Micro-swimming without flagella: Propulsion by internal structures

Since a first proof-of-concept for an autonomous micro-swimming device appeared in 2005 a strong interest on the subject ensued. The most common configuration consists of a cell driven by an external propeller, bio-inspired by bacteria such as E.coli. It is natural to investigate whether micro-robots powered by internal mechanisms could be competitive. We compute the translational and rotational velocity of a spheroid that produces a helical wave on its surface, as has been suggested for the rod-shaped cyanobacterium Synechococcus. This organisms swims up to ten body lengths per second without external flagella. For the mathematical analysis we employ the tangent plane approximation method, which is adequate for amplitudes, frequencies and wave lengths considered here. We also present a qualitative discussion about the efficiency of a device driven by an internal rotating structure.