Hindered Diffusion near Fluid-Solid Interfaces: Comparison of Molecular Dynamics to Continuum Hydrodynamics

Studying the near-wall hindered diffusion of a particle suspended in a fluid is critical for understanding other more complex, confined systems. We provide a review of the previous experimental and simulation efforts trying to verify the classic calculations in hydrodynamics by Brenner and Faxén. We discuss some of the challenges of extracting the hindered diffusion constants from the mean squared displacements as often done in the literature. We demonstrate that the use of total force autocorrelation functions is a reliable alternative for calculating the diffusion constants without similar challenges for our molecular dynamics (MD) simulations. We find that the change in the diffusion constant in the perpendicular direction calculated in MD is roughly consistent with the hydrodynamic result by Brenner provided that they are normalized by the diffusion constant at the center between the two walls. However, the discrepancy grows large when the colloidal particle is very close to the wall where molecular details matter. Even though the agreement can be considerably improved when the attractions between the particles are made stronger to reduce slip to better fulfill the no-slip condition in MD, we report that there is an underlying difference between the range of the wall interactions with the colloidal particle predicted by MD and hydrodynamics.