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Metachronal waves in a chain of rowers with hydrodynamic interactions

Abstract.

Hair-like appendages called cilia on the surface of a microorganism such as Paramecium or Opalina beat highly synchronized and form so-called metachronal waves that travel along the surfaces. In order to study under what principal conditions these waves form, we introduce a chain of beads, called rowers, each periodically driven by an external force on a straight line segment. To implement hydrodynamic interactions between the beads, they are considered point-like. Two beads synchronize in antiphase or in phase depending on the positive or negative curvature of their driving-force potential. Concentrating on in-phase synchronizing rowers, we find that they display only transient synchronization in a bulk fluid. On the other hand, metachronal waves with wavelengths of 7-10 rower distances emerge, when we restrict the range of hydrodynamic interactions either artificially to nearest neighbors or by the presence of a bounding surface as in any relevant biological system.

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Correspondence to C. Wollin.

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Wollin, C., Stark, H. Metachronal waves in a chain of rowers with hydrodynamic interactions. Eur. Phys. J. E 34, 42 (2011). https://doi.org/10.1140/epje/i2011-11042-7

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Keywords

  • Chain Segment
  • Hydrodynamic Interaction
  • Switching Point
  • Recovery Stroke
  • Rower Distance