Eur. Phys. J. E (2015) 38: 90
https://doi.org/10.1140/epje/i2015-15090-7

Regular Article

Efficient swimming of an assembly of rigid spheres at low Reynolds number

Institut für Theorie der Statistischen Physik, RWTH Aachen University, Templergraben 55, 52056, Aachen, Germany

^* e-mail: ufelder@physik.rwth-aachen.de

Received: 22 April 2015
Revised: 7 June 2015
Accepted: 30 July 2015
Published online: 28 August 2015

Abstract

The swimming of an assembly of rigid spheres immersed in a viscous fluid of infinite extent is studied in low-Reynolds-number hydrodynamics. The instantaneous swimming velocity and rate of dissipation are expressed in terms of the time-dependent displacements of sphere centers about their collective motion. For small-amplitude swimming with periodically oscillating displacements, optimization of the mean swimming speed at given mean power leads to an eigenvalue problem involving a velocity matrix and a power matrix. The corresponding optimal stroke permits generalization to large-amplitude motion in a model of spheres with harmonic interactions and corresponding actuating forces. The method allows straightforward calculation of the swimming performance of structures modeled as assemblies of interacting rigid spheres. A model of three collinear spheres with motion along the common axis is studied as an example.