Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics

Hemingway, E.J.; Cates, M.E.; Fielding, S.M.

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 τC. 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 τC 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 τC and persists even as τC→∞. 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 τC→∞. 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.

Citation

Hemingway, E., Cates, M., & Fielding, S. (2016). Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics. Physical Review E, 93(3), Article 032702. https://doi.org/10.1103/physreve.93.032702

• Journal Article Type: Article
• Acceptance Date: Feb 24, 2016
• Online Publication Date: Mar 15, 2016
• Publication Date: Mar 15, 2016
• Deposit Date: Mar 29, 2016
• Publicly Available Date: Mar 29, 2016
• Journal: Physical review . E, Statistical, nonlinear, and soft matter physics
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 93
• Issue: 3
• Article Number: 032702
• DOI: https://doi.org/10.1103/physreve.93.032702
• Public URL: https://durham-repository.worktribe.com/output/1388169