A mathematical model of turbulent drag reduction by high-molecular-weight polymeric additives in a shear flow - Barenblatt, Grigory Isaakovich (Physics of fluids (1994), 2008)
Drag reduction, or the 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), has been known already for more than 60 years. Long ago it was understood that this effect is related to supramolecular structures formed in the flow. Recent experiments by Chu, Shaqfeh, and 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) semiempirical theory of shear flow turbulence. This is the subject of the present letter.