Connecting the Hydrodynamics of Polymeric Fluids and Active Nematics

Abstract

We establish a correspondence between the continuum descriptions of polymer solutions and active nematics, two seemingly disparate but well-studied complex fluids. Through a mapping of the governing equations, we demonstrate that polymeric fluids can be interpreted as deformable, contractile, high-temperature active nematics, with an effective activity controlled by polymer extension. Using numerical simulations under Kolmogorov flow, we construct a phase diagram connecting the nematic and polymer limits, highlighting how their one- and two-dimensional instabilities depend on deformability. This encompasses both a flow-suppressed regime, in which active stresses oppose the imposed flow, and a transverse instability that generates secondary flows and leads towards elastic turbulence. The transverse instability is facilitated by spatial gradients in activity, which arise naturally in extensible polymers through variations in chain extension. We further show that the transition into the well-known traveling arrowhead structures in elastic turbulence is marked by the emergence of charge $\pm 1/2$ topological defects in the polymer director field, indicating emergent nematic ordering of stretched polymers. Our results establish a unified framework connecting polymer and active matter hydrodynamics, with implications for low-Reynolds-number turbulence, active polymer systems, and the mechanics of deformable living matter.