Polymer Stretching Histories Along Stresslines: A Lagrangian Particle-Tracking Approach to Elasto-Inertial Turbulence

The addition of minute quantities of polymers to a solvent can fundamentally alter turbulent flows, leading to chaos in otherwise laminar flows called elastic turbulence (ET) and elasto-inertial turbulence (EIT). This research focuses on EIT, where the most recent advances derive from Eulerian simulations of continuous viscoelastic models. A key result is the organization of the viscoelastic stress in sheets, whose thickness is controlled by the polymer diffusion. These sheets are a key feature of the EIT's self-sustaining cycle through complex interactions between viscoelastic stress, pressure, and velocity fields. In this work, particle-based simulations are used to extract Lagrangian statistics in EIT flows and to explore coupled Eulerian-Lagrangian simulations. Lagrangian statistics study the stretching and relaxation of polymer molecules following the stresslines created by arrowhead traveling waves. Stresslines are computed from the eigenvectors of viscoelastic stress. In the framework of these eigenvectors, the viscoelastic body force in the Navier-Stokes equations is expressed as a function of the local curvature of the sheets and the extension or compression of the polymer stress. The Lagrangian polymer molecules represented as dumbbells enable the investigation of the collective behavior of molecules in ultra-thin sheets of highly stretched polymers.