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

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 (ω1,ω2) in which the filaments are actuated. Higher orders oscillate at frequencies which are combinations of the actuation frequencies, where the first order includes the 2ω1,2ω2,ω1+ω2, and ω1-ω2 harmonics. For configurations with ω1≈ω2, the ω1-ω2 mode represents the dominant first-order interaction effect due to significantly smaller effective Sperm number. For in-phase actuation with ω1=ω2, 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.