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

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