Colloquium: Theory of drag reduction by polymers in wall-bounded turbulence

The flow of fluids in channels, pipes, or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases manyfold when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a "skin" or a "bulk" effect. In this Colloquium the phenomenology of drag reduction by polymers is summarized, stressing both its universal and nonuniversal aspects, and a recent theory is reviewed that provides a quantitative explanation of all the known phenomenology. Both flexible and rodlike polymers are treated, explaining the existence of universal properties like the maximum drag reduction asymptote, as well as nonuniversal crossover phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally other agents for drag reduction are discussed with a stress on the important example of bubbles