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Updated: Apr 4, 2026

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
Published on: February 17, 2019
Efficient swimming of an assembly of rigid spheres at low Reynolds number
1Institut für Theorie der Statistischen Physik, RWTH Aachen University, Templergraben 55, 52056, Aachen, Germany, ufelder@physik.rwth-aachen.de.
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.
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