A dynamic DFT approach to generalized diffusion equations in a system with long-ranged and hydrodynamic interactions.

We build on an existing approximation scheme to the Smoluchowski equation in order to derive a dynamic density functional theory (DDFT) including two-body hydrodynamic interactions. A generalized diffusion equation and a wavenumber-dependent diffusion coefficient D(k) are derived by linearization in the density fluctuations. The result is applied to a colloidal monolayer at a fluid interface, having bulk-like hydrodynamic interactions and/or interacting via long-ranged capillary forces.

3D hydrodynamic interactions lead to divergences in 2D diffusion.

We investigate the influence of 3D hydrodynamic interactions on confined colloidal suspensions, where only the colloids are restricted to one or two dimensions. In the absence of static interactions among the colloids, i.e.