Purely hydrodynamic ordering of rotating disks at a finite Reynolds number

TL;DR

This study investigates how hydrodynamic interactions among rotating disks in a viscous fluid lead to diverse self-organized phases, revealing fundamental nonequilibrium physical mechanisms at finite Reynolds numbers.

Contribution

It demonstrates that many-body hydrodynamic interactions cause rich phase behaviors in a zero-temperature system of rotating disks, highlighting the role of off-axis and nonlinear effects.

Findings

Identification of multiple distinct phases including fluid, cluster, hexatic, glassy, and phase demixing.

Hydrodynamic interactions induce complex self-organization without thermal noise.

Finite propagation time of momentum diffusion influences phase behavior.

Abstract

Self-organization of moving objects in hydrodynamic environments has recently attracted considerable attention in connection to natural phenomena and living systems. However, the underlying physical mechanism is much less clear due to the intrinsically nonequilibrium nature, compared with self-organization of thermal systems. Hydrodynamic interactions are believed to play a crucial role in such phenomena. To elucidate the fundamental physical nature of many-body hydrodynamic interactions at a finite Reynolds number, here we study a system of co-rotating hard disks in a two-dimensional viscous fluid at zero temperature. Despite the absence of thermal noise, this system exhibits rich phase behaviours, including a fluid state with diffusive dynamics, a cluster state, a hexatic state, a glassy state, a plastic crystal state and phase demixing.We reveal that these behaviours are induced by the off-axis and many-body nature of nonlinear hydrodynamic interactions and the finite time required for propagating the interactions by momentum diffusion.