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Optimal feeding is optimal swimming for all Péclet numbers
Michelin, Sébastien
Lauga, Eric
Laboratoire d'hydrodynamique (LadHyX) ; École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)
Department of Mechanical and Aerospace Engineering [Univ California San Diego] (MAE - UC San Diego) ; University of California [San Diego] (UC San Diego) ; University of California (UC)-University of California (UC)
International audience
ISSN: 1070-6631
EISSN: 1089-7666
Physics of Fluids
American Institute of Physics
hal-00997991
https://polytechnique.hal.science/hal-00997991
https://polytechnique.hal.science/hal-00997991/document
https://polytechnique.hal.science/hal-00997991/file/1.3642645.pdf
https://polytechnique.hal.science/hal-00997991
Physics of Fluids, 2011, 23 (10), pp.101901. ⟨10.1063/1.3642645⟩
DOI: 10.1063/1.3642645
info:eu-repo/semantics/altIdentifier/doi/10.1063/1.3642645
en
[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]
[SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]
info:eu-repo/semantics/article
Journal articles
Cells swimming in viscous fluids create flow fields which influence the transport of relevant nutrients, and therefore their feeding rate. We propose a modeling approach to the problem of optimal feeding at zero Reynolds number. We consider a simplified spherical swimmer deforming its shape tangentially in a steady fashion (so-called squirmer). Assuming that the nutrient is a passive scalar obeying an advection-diffusion equation, the optimal use of flow fields by the swimmer for feeding is determined by maximizing the diffusive flux at the organism surface for a fixed rate of energy dissipation in the fluid. The results are obtained through the use of an adjoint-based numerical optimization implemented by a Legendre polynomial spectral method. We show that, to within a negligible amount, the optimal feeding mechanism consists in putting all the energy expended by surface distortion into swimming-so-called treadmill motion-which is also the solution maximizing the swimming efficiency. Surprisingly, although the rate of feeding depends strongly on the value of the Péclet number, the optimal feeding stroke is shown to be essentially independent of it, which is confirmed by asymptotic analysis. Within the context of steady actuation, optimal feeding is therefore found to be equivalent to optimal swimming for all Péclet numbers. © 2011 American Institute of Physics.
2011
info:eu-repo/semantics/OpenAccess