The swimming of a deforming helix

Abstract

Many microorganisms and artificial microswimmers use helical appendages in order to generate locomotion. Though often rotated so as to produce thrust, some species of bacteria such Spiroplasma, Rhodobacter sphaeroides and Spirochetes induce movement by deforming a helical-shaped body.Recently, artificial devices have been created which also generate motion by deforming their helical body in a non-reciprocal way (Mourran et al. Adv. Mater. 29, 1604825, 2017). Inspired by these systems, we investigate the transport of a deforming helix within a viscous fluid. Specifically, we consider a swimmer that maintains a helical centreline and a single handedness while changing its helix radius, pitch and wavelength uniformly across the body. We first discuss how a deforming helix can create a non-reciprocal translational and rotational swimming stroke and identify its principle direction of motion. We then determine the leading-order physics for helices with small helix radius before considering the general behaviour for different configuration parameters and how these swimmers can be optimised. Finally, we explore how the presence of walls, gravity, and defects in the centreline allow the helical device to break symmetries, increase its speed, and generate transport in directions not available to helices in bulk fluids.

Geometric phase methods with Stokes theorem for a general viscous swimmer

“…2012; Cicconofri & DeSimone 2016; Koens et al. 2018) and height functions (see Hatton & Choset (2011) and references within).…”

“…The visualisation of this field can assist with the design of swimming stokes for specific tasks (Keaveny, Walker & Shelley 2013; Koens et al. 2018; Quispe, Oulmas & Regnier 2019) but is typically hard to do if there is more than three dimensions. In this section, we consider the behaviour of the net displacement throughout the entire embedded-configuration space of an arbitrary swimmer when the generalised Stokes theorem applies.…”

“…2012; Hatton & Choset 2015; Cicconofri & DeSimone 2016; Koens et al. 2018). However, the same treatment is not generally possible for more complicated swimmers because of (i) non-commuting variables within the gauge field and (ii) difficulties visualising the configuration space (Hatton & Choset 2015; Hatton, Dear & Choset 2017; Ramasamy & Hatton 2017; Bittner, Hatton & Revzen 2018).…”

Design, Modeling and Testing of a Flagellum-inspired Soft Underwater Propeller Exploiting Passive Elasticity

“…The hook is then anchored to a spinning structure, the flagellar motor, which is able to rotate in two directions. The torque of this motor is then transmitted across the hook to the filament, whose elastic response in interacting with the surrounding fluid enables the onset of helical waves [32]. The flagella of micro-organisms are commonly referred to as either left-handed or right-handed, identifying with this terminology the tendency of the helical wave to travel from the base to end of the filament or otherwise according to the orientation of the motor rotation [31].…”

Microgel that swims to the beat of light

“…It might contribute significantly to the understanding of the efficiency of such locomotion [13,14], but will also provide new capabilities for microrobotic systems that can search their own way to transport and deliver, e.g., by chemotaxis as the motility is effected by gradient in concentration, or which can mix, sort and circulate fluids [1,15]. Recently, we have described preparation and motility of helical ribbons that were actuated by periodic pulse irradiation with near IR-light [16][17][18][19]. We note that ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which produce unique shapes unobtainable by wires or filaments.…”