Brownian motion near a liquid-like membrane

TL;DR

This paper investigates how a tracer molecule's diffusion near a fluid membrane is affected by membrane fluctuations and hydrodynamic interactions, revealing memory effects and a transition from bulk to surface diffusion influenced by membrane elasticity.

Contribution

It introduces a detailed analysis of the interplay between particle position, membrane fluctuations, and hydrodynamics, highlighting the crossover in diffusion modes based on membrane properties.

Findings

Hydrodynamic interactions induce memory effects in diffusion.

Diffusion mode transitions depend on membrane elasticity.

Memory effects alter the particle's diffusive behavior near membranes.

Abstract

The dynamics of a tracer molecule near a fluid membrane is investigated, with particular emphasis given to the interplay between the instantaneous position of the particle and membrane fluctuations. It is found that hydrodynamic interactions creates memory effects in the diffusion process. The random motion of the particle is then shown to cross over from a ``bulk'' to a ``surface'' diffusive mode, in a way that crucially depends on the elastic properties of the interface.