Diffusion
on highly curved surfaces is important to many industrial
and biological processes. Despite the progress made in theoretical
studies, how diffusion is affected by the curvature is unclear due
to experimental challenges. Here, we measured the trajectories of
polystyrene nanoparticles diffusing on highly curved water-silicone
oil interface, where the oil droplet diameter ranges from several
μm to as small as ∼400 nm. To analyze the diffusion coefficients
on curved surface, an analytical solution developed by Castro-Villarreal
containing an infinite series can be used. Through Monte Carlo simulations,
we simplified the Castro-Villarreal equation and defined the conditions
that satisfy corresponding approximations. For the experiments, unexpectedly,
we found that the diffusion slows down significantly when the oil
droplet becomes smaller. Possible reasons were discussed, and a diffusion-induced
droplet deformation and interface fluctuation model is consistent
with the experimental results. This study reveals an unexpected decrease
of particle diffusion on small oil droplet surface and sheds new light
on understanding diffusion on highly curved interface.
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