Turbulent drag reduction by flexible and rodlike polymers: Crossover effects at small concentrations

Abstract

Drag reduction by polymers is bounded between two universal asymptotes, the von Kármán log law of the law and the maximum drag reduction (MDR) asymptote. It is theoretically understood why the MDR asymptote is universal, independent of whether the polymers are flexible or rodlike. The crossover behavior from the Newtonian von Kármán log law to the MDR is, however, not universal, showing different characteristics for flexible and rodlike polymers. In this paper we provide a theory for this crossover phenomenology.