Active polar ring polymer in shear flow-An analytical study

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 semiflexible 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 and rheological properties are equal to those of a passive ring under shear. The presence of characteristic time scales by relaxation and the activity-dependent frequencies give rise to a particular dynamical behavior. A tank-treading-like motion emerges for long relaxation times and high activities, specifically for stiff rings. In the case of very flexible polymers, the relaxation behavior dominates over activity contributions suppressing tank-treading. Shear strongly affects the crossover from a tank-treading to a relaxation-dominated dynamics, and the ring polymer exhibits tumbling motion at high shear rates. This is reflected in the tumbling frequency, which displays 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 high shear rates.