Single-file diffusion of macroscopic charged particles

In this paper, we study a macroscopic system of electrically interacting metallic beads organized as a sequence along an annulus. A random mechanical shaking mimics the thermal excitation. We exhibit non-Fickian diffusion (single-file diffusion) at large time. We measure the mobility of the particles and compare it to theoretical expectations. We show that our system cannot be accurately described by theories assuming only hard-sphere interactions. Its behavior is qualitatively described by a theory extended to more realistic potentials [M. Kollmann, Phys. Rev. Lett. 90, 180602 (2003)]. A correct quantitative agreement is shown and we interpret the discrepancies by the violation of the assumption of overdamped dynamics, which is a key point in the theory. We recast previous results on colloids with known interaction potentials and compare them quantitatively to the theory. Focusing on the transition between ordinary and single-file diffusions, we exhibit a dimensionless crossover time that is of order 1 both for colloids and our system, although the time and length scales differ by several orders of magnitude.