Energy-optimal small-amplitude strokes for multi-link microswimmers: Purcell's loops and Taylor's waves reconciled - Archive ouverte HAL Access content directly
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Energy-optimal small-amplitude strokes for multi-link microswimmers: Purcell's loops and Taylor's waves reconciled

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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.

Dates and versions

hal-01970740 , version 1 (05-01-2019)

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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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