Drag reduction in turbulent flows by polymers

Abstract

A hydrodynamic model for turbulence in dilute polymer solution is used to describe drag reduction. It is shown that flexible polymers lead to an enhancement of molecular viscosity at small length scales while at intermediate length scales the effective viscosity is decreased. The onset of drag reduction is predicted to occur only above a minimum value of the polymer concentration, c^m. A direct calculation of the dependence of c_m on the energy input per unit mass, ?, shows that c_m~?^-1. Comparing this result with the scaling theory of de Gennes allows us to conclude that the exponent describing the power-law dependence of polymer deformation on spatial scale is 4/5.