Flagellar Swimming at Low Reynolds Numbers: Zoospore-Inspired Robotic Swimmers with Dual Flagella for High-Speed Locomotion

Abstract

Traditional locomotion strategies become ineffective at low Reynolds numbers, where viscous forces predominate over inertial forces. To adapt, microorganisms have evolved specialized structures like cilia and flagella for efficient maneuvering in viscous environments. Among these organisms, Phytophthora zoospores demonstrate unique locomotion mechanisms that allow them to rapidly spread and attack new hosts while expending minimal energy. In this study, we present the design, fabrication, and testing of a zoospore-inspired robot, which leverages dual flexible flagella and oscillatory propulsion mechanisms to emulate the natural swimming behavior of zoospores. Our experiments and theoretical model reveal that both flagellar length and oscillation frequency strongly influence the robot's propulsion speed, with longer flagella and higher frequencies yielding enhanced performance. Additionally, the anterior flagellum, which generates a pulling force on the body, plays a dominant role in enhancing propulsion efficiency compared to the posterior flagellum's pushing force. This is a significant experimental finding, as it would be challenging to observe directly in biological zoospores, which spontaneously release the posterior flagellum when the anterior flagellum detaches. This work contributes to the development of advanced microscale robotic systems with potential applications in medical, environmental, and industrial fields. It also provides a valuable platform for studying biological zoospores and their unique locomotion strategies.

Figures (5)

• Figure 1: Zoospore-inspired robot design (A) Microscopic image of a biological zoospore showing its body and two flagella, anterior ($f_1$) and posterior ($f_2$). (B) Zoospore-inspired robot with anterior ($f_1$) and posterior ($f_2$) flagella, shown in a glycerine tank. (C) Isometric CAD view of the robot. The inset shows the electronics. (D) Dimensions of the zoospore robot: Top view, side view, and exploded view.
• Figure 2: Theoretical model of swimming zoospore robot using Resistive Force Theory. (A) Schematic representation of the zoospore robot swimming in a viscous fluid, modeled with a spherical body and two flagella, beating in a sine waveform. (B) The theoretical speed of the zoospore robot as a function of flagellum length ($L$) and amplitude ($A$) for different wave amplitudes ranging from 0.4 cm to 1.0 cm. (C) Propulsion efficiency of the robot at varying anterior ($f_1$) and posterior ($f_2$) flagellum frequencies for different frequencies from 0 to 6 Hz. (D) The speed of the robot as a function of different anterior ($f_1$) and posterior ($f_2$) flagellum frequencies, ranging from 0 to 6 Hz.
• Figure 3: Experimental Setup and Flagella Configurations.(A) Schematic of the experimental setup, showing the zoospore robot in a glycerine tank from both top and side views. The robot moves along the X-axis. (B) Top view of the robot's trajectory over 6 seconds, with color coding representing time. The inset shows the side view of the robot's path over time. (C) Dual flagella actuation experiments for different flagella lengths: L = 6.5 cm, L = 10 cm, and L = 12 cm. The displacement covered in 6 seconds is shown below each configuration (6 cm, 14 cm, and 20 cm, respectively). (D) Single flagella actuation experiments for the anterior and posterior flagella with L = 12 cm. The anterior flagella achieved a 10 cm displacement in 6 seconds, while the posterior flagella covered 3 cm in the same duration.
• Figure 4: Experimental and theoretical Results (A) Theoretical (dashed lines) and experimental (solid lines) speeds of the robot as a function of flagellum length ($L$) for different actuation frequencies ($f_1 = f_2$) at 2.05, 3.16, 4.41, and 5.18 Hz. (B) Comparison of speed as a function of anterior ($f_1$) and posterior ($f_2$) flagellum for frequencies of 2.05 Hz and 4.41 Hz. (C) The speed of the robot versus Cost of Transport (CoT) for different flagella combinations - dual flagella, anterior flagella, and posterior flagella (black-actuated, and grey-turned off) (D) Speed as a function of flagellum length ($L$) normalized to body lengths per second (BL/s) for different frequencies. Error bars indicate standard deviations.
• Figure 5: Comparison of macro-sized robots and biological models based on flagella-inspired propulsion systems. The left panel shows macro-sized robots, including (i) temel_characterization_2014 and (ii) das_force_2022 Monotrichous bacteria-inspired robots, (iii) chikere_harnessing_2024 and (iv) diaz_minimal_2021 quadriflagellate algae-inspired robots, and (v) our zoospore-inspired robot, with their corresponding flagella lengths and speeds normalized to flagellar lengths (FL/s). The right panel displays the biological models for each category: Monotrichous bacteria with helical propulsion, quadriflagellate algae with planar propulsion, and heterokont zoospores with planar propulsion.