Statistics of Polymer Extension in a Random Flow with Mean Shear

TL;DR

This paper analyzes how the extension statistics of a finite polymer in a chaotic shear flow vary with the Weissenberg number, identifying four distinct regimes and explaining the underlying polymer dynamics.

Contribution

It introduces a detailed regime classification of polymer extension behavior in shear flows based on Weissenberg number and explains the dynamics in each regime.

Findings

Four regimes of polymer extension identified based on Wi

Extension statistics change significantly across regimes

Dynamics explained in terms of polymer behavior in flow

Abstract

Considering the dynamics of a polymer with finite extensibility placed in a chaotic flow with large mean shear, we explain how the statistics of polymer extension changes with Weissenberg number, ${\it Wi}$, defined as the product of the polymer relaxation time and the Lyapunov exponent of the flow. Four regimes, of the ${\it Wi}$ number, are identified. One below the coil-stretched transition and three above the coil-stretched transition. Specific emphasis is given to explaining these regimes in terms of the polymer dynamics.