Optimization and small-amplitude analysis of Purcell's three-link microswimmer model

Abstract

This work studies the motion of Purcell's three-link microswimmer in viscous flow, by using perturbation expansion of its dynamics under small-amplitude strokes. Leading-order expressions and next-order correction terms for the displacement of the swimmer are obtained for the cases of a square or circular gait in the plane of joint angles. The correction terms demonstrate the reversal in movement direction for large stroke amplitudes, which has previously only been shown numerically. In addition, asymptotic expressions for Lighthill's energetic efficiency are obtained for both gaits. These approximations enable calculating optimal stroke amplitudes and swimmer's geometry (i.e. ratio of links' lengths) for maximizing either the displacement or Lighthill's efficiency.

Accepted to "Royal Society, Proceedings A"

References in corpus (4)

• The hydrodynamics of swimming microorganisms
• Bacterial hydrodynamics
• Geometric visualization of self-propulsion in a complex medium
• Optimal Design for Purcell Three-link Swimmer

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