Canonical orbits for rapidly deforming planar microswimmers in shear flow

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

doi:10.1103/physrevfluids.7.l022101

Eamonn A Gaffney, Clément Moreau + Show 3 more

Open Access

https://doi.org/10.1103/physrevfluids.7.l022101

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Abstract

Classically, the rotation of ellipsoids in shear Stokes flow is captured by Jeffery's orbits. Here, we demonstrate that Jeffery's orbits also describe high-frequency shape-deforming swimmers moving in the plane of a shear flow. In doing so, we support the use of these simple models for capturing shape-changing swimmer dynamics in studies of active matter and highlight the ubiquity of ellipsoid-like dynamics in complex systems.

Highlights

[22] In writing this, we are minimally abusing notation by interpreting xS as a two-dimensional vector field in order to write the scalar product between it and LU r, which we will continue to do throughout, noting that this is unambiguous as xS · ez ≡ 0
A similar correspondence holds between rigid bodies and ellipsoids in Stokesian fluid dynamics, with the angular motion of a broad class of particles in shear flow known to be equivalent to those of an ellipsoid
Though we have focused on the motion of rapidly deforming swimmers, Eq (4) can be further analysed in two additional cases: slow swimmer evolution, where ω 1, and a rigid body, where ω = 0 and T is constant

Summary

Introduction

[22] In writing this, we are minimally abusing notation by interpreting xS as a two-dimensional vector field in order to write the scalar product between it and LU r, which we will continue to do throughout, noting that this is unambiguous as xS · ez ≡ 0. The rotation of ellipsoids in shear Stokes flow is captured by Jeffery’s orbits.

Results

Conclusion