The onset of drag reduction by dilute polymer additives, and the maximum drag reduction asymptote

Drag reduction due to dilute addition of high polymers has been known for about fifty years. In spite of this long history, many aspects of the problem remain poorly understood. Two of its features for pipe flow are considered here in the context of the elastic theory of de Gennes: the onset of drag reduction and the so-called maximum drag reduction (MDR) asymptote. A cautious conclusion is that a version of the theory agrees qualitatively with existing experiments.