Active Polar Ring Polymer in Shear Flow -- An Analytical Study

TL;DR

This study provides an analytical understanding of the conformational and dynamical behavior of active polar ring polymers under shear flow, revealing activity-independent stationary states but activity-influenced dynamics such as tank-treading and tumbling.

Contribution

It introduces an analytical model for active polar ring polymers under shear flow, highlighting how activity influences dynamical regimes without affecting stationary conformations.

Findings

Stationary states are activity-independent and match passive rings.

Tank-treading motion occurs at high relaxation times and frequencies.

Tumbling frequency shows two shear-rate regimes with activity-dependent behavior.

Abstract

We theoretically study the conformational and dynamical properties of semiflexible active polar ring polymers under linear shear flow. A ring is described as a continuous Gaussian polymer with a tangential active force of a constant density along its contour. The linear but non-Hermitian equation of motion is solved using an eigenfunction expansion, which yields activity-independent, but shear-rate-dependent, relaxation times and activity-dependent frequencies. As a consequence, the ring's stationary-state properties are independent of activity, and its conformations as well as rheological properties are equal to those of a passive ring under shear. The presence of characteristic time scales by the relaxation and the frequency gives rise to a particular dynamical behavior. A tank-treading-like motion emerges for large relaxation times and high frequencies, specifically for stiffer rings, governed by the activity-dependent frequencies. In the case of very flexible polymers, the relaxation behavior dominates over tank-treading. Shear strongly affects the crossover from a tank-treading to a relaxation-time dominated dynamics and suppresses tank-treading. This is reflected in the tumbling frequency, which exhibits two shear-rate dependent regimes, with an activity-dependent plateau at low shear rates followed by a power-law regime with increasing tumbling frequency for large shear rates.