Frequency-dependent Hydrodynamic Interaction Between Two Solid Spheres

TL;DR

This paper investigates how the compressibility of a fluid influences the frequency-dependent hydrodynamic interactions between two solid spheres, combining theoretical analysis with molecular dynamics simulations.

Contribution

It advances understanding by analyzing the time-dependent hydrodynamic interactions in compressible fluids using the linearized Navier-Stokes equation, validated against simulations.

Findings

Fluid compressibility significantly affects frequency-dependent interactions.

Simulation results align well with theoretical predictions.

Theory enables more accurate non-Markovian modeling of hydrodynamics.

Abstract

Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions in a compressible fluid on the basis of the linearized Navier-Stokes equation. The theoretical results show that the compressibility of the fluid has a significant impact on frequency-dependent pair interactions. The predictions of the hydrodynamic theory are compared to molecular dynamics simulations of two solid spheres in a Lennard-Jones fluid. For this system we reconstruct memory functions by extending the inverse Volterra technique. The simulation data agree very well with the theory, therefore, the theory can be used to implement dynamically consistent hydrodynamic interactions in the increasingly popular field of non-Markovian modeling.