Anomalous lateral diffusion in a viscous membrane surrounded by viscoelastic media

TL;DR

This paper studies how viscoelastic surrounding media cause anomalous lateral diffusion of particles in a viscous membrane, providing theoretical tools for analyzing particle motion in complex fluids.

Contribution

It introduces a generalized frequency-dependent mobility tensor for membranes in viscoelastic media and derives relations linking mean square displacement to solvent properties.

Findings

Mean square displacement shows anomalous diffusion due to viscoelasticity

Derived a relation connecting MSD and solvent modulus

Calculated cross-correlations for two-particle tracking experiments

Abstract

We investigate the lateral dynamics in a purely viscous lipid membrane surrounded by viscoelastic media such as polymeric solutions. We first obtain the generalized frequency-dependent mobility tensor and focus on the case when the solvent is sandwiched by hard walls. Due to the viscoelasticity of the solvent, the mean square displacement of a disk embedded in the membrane exhibits an anomalous diffusion. An useful relation which connects the mean square displacement and the solvent modulus is provided. We also calculate the cross-correlation of the particle displacements which can be applied for two-particle tracking experiments.