Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics

Abstract

Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review E 93, 032702 c (2016) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modi ed, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 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 τ C . To explore the resulting interplay between active and polymeric dynamics, we first generalize 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 τ C and is a simple generalization of the instability known previously without polymer. The second is an elastomeric mode, associated with strain perturbations, which dominates at large τ C and persists even as τ C → ∞. We explore the dynamical states to which these instabilities lead by means of direct numerical simulations. These reveal oscillatory shear-banded states in one dimension and activity-driven turbulence in two dimensions even in the elastomeric limit τ C → ∞. Adding polymer can also have calming effects, increasing the net throughput of spontaneous flow along a channel in a type of drag reduction. The effect of including strong antagonistic coupling between the nematic and polymer is examined numerically, revealing a rich array of spontaneously flowing states.

Activity pulses induce spontaneous flow reversals in viscoelastic environments

“…The indicator function ϕ is only defined to distinguish between the active and passive regions and as such it is fixed, without any dynamical evolution. Activity and viscoelasticity are incorporated by introducing a generic two-phase model of active matter in viscoelastic domains [22,36], which is summarized below.…”

Active nematics

“…The continuum equations have been extended to two-phase 44 and viscoelastic 45 flows of active nematics by adding a concentration field or a polymer conformation tensor as additional order parameters, respectively. These calculations identify oscillatory, shear banded states, and active turbulence even in the limit of high polymer density 45 .…”

Activity pulses induce spontaneous flow reversals in viscoelastic environments

“…The indicator function φ is only defined to distinguish between the active and passive region and as such it is fixed, without any dynamical evolution. Activity and viscoelasticity are incorporated by introducing a generic two-phase model of active matter in viscoelastic domains [22, 36] which is summarised below.…”