Polymer-induced drag reduction in turbulent flows

Abstract

We present a hydrodynamic model for polymer-induced drag reduction in turbulent flows. Our theory uses the stirred fluid model for isotropic turbulence. The effect of a polymer additive on the velocity field of the fluid is taken into account to lowest order in the concentration of the solute. The resulting theory predicts that the presence of the polymer molecules leads to the usual enhancement of viscosity at small length scales, while at intermediate length scales the effective viscosity is decreased, provided the concentration of the polymer exceeds a minimum value. We also suggest the existence of a polymer turbulent flow induced length scale l^p. An explicit calculation of l_p is in excellent agreement with recent experiments. The theory also suggests that the phenomenon of drag reduction can exist in the presence of nonpolymer additives, provided that cRe², with c being the concentration of the solute and Re the Reynold's number, is large enough.