Effects of rapid yawing on simple swimmer models and planar Jeffery's orbits

Benjamin J. Walker, Kenta Ishimoto, Eamonn A. Gaffney, Clément Moreau, Mohit P. Dalwadi

Research output: Contribution to journalArticlepeer-review

6 Citations (SciVal)

Abstract

Over a sufficiently long period of time, or from an appropriate distance, the motion of many swimmers can appear smooth, with their trajectories appearing almost ballistic in nature and slowly varying in character. These long-time behaviors, however, often mask more complex dynamics, such as the side-to-side snakelike motion exhibited by spermatozoa as they swim, propelled by the frequent and periodic beating of their flagellum. Many models of motion neglect these effects in favour of smoother long-term behaviors, which are often of greater practical interest than the small-scale oscillatory motion. While it may be tempting to ignore any yawing motion, simply assuming that any effects of rapid oscillations cancel out over a period, a precise quantification of the impacts of high-frequency yawing is lacking. In this study, we systematically evaluate the long-term effects of general high-frequency oscillations on translational and angular motion, cast in the context of microswimmers but applicable more generally. Via a multiple-scales asymptotic analysis, we show that rapid oscillations can cause a long-term bias in the average direction of progression. We identify sufficient conditions for an unbiased long-term effect of yawing, and we quantify how yawing modifies the speed of propulsion and the effective hydrodynamic shape when in shear flow. Furthermore, we investigate and justify the long-time validity of the derived leading-order solutions and, by direct computational simulation, we evidence the relevance of the presented results to a canonical microswimmer.

Original languageEnglish
Article number023101
JournalPhysical Review Fluids
Volume7
Issue number2
DOIs
Publication statusPublished - 4 Feb 2022

Bibliographical note

Funding Information:
The authors are grateful to Prof. E. Lauga, University of Cambridge, for interesting and motivating discussions on the separated timescales of motion found in many microswimming problems. B.J.W. is supported by the U.K. Engineering and Physical Sciences Research Council (EPSRC), Grant No. EP/R513295/1. K.I. acknowledges JSPS-KAKENHI for Young Researchers (Grant No. 18K13456) and JST, PRESTO, Japan (Grant No. JPMJPR1921). C.M. is a JSPS International Research Fellow (PE20021). K.I. and C.M. were partially supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located at Kyoto University.

Publisher Copyright:
© 2022 authors. Published by the American Physical Society.

ASJC Scopus subject areas

  • Computational Mechanics
  • Modelling and Simulation
  • Fluid Flow and Transfer Processes

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