Turbulent stretching of dumbbells with hydrodynamic interactions: an analytical study

TL;DR

This paper analytically investigates how hydrodynamic interactions influence the stretching behavior of elastic dumbbells in turbulent flows, revealing that HI enhances stretching of stiff dumbbells and affects coil-stretch transition.

Contribution

It provides an analytical solution for the probability distribution of dumbbell extension considering hydrodynamic interactions in turbulent flow, and compares different HI approximations.

Findings

Hydrodynamic interactions increase stretching of stiff dumbbells.

HI results in a less-pronounced coil-stretch transition.

Analytical results agree with Brownian dynamics simulations.

Abstract

We study the stretching of an elastic dumbbell in a turbulent flow, with the aim of understanding and quantifying the effect of hydrodynamic interactions (HI) between the beads of the dumbbell. Adopting the Batchelor-Kraichnan model for the flow, we derive a Fokker-Planck equation and solve it analytically to obtain the probability distribution of the dumbbell's extension. Using different formulations of the HI tensor, we find that HI preferentially enhances the stretching of stiff dumbbells, i.e., those with a small Weissenberg number. We also evaluate the averaging approximations commonly used to simplify the description of HI effects; the consistently-averaged approximation shows that HI result in a less-pronounced coil-stretch transition in chaotic flows. Finally, we confirm the relevance of our analytical results by a comparison with Brownian dynamics simulations of dumbbells transported in a direct numerical simulation of homogeneous isotropic turbulence.