Tumbling of Polymers in a Random Flow with Mean Shear

TL;DR

This paper investigates how polymers tumble in chaotic flows with mean shear, analyzing their orientation and tumbling time distributions, revealing algebraic and exponential tail behaviors influenced by flow dynamics.

Contribution

It provides a detailed statistical description of polymer tumbling in shear flows, including orientation PDFs and tumbling time distributions, highlighting new algebraic and exponential tail characteristics.

Findings

Orientation PDF peaks around shear direction

Tumbling time PDF has a maximum near inverse Lyapunov exponent

Large tumbling times exhibit exponential tail behavior

Abstract

A polymer placed in chaotic flow with large mean shear tumbles, making a-periodic flips. We describe the statistics of angular orientation, as well as of tumbling time (separating two subsequent flips) of polymers in this flow. The probability distribution function (PDF) of the polymer orientation is peaked around a shear-preferred direction. The tails of this angular PDF are algebraic. The PDF of the tumbling time, $\tau$, has a maximum at the value estimated as inverse Lyapunov exponent of the flow. This PDF shows an exponential tail for large $\tau$ and a small-$\tau$ tail determined by the simultaneous statistics of velocity PDF.