Velocity Fluctuations in Helical Propulsion: How Small Can a Propeller Be

Abstract

Helical propulsion is at the heart of locomotion strategies utilized by various natural and artificial swimmers. We used experimental observations and a numerical model to study the various fluctuation mechanisms that determine the performance of an externally driven helical propeller as the size of the helix is reduced. From causality analysis, an overwhelming effect of orientational noise at low length scales is observed, which strongly affects the average velocity and direction of motion of a propeller. For length scales smaller than a few micrometers in aqueous media, the operational frequency for the propulsion system would have to increase as the inverse cube of the size, which can be the limiting factor for a helical propeller to achieve locomotion in the desired direction.

Theoretical modeling in microscale locomotion

“…In this section of our review, we discuss the range of dimensions in which Brownian motion may neglected, without going into further details of how the effects should be incorporated. Schamel et al (2014) found that 0.40-µm nanoscrews experience strong diffusion and are unable to propel effectively in pure water, in line with the observation that propellers below the length of 0.90 µm are dominated by Brownian motion and directional motion is not discernible (Ghosh et al 2013). For bacterial cells smaller than 1 µm, simulations which ignore Brownian motion leads to results that contradict microscopy observations, regardless (Li et al 2008).…”

Magnetic Actuation Based Motion Control for Microrobots: An Overview

“…A closed-loop control of microrobots is necessary for precise motion in presence of perturbations generated by thermal noise [80], or drifting due to boundary effects [35,81,82]. A robust and efficient control system is required for microrobots, because the high sensitivity of the micro-systems to environmental variables, and the high velocities at the microscale.…”

Planar Path Following of 3-D Steering Scaled-Up Helical Microswimmers

“…As explained in [21], "Nonholonomic systems are, roughly speaking, mechanical systems with constraints on their velocity that are not derivable from position constraints." All the lateral motions applied on a helical swimmer generated by thermal noise [16], or drifting due to boundary effect [17] can be considered as a perturbation, and should be corrected. Compensation of thermal noises is both a motivation of the closed-loop control and a major technical challenge.…”

“…A closed-loop control of helical swimmers is necessary for precise motion in the presence of perturbations generated by thermal noise [16] or drifting due to boundary effects [17]. The aim of this paper is to control a magnetic-actuated helical swimmer using visual feedback.…”