Modeling active nematics via the nematic locking principle

TL;DR

This paper introduces the nematic locking principle to model active nematics, deriving a transport equation that enforces local rotational constraints and modifying existing models to better match experimental behaviors.

Contribution

It proposes the nematic locking principle as a fundamental modeling approach and modifies the Beris-Edwards model to enforce this principle in active nematic systems.

Findings

Nematic locking holds in most of the material, except near defects.

Modified model enforces nematic locking, reducing fracturing.

Simulations align with experimental observations of active nematics.

Abstract

Active nematic systems consist of rod-like internally driven subunits that interact with one another to form large-scale coherent flows. They are important examples of far-from-equilibrium fluids, which exhibit a wealth of nonlinear behavior. This includes active turbulence, in which topological defects braid around one another in a chaotic fashion. One of the most studied examples of active nematics is a dense two-dimensional layer of microtubules, crosslinked by kinesin molecular motors that inject extensile deformations into the fluid. Though numerous studies have modeled microtubule-based active nematics, no consensus has emerged on how to fully capture the features of the experimental system. To better understand the foundations for modeling this system, we propose a fundamental principle we call the nematic locking principle: individual microtubules cannot rotate without all neighboring microtubules also rotating. Physically, this is justified by the high density of the microtubules, their elongated nature, and their corresponding steric interactions. We assert that nematic locking holds throughout the majority of the material but breaks down in the neighborhood of topological defects and other regions of low density. We derive the most general nematic transport equation consistent with this principle and also derive the most general term that violates it. We examine the standard Beris-Edwards approach used to model this system and show that it violates nematic locking throughout the majority of the material. We then propose a modification to the Beris-Edwards model that enforces nematic locking nearly everywhere. This modification shuts off fracturing except in regions where the order parameter is reduced. The resulting simulations show strong nematic locking throughout the bulk of the material, consistent with experimental observation.