Frequency-dependent hydrodynamic interactions: theory and simulations
Gerhard Jung (Institut für Physik)

The dynamics of fluids are subject of extensive research since over 300 years. In the second book of the ”Principa” Newton investigates the dynamics of viscous fluids to disprove the Cartesian idea that the planetary orbits are created by fluid vortices. Since then this problem has drawn the attention of many great physicists and mathematicians. However, there are still many fundamental questions in the field of fluid dynamics like for example the understanding of hydrodynamic interactions between two particles submerged in a fluid. The first and most basic analytic derivation was published by Oseen describing the interaction between two point particles in a steady-state Stokes flow. Based on work by Ardekani et al. we extended this approach by considering finite-sized particles in an unsteady compressible flow, described by the linearized Navier-Stokes equations. This theoretical extension enables us to compare results from hydrodynamic theory to molecular dynamics simulations of nanocolloids in a Lennard-Jones fluid. We show that the simulation data agree qualitatively and quantitatively with our theoretical findings. The analytic results can therefore be used to include dynamically consistent hydrodynamic interactions into non-Markovian coarse-grained models.