Energy-optimal small-amplitude strokes for multi-link microswimmers: Purcell's loops and Taylor's waves reconciled

Abstract : Micron-scale swimmers move in the realm of negligible inertia, dominated by viscous drag forces. Actuation of artificial micro-robotic swimmers for various biomedical applications is inspired by natural propulsion mechanisms of swimming microorganisms such as bacteria and sperm cells, which perform periodic strokes by waving a slender tail. Finding energy-optimal swimming strokes is a key question with high relevance for both biological and robotic microswimmers. In this paper, we formulate the leading-order dynamics of a slender multi-link microswimmer assuming small-amplitude undulations about its straightened configuration. The energy-optimal stroke for achieving a given displacement at a given period time is obtained as the eigenvalue solution associated with a constrained optimal control problem. Remarkably, the optimal stroke for N-link microswimmer is a trajectory lying within a two-dimensional plane in the space of joint angles. For Purcell's famous three-link model, we analyze the differences between our optimal stroke and that of Tam and Hosoi that maximizes Lighthill's efficiency. For a large number of links N, the optimal stroke becomes a travelling wave with the shortest possible wavelength of three links, in agreement with the well-known result of Taylor's infinite sheet. Finally, we analyze the scaling of minimal swimming energy for large N.
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https://hal.inria.fr/hal-01970740
Contributor : Jean-Baptiste Pomet <>
Submitted on : Saturday, January 5, 2019 - 11:28:40 PM
Last modification on : Monday, May 6, 2019 - 5:19:12 PM

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  • HAL Id : hal-01970740, version 1
  • ARXIV : 1801.04687

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Oren Wiezel, Laetitia Giraldi, Antonio Desimone, Yizhar Or, François Alouges. Energy-optimal small-amplitude strokes for multi-link microswimmers: Purcell's loops and Taylor's waves reconciled. 2019. ⟨hal-01970740⟩

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