Theory of anomalous collective diffusion in colloidal monolayers on a spherical interface

TL;DR

This paper explores how the curvature of a spherical droplet influences the anomalous collective diffusion of colloidal monolayers, revealing that while timescales remain similar to flat surfaces, spatial distribution is affected by the droplet's radius.

Contribution

It extends the understanding of anomalous diffusion from flat to curved interfaces, analyzing the effects of spherical curvature on diffusion dynamics.

Findings

Characteristic times retain anomalous scaling on spherical interfaces.

Spatial distribution depends on the droplet's radius and curvature.

Open question on which curvature feature dominates in general cases.

Abstract

A planar colloidal monolayer exhibits anomalous collective diffusion due to the hydrodynamic interactions. We investigate how this behavior is affected by the curvature of the monolayer when it resides on the interface of a spherical droplet. It is found that the characteristic times of the dynamics still exhibit the same anomalous scaling as in the planar case. The spatial distribution, however, shows a difference due to the relevance of the radius of the droplet. Since for the droplet this is both a global magnitude, i.e., pertaining the spatial extent of the spherical surface, and a local one, i.e., the radius of curvature, the question remains open as to which of these two features actually dominates in the case of a generically curved interface.