Maximally mixing active nematics

TL;DR

This paper demonstrates that active nematic systems can exhibit stable, maximally mixing periodic motions under confinement, with potential for enhanced chaotic mixing surpassing chaotic defect motion, and discusses how to stabilize these states for experimental observation.

Contribution

It reveals that confined active nematics can produce stable, maximally mixing periodic flows, and introduces methods to stabilize these states for experimental realization.

Findings

Periodic motion maximizes topological entropy.

Stable periodic orbits can be stabilized and tiled.

Maximal mixing exceeds that of chaotic defect motion.

Abstract

Active nematics are an important new paradigm in soft condensed matter systems. They consist of rod-like components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this Letter shows that this system can exhibit stable periodic motion when sufficiently confined to a square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) ``topological entropy'' -- the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.