2014/06/04 by Thomas D. Montenegro‐Johnson, Eric Lauga, Montenegro-Johnson, Thomas D. +1
Engineering · #76 #92 #Biological Physics (physics.bio-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Sports Dynamics and Biomechanics
paper · pdf · doi:10.48550/arxiv.1406.1070
openalex publication_date 2014/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Propulsion at microscopic scales is often achieved through propagating traveling waves along hair-like organelles called flagella. Taylor's two-dimensional swimming sheet model is frequently used to provide insight into problems of flagellar propulsion. We derive numerically the large-amplitude waveform of the two-dimensional swimming sheet that yields optimum hydrodynamic efficiency; the ratio of the squared swimming speed to the rate-of-working of the sheet against the fluid. Using the boundary element method, we show the optimal waveform is a front-back symmetric regularized cusp that is 25% more efficient than the optimal sine-wave. This optimal two-dimensional shape is smooth, qualitatively different from the kinked form of Lighthill's optimal three-dimensional flagellum, not predicted by small-amplitude theory, and different from the smooth circular-arc-like shape of active elastic filaments.