Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics

TL;DR

This paper investigates the linear stability and nonlinear dynamics of active viscoelastic matter, revealing two distinct instability modes and novel flow states through analytical and numerical methods.

Contribution

It extends linear stability analysis to include polymer dynamics in active nematic fluids, identifying new instability modes and flow behaviors.

Findings

Identified viscous and elastomeric instability modes.

Discovered oscillatory shear-banded states and activity-driven turbulence.

Showed polymer can enhance flow throughput and induce complex flow states.

Abstract

We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid-crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time $\tau_C$. To explore the resulting interplay between active and polymeric dynamics, we first generalise a linear stability analysis (from earlier studies without polymer) to derive criteria for the onset of spontaneous heterogeneous flows (strain rate) and/or deformations (strain). We find two modes of instability. The first is a viscous mode, associated with strain rate perturbations. It dominates for relatively small values of $\tau_C$ and is a simple generalisation of the instability known previously without polymer. The second is an elastomeric mode, associated with strain perturbations, which dominates at large $\tau_C$ and persists even as $\tau_C\to\infty$. We explore the novel dynamical states to which these instabilities lead by means of direct numerical simulations. These reveal oscillatory shear-banded states in 1D, and activity-driven turbulence in 2D even in the elastomeric limit $\tau_C\to\infty$. Adding polymer can also have calming effects, increasing the net throughput of spontaneous flow along a channel in a new type of "drag-reduction". Finally the effect of including strong, antagonistic coupling between nematic and polymer is examined numerically, revealing a rich array of spontaneously flowing states.