Drag reduction in turbulent flows by polymers

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, ${\mathit{c}}_{\mathit{m}}$. A direct calculation of the dependence of ${\mathit{c}}_{\mathit{m}}$ on the energy input per unit mass, ɛ, shows that ${\mathit{c}}_{\mathit{m}}$∼${\mathrm{\varepsilon }}^{\mathrm{-}1}$. 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.