Minimal two-sphere model of the generation of fluid flow at low Reynolds numbers

M. Leoni, B. Bassetti, J. Kotar, P. Cicuta, and M. Cosentino Lagomarsino
Phys. Rev. E 81, 036304 – Published 4 March 2010

Abstract

Locomotion and generation of flow at low Reynolds number are subject to severe limitations due to the irrelevance of inertia: the “scallop theorem” requires that the system have at least two degrees of freedom, which move in non-reciprocal fashion, i.e. breaking time-reversal symmetry. We show here that a minimal model consisting of just two spheres driven by harmonic potentials is capable of generating flow. In this pump system the two degrees of freedom are the mean and relative positions of the two spheres. We have performed and compared analytical predictions, numerical simulation and experiments, showing that a time-reversible drive is sufficient to induce flow.

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  • Received 2 November 2009

DOI:https://doi.org/10.1103/PhysRevE.81.036304

©2010 American Physical Society

Authors & Affiliations

M. Leoni1,2,3,4, B. Bassetti1,4, J. Kotar2, P. Cicuta2, and M. Cosentino Lagomarsino1,4

  • 1Dip. Fisica, Università di Milano, Via Celoria, 16, 20133 Milano, Italy
  • 2Cavendish Laboratory and Nanoscience Centre, University of Cambridge, Cambridge CB3 0HE, United Kingdom
  • 3Department of Mathematics, University of Bristol, Clifton, Bristol BS8 1TW, United Kingdom
  • 4INFN, Milano, Italy

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Vol. 81, Iss. 3 — March 2010

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