Effect of internal friction on the coil-stretch transition in turbulent flows

TL;DR

This study investigates how internal friction influences the coil-stretch transition of polymers in turbulent flows, revealing that it sharpens the transition without changing the critical Weissenberg number, and explains experimental observations.

Contribution

It introduces a combined simulation and analytical approach to understand the role of internal friction in the coil-stretch transition in turbulence.

Findings

Internal friction does not alter the critical Weissenberg number.

It steepens the probability distribution of polymer extensions.

Provides an explanation for the sharpness observed in experiments.

Abstract

A polymer in a turbulent flow undergoes the coil-stretch transition when the Weissenberg number, i.e. the product of the Lyapunov exponent of the flow and the relaxation time of the polymer, surpasses a critical value. The effect of internal friction on the transition is studied by means of Brownian dynamics simulations of the elastic dumbbell model in a homogeneous and isotropic, incompressible, turbulent flow and analytical calculations for a stochastic velocity gradient. The results are explained by adapting the large deviations theory of Balkovsky et al. [Phys. Rev. Lett., 2000, 84, 4765] to an elastic dumbbell with internal viscosity. In turbulent flows, a distinctive feature of the probability distribution of polymer extensions is its power-law behaviour for extensions greater than the equilibrium length and smaller than the contour length. It is shown that although internal friction does not modify the critical Weissenberg number for the coil-stretch transition, it makes the slope of the probability distribution steeper, thus rendering the transition sharper. Internal friction therefore provides a possible explanation for the steepness of the distribution of polymer extensions observed in experiments at large Weissenberg numbers.