Rotation of slender swimmers in isotropic-drag media

Abstract

The drag anisotropy of slender filaments is a critical physical property allowing swimming in low-Reynolds number flows, and without it linear translation is impossible. Here we show that, in contrast, net rotation can occur under isotropic drag. We first demonstrate this result formally by considering the consequences of the force-and torque-free conditions on swimming bodies and we then illustrate it with two examples (a simple swimmers made of three rods and a model bacterium with two helical flagellar filaments). Our results highlight the different role of hydrodynamic forces in generating translational vs. rotational propulsion. *

Geometric phase methods with Stokes theorem for a general viscous swimmer

“…The body frame linear velocities are 0 if while the rotation remains non-zero. This is consistent with the current understanding of the swimming of slender bodies (Koens & Lauga 2016 a ).…”

“…2020), while including models for internal activation allows us to understand how spermatozoa and cilia generate their waveforms (Ishimoto & Gaffney 2018; Chakrabarti & Saintillan 2019 a , b ; Man, Ling & Kanso 2020). These approaches have also been extended to consider the dynamics of microswimmers in complex media (Koens & Lauga 2016 a ; Wróbel et al. 2016; Hewitt & Balmforth 2018; Omori & Ishikawa 2019).…”

Microscale flow dynamics of ribbons and sheets

“…[17][18][19][20] Recently, slender-ribbon theory (SRT) was developed to accurately explore the microscale hydrodynamics of slender ribbons. 21,22 This method expanded on the work of Johnson 16 and so captures the non-local interactions of the shape and is accurate to order w/ . The slenderness condition in SRT is contingent on the assumption that all three internal length scales of the ribbon, the length, , width, w, and thickness, h, are separated w h (Fig.…”

“…1c), and the leading order flow is found by asymptotically expanding the flow from a plane of point forces representing the ribbon with respect to these length scales. The flow at the ribbon's surface is then given in terms of a line integral 22 of unknown forces, as in SBT, which can be inverted to determine the force on the fluid. This technique allows the asymptotic exploration of a range of ribbon structures, such as artificial microswimmers comprising a magnetic head and a ribbon tail.…”

The swimming of a deforming helix

“…Notably, under the same conditions, the order 3 terms of the angular velocity are non-zero and so net rotation is still possible under isotropic drag. This rotation is a consequence of the anisotropy of the swimmer's shape alone [65].…”