Hydrodynamic theory of flocking at a solid-liquid interface: long range order and giant number fluctuations

TL;DR

This paper develops a hydrodynamic theory for flocking behavior at solid-liquid interfaces, revealing stable long-range order, giant number fluctuations, and anisotropic diffusion of passive particles.

Contribution

It introduces a hydrodynamic framework for active particles at interfaces, demonstrating stability conditions, long-range order, and fluctuation behaviors not previously characterized.

Findings

Systems exhibit stable long-range orientational order.

Giant number fluctuations grow as the 3/4 power of mean number.

Passive particle diffusion is anomalously rapid parallel to the interface.

Abstract

We construct the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface. The polar order parameter and concentration of a collection of "active" (self-propelled) particles at a planar interface between a passive, isotropic bulk fluid and a solid surface are dynamically coupled to the bulk fluid. We find that such systems are stable, and have long-range orientational order, over a wide range of parameters. When stable, these systems exhibit "giant number fluctuations", i.e., large fluctuations of the number of active particles in a fixed large area. Specifically, these number fluctuations grow as the $3/4$th power of the mean number within the area. Stable systems also exhibit anomalously rapid diffusion of tagged particles suspended in the passive fluid along any directions in a plane parallel to the solid-liquid interface, whereas the diffusivity along the direction perpendicular to the plane is non-anomalous. In other parameter regimes, the system becomes unstable.