Active nematic response to a deformable body or boundary: elastic deformations and anchoring-induced flow

TL;DR

This paper investigates how active nematic fluids interact with deformable bodies, deriving exact solutions for flow, stresses, and deformations, revealing differences from passive elastic responses and proposing new measurement methods for active stresses.

Contribution

It provides exact analytical expressions for the flow, stresses, and deformations of elastic bodies in active nematic fluids, highlighting qualitative differences from passive elastic behavior.

Findings

Active stresses can induce large-scale flows and deformations.

Elastic and active stress-driven deformations differ qualitatively.

The results suggest new ways to measure mechanical stresses in active environments.

Abstract

A body immersed in a nematic liquid crystal disturbs the fluid's preferred molecular configuration and increases its stored elastic energy. In an active nematic, the fluid components also generate a stress in the bulk fluid. By introducing either an immersed body or boundary, a large scale flow can be triggered due to anchoring boundary conditions alone -- a global pressure built by active stresses at equilibrium is instantly released everywhere. The fluid then imposes viscous, elastic, and active stresses on such surfaces which, if compliant, may result in a surface deformation. We study the deformations and stresses of a linearly elastic body placed in an active nematic in two dimensions. Using complex variables techniques, exact expressions for the fluid flow, director field, surface tractions, and body deformation are derived. Qualitative differences between elastic and active stress-driven deformations are identified, depending on an active Ericksen number, anchoring conditions, and body material properties, thereby suggesting a new method for measuring mechanical stresses in active anisotropic environments. Flow profiles, external confinement, and anchoring-induced stirring are also addressed.