to $t^{1/2}$, as in the one-dimensional case. On an intermediate timescale the MSD is further reduced. It scales with a minimal exponent that decreases with the number of layers in the channel. In the limit of infinite width of the channel, the MSD time evolution shows a crossover to a logarithmic time dependence.

Figure 1

Snapshot of the colloidal particles in a part of a channel of width $L_Y=14.5$ forming $n_l=10$ layers and a sketch of the initial condition of the lattice-gas model with particle spacing $d=3$ and $n_l$ layers.

Figure 2

(a) Mean-square displacement and (b) time-dependent exponent $\alpha \left(t\right)$ for the colloidal channel of width $L_Y$, corresponding to $n_l=3,4,5,7,10,12,24$ layers, and (c) MSD in a master plot with all average particle spacings $d=2,3,6$ and (d) time-dependent exponent $\alpha \left(t\right)$ in the corresponding lattice-gas system with $n_l$ layers.

Figure 3

Minimal diffusion exponent ${\alpha }_{\text{min}}$ of the Brownian system as a function of reduced width $L_Y/R$ for different interaction strength $\mathrm{\Gamma }$ and minimal diffusion exponent of the lattice-gas system as a function of the number of layers $n_l$ with different mean particle separation $d$.

Figure 4

(a) Mean-square displacement in the direction orthogonal to the walls for the colloidal channel of width $L_Y$ and (b) MSD for the corresponding lattice-gas model with many layers and a finite length $L_Y=Nd$ with closed ends (only for average particle spacing $d=2$).