Hydrodynamic inflation of ring polymers under shear

Hydrodynamic interactions can dramatically influence the dynamics of fully flexible, ring-shaped polymers in ways unknown for any other polymer architecture or topology. Tumbling under shear is a common dynamic pattern of motion for all polymer architectures. Here we show the existence of a shear-induced inflation phase exclusive to ring polymers, the onset of which depends on the ring’s contour length. This is accompanied by a strong suppression of tumbling, which resumes at even higher shear rates. The ring swells in the vorticity direction, and the horseshoe regions on the stretched and swollen ring are effectively locked in place relative to its center-of-mass. Furthermore, knots tied onto such rings can serve as additional ‘stabilisation anchors'. Under strong shear, the knotted section remains well-localised while tank-treading from one horseshoe region to the other in sudden bursts. We find knotted polymers of high contour length behave very similarly to unknotted rings of the same contour length.