Turbulence of Dilute Polymer Solution

TL;DR

This paper develops a theory describing how dilute long-chain polymers affect the energy cascade in turbulent flows, introducing a new elastic length scale and validating it with experimental data.

Contribution

The paper introduces a refined elastic length scale, $r_ ext{ε}$, to describe polymer effects on turbulence energy cascade, supported by experimental validation.

Findings

Excellent agreement between theory and experiments.

Polymer elasticity modifies the inertial range of turbulence.

New elastic length scale accurately predicts turbulence behavior with polymers.

Abstract

In fully developed three dimensional fluid turbulence the fluctuating energy is supplied at large scales, cascades through intermediate scales, and dissipates at small scales. It is the hallmark of turbulence that for intermediate scales, in the so called inertial range, the average energy flux is constant and independent of viscosity [1-3]. One very important question is how this range is altered, when an additional agent that can also transport energy is added to the fluid. Long-chain polymers dissolved at very small concentrations in the fluid are such an agent [4,5]. Based on prior work by de Gennes and Tabor [6,7] we introduce a theory that balances the energy flux through the turbulent cascade with that of the energy flux into the elastic degrees of freedom of the dilute long-chain polymer solution. We propose a refined elastic length scale, $r_\varepsilon$, which describes the effect of polymer elasticity on the turbulence energy cascade. Our experimental results agree excellently with this new energy flux balance theory.