title: Efficient swimming of an assembly of rigid spheres at low Reynolds number.
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.
authors: Institut für Theorie der Statistischen Physik, RWTH Aachen University, Templergraben 55, 52056, Aachen, Germany, ufelder@physik.rwth-aachen.de.
authors: B U
authors: BU
authors: Felderhof
mesh_terms: D057446:Hydrodynamics; D044085:Microfluidics; D008962:Models, Theoretical; D014783:Viscosity