Local Diffusion Coefficients in Spherically Symmetric Systems Using the Smoluchowski Equation and Molecular Dynamics

Interfacial systems with spherical symmetry are ubiquitous in nature and the accurate estimation of local self-diffusion coefficients in these systems is crucial to our understanding of processes such as the partitioning of atmospheric species to aerosol droplets and water transport across cell membranes. In this work, we extend a method originally developed to estimate local diffusion coefficients in systems with flat interfaces to the spherically symmetric case. Specifically, we derive an analytical solution to the linearized Smoluchowski equation in spherical coordinates and utilize molecular dynamics simulations to obtain a parameter required to estimate the local self-diffusion coefficient from the solution. We demonstrate that the derived solution is indeed accurate by comparing it to the numerical solution and also validate that the assumptions under which our solution was derived are not too stringent. We further validate our solution by computing the local diffusion coefficients at different radial positions in bulk SPC/E water and comparing the results to the overall diffusion coefficient obtained from Einstein's mean squared displacement method. Finally, we apply the method to an SPC/E water droplet suspended in its own vapor. We observe that the diffusion coefficient increases from the center of the droplet toward the interface, a result in line with previous results reported for flat interfaces.