Effective surface motion on a reactive cylinder of particles that perform intermittent bulk diffusion

TL;DR

This paper models the effective surface motion of particles intermittently binding and diffusing on a reactive cylinder, revealing regimes of sub- and superdiffusion and stalling effects, with explicit solutions for key quantities.

Contribution

It derives explicit analytical solutions for particle surface displacement and propagator considering bulk diffusion and surface diffusion, including first passage properties.

Findings

Identifies sub- and superdiffusive regimes of particle motion.

Shows effective stalling of diffusion as a plateau in MSD.

Provides explicit formulas for adsorbed particle number and surface propagator.

Abstract

In many biological and small scale technological applications particles may transiently bind to a cylindrical surface. In between two binding events the particles diffuse in the bulk, thus producing an effective translation on the cylinder surface. We here derive the effective motion on the surface, allowing for additional diffusion on the cylinder surface itself. We find explicit solutions for the number of adsorbed particles at one given instant, the effective surface displacement, as well as the surface propagator. In particular sub- and superdiffusive regimes are found, as well as an effective stalling of diffusion visible as a plateau in the mean squared displacement. We also investigate the corresponding first passage and first return problems.