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Drag reduction by microbubbles is a promising engineering method forimproving ship performance. A fundamental theory of the phenomenon is lackinghowever, making actual design quite uphazard. We offer here a theory of dragreduction by microbubbles in the limit of very small bubbles, when the effectof the bubbles is mainly to normalize the density and the viscosity of thecarrier fluid. The theory culminates with a prediction of the degree of dragreduction given the concentration profile of the bubbles. Comparisons withexperiments are discussed and the road ahead is sketched.Comment: 4 pages, 2 figs., included, PRL submitte

Drag Reduction by Microbubbles in Turbulent Flows: The Limit of Minute Bubbles