Confinement without boundaries: Anisotropic diffusion on the surface of a cylinder

TL;DR

This study investigates how the shape of a cylindrical surface influences particle diffusion, revealing anisotropic diffusion behavior caused by geometric confinement and packing arrangements.

Contribution

It introduces the concept of shape-based confinement affecting diffusion, highlighting anisotropic effects on a curved surface without rigid boundaries.

Findings

Diffusion magnitude and directionality depend on cylinder radius.

Anisotropy arises from packing-induced collective motions.

Finite size effects increase circumferential diffusivity.

Abstract

Densely packed systems of thermal particles in curved geometries are frequently encountered in biological and microfluidic systems. In 2D systems, at sufficiently high surface coverage, diffusive motion is widely known to be strongly affected by physical confinement, e.g., by the walls. In this Letter, we explore the effects of confinement by shape, not rigid boundaries, on the diffusion of particles by confining them to the surface of a cylinder. We find that both the magnitude and the directionality of lateral diffusion is strongly influenced by the radius of the cylinder. An anisotropy between diffusion in the longitudinal and circumferential direction of the cylinder develops. We demonstrate that the origin of this effect lies in the fact that screw-like packings of mono- and oligodisperse discs on the surface of a cylinder induce preferential collective motions in the circumferential direction, but also show that even in polydisperse systems lacking such order an intrinsic finite size confinement effect increases diffusivity in the circumferential direction.