On the maximum drag reduction due to added polymers in Poiseuille flow

摘要

The addition of elastic polymers to turbulent liquids is known to produce significant drag reduction. In this study, we prove that the drag in pipe and channel flows of an unforced laminar fluid constitutes a lower bound for the drag of a fluid containing dilute elastic polymers. Further, the addition of elastic polymers to laminar fluids invariably increases drag. This proof does not rely on the adoption of a particular constitutive equation for the polymer force, and would also be applicable to other similar methods of drag reduction, which are also achieved by the addition of certain particles to a flow. Examples of such methods include the addition of surfactants to a flowing liquid and the presence of sand particles in sandstorms and water droplets in cyclones.