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Updated: Apr 20, 2026

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
Published on: February 17, 2019
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:
A matrix formulation is derived for the calculation of the swimming speed and the power required for swimming of an assembly of rigid spheres immersed in a viscous fluid of infinite extent. The spheres may have arbitrary radii and may interact with elastic forces. The analysis is based on the Stokes mobility matrix of the set of spheres, defined in low Reynolds number hydrodynamics. For small amplitude, swimming optimization of the swimming speed at given power leads to an eigenvalue problem. The method allows straightforward calculation of the swimming performance of structures modeled as assemblies of interacting rigid spheres.
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