Bulk-mediated diffusion on a planar surface: full solution

TL;DR

This paper derives exact equations for a particle's surface diffusion influenced by intermittent bulk excursions, revealing superdiffusive behavior and providing a comprehensive analytical framework for understanding surface-bulk coupled motion.

Contribution

It presents an exact analytical solution for the effective surface diffusion process considering surface-bulk coupling and bulk excursions, including the propagator and long-time dynamics.

Findings

Superdiffusive, Cauchy-type surface behavior identified

Exact propagator derived for surface motion

Long-time dynamics characterized with precise cutoffs

Abstract

We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random walk approach we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover we study the long-time dynamics for the surface motion.