Synchronization of flexible sheets
arXiv:1108.5791 · doi:10.1017/S0022112011000814
Abstract
When swimming in close proximity, some microorganisms such as spermatozoa synchronize their flagella. Previous work on swimming sheets showed that such synchronization requires a geometrical asymmetry in the flagellar waveforms. Here we inquire about a physical mechanism responsible for such symmetry-breaking in nature. Using a two-dimensional model, we demonstrate that flexible sheets with symmetric internal forcing, deform when interacting with each other via a thin fluid layer in such a way as to systematically break the overall waveform symmetry, thereby always evolving to an in-phase conformation where energy dissipation is minimized. This dynamics is shown to be mathematically equivalent to that obtained for prescribed waveforms in viscoelastic fluids, emphasizing the crucial role of elasticity in symmetry-breaking and synchronization.
8 pages, 4 figures
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Cited by in corpus (8)
- Green Algae as Model Organisms for Biological Fluid Dynamics
- Bistability in the synchronization of actuated microfilaments
- An elastic two-sphere swimmer in Stokes flow
- Hydrodynamic interactions of cilia on a spherical body
- Energetics of synchronisation for model flagella and cilia
- Interaction Between Two Closely-Spaced Waving Slender Elastic Cylinders Immersed in a Viscous Fluid
- Competing effects of inertia, sheet elasticity, and fluid viscoelasticity on the synchronization of two actuated sheets
- Elastohydrodynamic synchronization of rotating bacterial flagella