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

作者：Bleibel Johannes^*; Dominguez Alvaro^*; Oettel Martin^*

来源：Journal of Physics: Condensed Matter , 2016, 28(24): 244021.

DOI：10.1088/0953-8984/28/24/244021

• colloids
• hydrodynamic interactions
• capillary interactions
• DDFT
• generalized diffusion
• long ranged 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. In these cases, D(k) shows characteristic singularities as k -> 0. The consequences of these singularities are studied by means of analytical perturbation theory, numerical solution of DDFT and simulations for an explicit example: the capillary collapse of a finite, disk-like distribution of particles. There is in general a good agreement between DDFT and simulations if the initial density distributions for the theoretical prediction correspond to the actual initial configurations of simulations, rather than to an average over them. Otherwise, discrepancies arise that are discussed in detail.

• 出版日期2016-6-22