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On the hydrodynamic interaction of two spheres oscillating in a viscous fluid. II. Three dimensional case

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Abstract

Asymptotic solution of the Navier-Stokes equations is derived for the problem of the viscous flow induced by two spheres oscillating in a direction perpendicular to their central line.

The main purpose of the paper is to study the effect of the hydrodynamic interaction of the spheres on the forces acting upon them in this complicated three dimensional flow.

It is shown that the drag on each of the two spheres decreases as the distance between them increases and also that each sphere experiences a repulsive force in a direction perpendicular to the oscillating stream.

Zusammenfassung

Das asymptotische Verfahren für die Lösung der Navier-Stokesschen Gleichungen wird angewendet für die Strömung, die bei der Schwingung von zwei Kugeln senkrecht zur Verbindungslinie ihrer Mittelpunkte entsteht.

Das wichtigste Ziel der Arbeit ist die Untersuchung der hydrodynamischen Beeinflussung der Kugeln durch die Kräfte, die bei dieser komplizierten dreidimensionalen Strömung entstehen.

Es wurde gefunden, daß der Widerstand der Kugeln sich mit wachsendem Abstand zwischen ihnen verringert. In Richtung senkrecht zur Schwingung wirkt auf jede Kugel eine abstoßende Kraft.

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References

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Authors and Affiliations

  1. Dept. of Fluid Mechanics, Institute of Mechanics and Biomechanics BAS, Sofia, Bulgaria

    S. S. Tabakova & Z. D. Zapryanov

Authors
  1. S. S. Tabakova
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  2. Z. D. Zapryanov
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Tabakova, S.S., Zapryanov, Z.D. On the hydrodynamic interaction of two spheres oscillating in a viscous fluid. II. Three dimensional case. Z. angew. Math. Phys. 33, 487–502 (1982). https://doi.org/10.1007/BF00955698

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  • DOI: https://doi.org/10.1007/BF00955698

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