On the self-propulsion of an N-sphere micro-robot

The aim of this paper is to describe the self-propulsion of a micro-robot (or micro-swimmer) consisting of N spheres moving along a fixed line. The spheres are linked to each other by arms with their lengths changing periodically. We use the asymptotic procedure containing the two-timing method and a distinguished limit. We show that self-propulsion velocity appears (in the main approximation) as a linear combination of velocities of all possible triplets of spheres. Velocities and efficiencies of three-, four-and five-sphere swimmers are calculated.