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

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 to 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.

Figure 1

Definition of the angle $\alpha$ used in Eq. (19).

Figure 2

Plot of the Green's function, Eq. (19), at different times when the hydrodynamic interactions are considered (thick lines) or not (dashed lines). The vertical axis is in logarithmic scale.