Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 107, Issue 17, Pages 7669-7673Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.0912455107
Keywords
colloidal particles; hydrodynamic interaction; metachronal wave; optical tweezers; nonlinear dynamical system
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Funding
- Engineering and Physical Sciences Research Council
- Royal Society
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Two colloidal spheres are maintained in oscillation by switching the position of an optical trap when a sphere reaches a limit position, leading to oscillations that are bounded in amplitude but free in phase and period. The interaction between the oscillators is only through the hydrodynamic flow induced by their motion. We prove that in the absence of stochastic noise the antiphase dynamical state is stable, and we show how the period depends on coupling strength. Both features are observed experimentally. As the natural frequencies of the oscillators are made progressively different, the coordination is quickly lost. These results help one to understand the origin of hydrodynamic synchronization and how the dynamics can be tuned. Cilia and flagella are biological systems coupled hydrodynamically, exhibiting dramatic collective motions. We propose that weakly correlated phase fluctuations, with one of the oscillators typically precessing the other, are characteristic of hydrodynamically coupled systems in the presence of thermal noise.
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