%X The observed behaviour of passive objects in simple flows can be surprisingly intricate, and is complicated further by object activity. Inspired by the motility of bacterial swimmers, in this two-part study we examine the three-dimensional motion of rigid active particles in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. In Part 1 we develop a multiscale framework to investigate these emergent dynamics and apply it to simple spheroidal objects. In Part 2 (Dalwadi et al., J. Fluid Mech., vol. 979, 2024, A2) we apply our framework to understand the emergent dynamics of more complex shapes; helicoidal objects with chirality. Via a multiple scales asymptotic analysis for nonlinear systems, we systematically derive emergent equations of motion for long-term trajectories that explicitly account for the strong (leading-order) effects of fast spinning. Supported by numerical examples, we constructively link these effective dynamics to the well-known Jeffery's orbits for passive spheroids, deriving an explicit closed-form expression for the effective shape of the active particle, broadening the scope of Jeffery's seminal study to spinning spheroids.
%V 979
%A Mohit Dalwadi
%A Clément Moreau
%A Eamonn Gaffney
%A Kenta Ishimoto
%A Benjamin Walker
%J Journal of Fluid Mechanics
%D 2024
%L discovery10180127
%I Cambridge University Press
%T Generalised Jeffery’s equations for rapidly spinning particles. Part 1: Spheroids
%O © The Author(s), 2024. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0).