Emergent three-dimensional dynamics of rapidly spinning, self-propelled particles in shear flow. Part II: Chiral objects

In the second part of this two-part study, we investigate the motion of three-dimensional, rigid, active particles in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. We consider the general class of objects with helicoidal symmetry, focusing on chiral objects without reflectional fore-aft symmetry, significantly broadening the class of objects studied in Part I. We perform an intricate multiple-scales asymptotic analysis to systematically derive emergent equations of motion for the angular and translational dynamics of the object that explicitly account for the significant effects of fast spinning. We show that the emergent dynamics due to rapid rotation can be described by generalized Jeffery's equations for the wide class of objects that exhibit helicoidal symmetry, significantly expanding the scope of Jeffery's seminal study. Furthermore, we use our analytic results to characterise and quantify the explicit effect of rotation on the effective hydrodynamic shape of the objects.