Bulk-mediated surface diffusion on a cylinder: propagators and crossovers

TL;DR

This paper analyzes how particles diffusing in the bulk intermittently bind to a cylindrical surface, revealing regimes of superdiffusion, saturation, and eventual normal diffusion, with implications for real systems.

Contribution

It provides an exact theoretical framework for understanding bulk-mediated surface diffusion on cylinders, including regimes and crossover behaviors.

Findings

Identifies superdiffusive transient regime

Discovers saturation regime due to cylindrical geometry

Describes crossover to normal diffusion in finite systems

Abstract

We consider the effective surface motion of a particle that freely diffuses in the bulk and intermittently binds to that surface. From an exact approach we derive various regimes of the effective surface motion characterized by physical rates for binding/unbinding and the bulk diffusivity. We obtain a transient regime of superdiffusion and, in particular, a saturation regime characteristic for the cylindrical geometry. This saturation, however, in a finite system is not terminal but eventually turns over to normal surface diffusion. The first passage behavior of particles to the cylinder surface is derived. Consequences for actual systems are discussed.