Propagation of hydrodynamic interactions between particles in a compressible fluid

TL;DR

This paper investigates how hydrodynamic interactions between particles evolve over time in compressible fluids, highlighting the roles of viscous diffusion and sound propagation through direct numerical simulations.

Contribution

It introduces the concept of an interactive compressibility factor to characterize the effects of finite sound speed on hydrodynamic interactions.

Findings

In incompressible fluids, interactions propagate instantaneously via sound.

In compressible fluids, sound speed influences the temporal evolution of interactions.

The study quantifies the impact of compressibility on hydrodynamic interaction dynamics.

Abstract

Hydrodynamic interactions are transmitted by viscous diffusion and sound propagation: the temporal evolution of hydrodynamic interactions by both mechanisms is studied by direct numerical simulation in this paper. The hydrodynamic interactions for a system of two particles in a fluid are estimated by the velocity correlation of the particles. In an incompressible fluid, hydrodynamic interactions propagate instantaneously at the infinite speed of sound, followed by the temporal evolution of viscous diffusion. On the other hand, in a compressible fluid, sound propagates at a finite speed, which affects the temporal evolution of the hydrodynamic interactions by the order of magnitude relation between the time scales of viscous diffusion and sound propagation. The hydrodynamic interactions are characterized by introducing the ratio of these time scales as an interactive compressibility factor.