[0805.0110] A mathematical model of turbulent drag reduction by high-molecular-weight polymeric additives in a shear flow

by Barenblatt himself

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.

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