Optimizing the stroke of Purcell's rotator, a low Reynolds number swimmer

Abstract

Purcell's rotator is a theoretical low Reynolds number swimmer that can act as a model of more complex natural microorganisms, such as E.coli. Because of the low Reynolds number environment, the swimmer has approximately no inertia and it's motion is dominated by viscous forces. The version of Purcell's rotator examined in this paper is two dimensional and has three rigid links which rotate about the center of the body. It is able to propel itself by moving these links in a repetitive, nonreciprocal stroke motion. Using a mathematical model of the swimmer, two strokes were found, one which optimizes its rotation of the swimmer and one which optimizes its translation.