Optimal shapes of artificial bead-spring micro-carriers at low Reynolds numbers

Abstract

Bead-based micro-swimmers are promising systems for payload delivery on the micro-scale. However, the principles underlying their optimal design are not yet fully understood. Here we study a simple device consisting of three arbitrarily-shaped beads connected by two springs. We analytically determine the most favorable kinematic parameters for sinusoidal driving, and show how the swimmer changes from being a pusher to a puller. For cargo carrying ellipsoidal beads, we perform geometric optimization under the constraint of a constant total volume or surface area, with the aim of maximizing the device transport velocity and efficiency. Interestingly, we identify two major transport regimes, which arise from the competition between the elastic and the drag forces faced by the swimmer. We construct a phase diagram that indicates when the fastest swimming emerges because of minimized drag, and when due to heightened interactions among the beads.