Investigating Diffusing on Highly Curved Water–Oil Interface Using Three-Dimensional Single Particle Tracking

Abstract

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.