A mathematical model of turbulent drag reduction by high-molecular-weight polymeric additives in a shear flow

TL;DR

This paper presents a mathematical model explaining how high-molecular-weight polymers reduce turbulence drag by forming supramolecular structures, integrating recent experimental insights with classical turbulence theories.

Contribution

It introduces a novel mathematical model of turbulent drag reduction that incorporates recent experimental observations of supramolecular structures in shear flow.

Findings

Model aligns with experimental data on polymer-induced drag reduction

Quantifies interaction between supramolecular structures and turbulent flow

Provides a theoretical framework for future research in flow control

Abstract

Drag reduction, or, what is the same, mean velocity increase in a turbulent flow at a fixed pressure drop through the addition of tiny amounts (several parts per million) of high molecular weight polymers (Thoms effect), is known already for more than sixty years. Rather long ago it was understood that this effect is related to supramolecular structures formed in the flow. Recent experiments by S. Chu, E.S.G. Shaqfeh and their associates, where the motion of supramolecular structures was directly observed, made it possible to understand and quantify the dynamic interaction of the polymeric structures with the solvent (water) flow. These results lead to the construction of a mathematical model of the Thoms effect, based on the Kolmogorov(1942)-Prandtl(1945) semi-empirical theory of shear flow turbulence.