Applied Math Seminar
Spring Quarter 2008
3:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-D (note room change!)

Friday, May 9, 2008

Grigory Barenblatt
Mathematics
University of California at Berkeley

A Mathematical Model of Turbulent Drag Reduction by High-Molecular Polymeric Additives in a Shear Flow


Abstract:

Drag reduction, or, what is the same, mean velocity increase at a fixed pressure drop in a turbulent flow by adding 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 supra-molecular structures formed in the flow. Recent experiments by S.Chu, E.Shaqfeh and their associates allowed to understand and quantify the dynamic interaction of the polymeric structures with the solvent ( water ) flow . These results allow to construct a mathematical model of Thoms effect, based on Kolmogorov (1942)--Prandtl( 1945) semi-empirical theory of shear flow turbulence.