Metachronal waves in a chain of rowers with hydrodynamic interactions
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623, Berlin, Germany
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Accepted: 22 March 2011
Published online: 21 April 2011
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.
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2011