Optimizing the mean swimming velocity of a model two-sphere swimmer

Physics of Fluids, vol. 34

Abstract

The swimming of a two-sphere system oscillating in a viscous fluid is studied on the basis of simplified equations of motion which take account of both friction and inertial effects. In the model, the friction follows from an Oseen approximation to the mobility matrix, and the inertial effects follow from a dipole approximation to the added mass matrix. The resulting mean swimming velocity is evaluated analytically in a first harmonics approximation. For specific choices of the parameters, this is compared with the exact result following from a numerical calculation including higher harmonics. The Oseen-dipole model is compared with the simpler Oseen* model, in which the added mass effects are approximated by just the effective mass of the single spheres and dipole interactions are neglected. The expression for the mean swimming velocity can be reduced to a dimensionless scaling form. For given viscosity and mass density of the fluid, the frequency of the stroke and the ratio of radii can be chosen such that the swimming velocity is optimized.

Authors 1

1. B. U. Felderhof corresponding Aachen Institut für Theorie der Statistischen Physik

   RWTH Aachen University

   Affiliation as printed

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