Hydrodynamics of Active Defects: From Order to Chaos to Defect Ordering

Abstract

Topological defects play a prominent role in the physics of two-dimensional materials. When driven out of equilibrium in active nematics, disclinations can acquire spontaneous self-propulsion and drive self-sustained flows upon proliferation. Here, we construct a general hydrodynamic theory for a two-dimensional active nematic interrupted by a large number of such defects. Our equations describe the flows and spatiotemporal defect chaos characterizing active turbulence, even close to the defect-unbinding transition. At high activity, nonequilibrium torques combined with many-body screening cause the active disclinations to spontaneously break rotational symmetry, forming a collectively moving defect-ordered polar liquid. By recognizing defects as the relevant quasiparticle excitations, we construct a comprehensive phase diagram for two-dimensional active nematics. Using our hydrodynamic approach, we additionally show that activity gradients can act like “electric fields,” driving the sorting of topological charge. This result demonstrates the versatility of our continuum model and its relevance for quantifying the use of spatially inhomogeneous activity for controlling active flows and for the fabrication of active devices with targeted transport capabilities.

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Plain Language Summary

Active nematics are ordered fluids of self-driven elongated particles that combine the collective behavior of active materials with the rich flow properties of liquid crystals. Active nematics spontaneously exhibit seemingly chaotic flows dubbed “active turbulence,” with swirling motions accompanied by regions of dramatic distortion of the liquid crystalline order known as topological defects. Such defects appear ubiquitously in equilibrium systems when ordered structures are frustrated by geometry or external forces. In active nematics, however, defects become dynamical entities, driving flows upon proliferation. Here, we present a new theory for how these defects move.

By viewing the active nematic as a collection of swarming and interacting active defects, we develop a theoretical framework that describes active turbulence and predicts new states of hierarchically organized active matter, where the defects themselves line up into a flock. By exploiting an analogy with electrostatics, we additionally show how activity gradients can segregate defects, analogous to an electric field separating electric charges.

Our theoretical model provides a versatile framework for investigating the use of spatially modulated activity to pattern and direct active flows, paving the way to the design of active devices with targeted transport functionalities.