Propulsion and maneuvering of an artificial microswimmer by two closely spaced waving elastic filaments

Abstract

This work examines the effect of hydrodynamic interaction between two closely spaced waving elastic filaments on the propulsion and maneuvering of an artificial microswimmer. The filaments are actuated by a forced oscillation of the slope at their clamped end and are free at the opposite end. We obtain an expression for the interaction force and apply an asymptotic expansion based on a small parameter representing the ratio between the elastic deflections and the distance between the filaments. The leading-order interaction forces yield asymmetric oscillation patterns at the two frequencies (ω 1 ,ω 2) in which the filaments are actuated. Higher orders oscillate at frequencies which are combinations of the actuation frequencies, where the first order includes the 2ω 1 , 2ω 2 , ω 1 + ω 2 , and ω 1 − ω 2 harmonics. For configurations with ω 1 ≈ ω 2 , the ω 1 − ω 2 mode represents the dominant first-order interaction effect due to significantly smaller effective Sperm number. For in-phase actuation with ω 1 = ω 2 , the deflection dynamics are identical to an isolated filament with a modified Sperm number. Phase difference between the filaments is shown to have significant effect on the time-averaged forces. Optimal Sperm numbers for in-phase and antiphase actuation are calculated. Turning moments due to phase difference between the filaments are presented, yielding optimal maneuvering for phase of 90 •. Calculation of the effect of hydrodynamic interaction on the propulsive forces yielded that antiphase beating is more efficient than the in-phase scenario, in contrast with the commonly used assumption of maximal efficiency of the synchronized state. Experiments are conducted to verify and illustrate some of the theoretical predictions.

Soft Robots for Ocean Exploration and Offshore Operations: A Perspective

“…Furthermore, the inherent dexterity of soft materials empowered bioinspired propulsion, paving the way for novel navigation techniques achievable for soft robots 17,18,36,38,43,[56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74] (Fig. 5A-F, K).…”

Motion of several slender rigid filaments in a Stokes flow

“…We are interested in the limit of the dynamics (specified below) as ε Ñ 0 for given, ε-independent initial data for the centerlines of the filaments. More precisely, we fix h i p0q P R 3 , Q i p0q P SOp3q such that (9) C i p0q " C i p0q :" h i p0q ` Q i p0qC i , are the positions of the centerlines at time 0 for all ε ą 0.…”

“…The main novelty of our work is the mathematically study of the coupled dynamics of a collection of slender filaments. Hydrodynamic interactions between filaments have been extensively studied in the physics and engineering literature, in particular regarding the behavior of polymers and microorganisms, see for example [8,9,27,28,29]. As far as we know, previous mathematical works on filaments in Stokes flows are focused on static problems with only a single filament.…”

Enhanced clamshell swimming with asymmetric beating at low Reynolds number

“…32 A simple design strategy of artificial swimmers involves elastic filaments with boundary actuations, such as angular or positional oscillations at the filament's ends, that send travelling waves along the filaments. [33][34][35] The effects of various mechanisms on swimming performance have been studied, such as the hydrodynamic interactions, [36][37][38] the number of filaments, 39 and the filament intrinsic curvature. [38][39][40] It has been demonstrated in experiments that the velocity of a swimmer propelled by multiple filaments may be enhanced by intrinsically curved filaments, 39 which was subsequently explored in numerical simulations based on discrete elastic rod model.…”