Dynamics of threads and polymers in turbulence: power-law distributions and synchronization

TL;DR

This paper investigates the statistical behavior of threads and polymers in turbulent flows, revealing universal power-law distributions, the coil-stretch transition, and flow-induced synchronization phenomena.

Contribution

It introduces the universality of power-law exponents for shrinking fluctuations and characterizes the coil-stretch transition and synchronization in turbulent flows.

Findings

Power-law decay of shrinking fluctuations with a universal exponent.

Existence of a coil-stretch transition depending on flow Lyapunov exponent.

Synchronization of end-to-end distances of polymers and threads above the transition.

Abstract

We study the behavior of threads and polymers in a turbulent flow. These objects have finite spatial extension, so the flow along them differs slightly. The corresponding drag forces produce a finite average stretching and the thread is stretched most of the time. Nevertheless, the probability of shrinking fluctuations is significant and is known to decay only as a power-law. We show that the exponent of the power law is a universal number independent of the statistics of the flow. For polymers the coil-stretch transition exists: the flow must have a sufficiently large Lyapunov exponent to overcome the elastic resistance and stretch the polymer from the coiled state it takes otherwise. The probability of shrinking from the stretched state above the transition again obeys a power law but with a non-universal exponent. We show that well above the transition the exponent becomes universal and derive the corresponding expression. Furthermore, we demonstrate synchronization: the end-to-end distances of threads or polymers above the transition are synchronized by the flow and become identical. Thus, the transition from Newtonian to non-Newtonian behavior in dilute polymer solutions can be seen as an ordering transition.