Encoding spatiotemporal asymmetry in artificial cilia with a ctenophore-inspired soft-robotic platform.

A remarkable variety of organisms use metachronal coordination (i.e. numerous neighboring appendages beating sequentially with a fixed phase lag) to swim or pump fluid. This coordination strategy is used by microorganisms to break symmetry at small scales where viscous effects dominate and flow is time-reversible. Some larger organisms use this swimming strategy at intermediate scales, where viscosity and inertia both play important roles. However, the role of individual propulsor kinematics-especially across hydrodynamic scales-is not well-understood, though the details of propulsor motion can be crucial for the efficient generation of flow. To investigate this behavior, we developed a new soft robotic platform using magnetoactive silicone elastomers to mimic the metachronally coordinated propulsors found in swimming organisms. Furthermore, we present a method to passively encode spatially asymmetric beating patterns in our artificial propulsors. We investigated the kinematics and hydrodynamics of three propulsor types, with varying degrees of asymmetry, using Particle Image Velocimetry and high-speed videography. We find that asymmetric beating patterns can move considerably more fluid relative to symmetric beating at the same frequency and phase lag, and that asymmetry can be passively encoded into propulsors via the interplay between elastic and magnetic torques. Our results demonstrate that nuanced differences in propulsor kinematics can substantially impact fluid pumping performance. Our soft robotic platform also provides an avenue to explore metachronal coordination at the meso-scale, which in turn can inform the design of future bioinspired pumping devices and swimming robots.

Propulsive efficiency of spatiotemporally asymmetric oscillating appendages at intermediate Reynolds numbers.

Many organisms use flexible appendages for locomotion, feeding, and other functional behaviors. The efficacy of these behaviors is determined in large part by the fluid dynamics of the appendage interacting with its environment. For oscillating appendages at low Reynolds numbers, viscosity dominates over inertia, and appendage motion must be spatially asymmetric to generate net flow. At high Reynolds numbers, viscous forces are negligible and appendage motion is often also temporally asymmetric, with a fast power stroke and a slow recovery stroke; such temporal asymmetry does not affect the produced flow at low Reynolds numbers. At intermediate Reynolds numbers, both viscous and inertial forces play non-trivial roles---correspondingly, both spatial and temporal asymmetry can strongly affect overall propulsion. Here we perform experiments on three robotic paddles with different material flexibilities and geometries, allowing us to explore the effects of motion asymmetry (both spatial and temporal) on force production. We show how a flexible paddle's time-varying shape throughout the beat cycle can reorient the direction of the produced force, generating both thrust and lift. We also evaluate the propulsive performance of the paddle by introducing a new quantity, which we term "integrated efficiency". This new definition of propulsive efficiency can be used to directly evaluate an appendage's performance independently from full-body swimming dynamics. Use of the integrated efficiency allows for accurate performance assessment, generalization, and comparison of oscillating appendages in both robotic devices and behaving organisms. Finally, we show that a curved flexible paddle generates thrust more efficiently than a straight paddle, and produces spatially asymmetric motion---thereby improving performance---without the need for complex actuation and controls, opening new avenues for bioinspired technology development.

Omnidirectional propulsion in a metachronal swimmer.

Aquatic organisms often employ maneuverable and agile swimming behavior to escape from predators, find prey, or navigate through complex environments. Many of these organisms use metachronally coordinated appendages to execute complex maneuvers. However, though metachrony is used across body sizes ranging from microns to tens of centimeters, it is understudied compared to the swimming of fish, cetaceans, and other groups. In particular, metachronal coordination and control of multiple appendages for three-dimensional maneuvering is not fully understood. To explore the maneuvering capabilities of metachronal swimming, we combine 3D high-speed videography of freely swimming ctenophores (Bolinopsis vitrea) with reduced-order mathematical modeling. Experimental results show that ctenophores can quickly reorient, and perform tight turns while maintaining forward swimming speeds close to 70% of their observed maximum-performance comparable to or exceeding that of many vertebrates with more complex locomotor systems. We use a reduced-order model to investigate turning performance across a range of beat frequencies and appendage control strategies, and reveal that ctenophores are capable of near-omnidirectional turning. Based on both recorded and modeled swimming trajectories, we conclude that the ctenophore body plan enables a high degree of maneuverability and agility, and may be a useful starting point for future bioinspired aquatic vehicles.

Spatiotemporal Asymmetry in Metachronal Rowing at Intermediate Reynolds Numbers.

In drag-based swimming, individual propulsors operating at low Reynolds numbers (where viscous forces dominate over inertial forces) must execute a spatially asymmetric stroke to produce net fluid displacement. Temporal asymmetry (that is, differing duration between the power vs. recovery stroke) does not affect the overall generated thrust in this time-reversible regime. Metachronal rowing, in which multiple appendages beat sequentially, is used by a wide variety of organisms from low to intermediate Reynolds numbers. At the upper end of this range, inertia becomes important, and increasing temporal asymmetry can be an effective way to increase thrust. However, the combined effects of spatial and temporal asymmetry are not fully understood in the context of metachronal rowing. To explore the role of spatiotemporal asymmetry in metachronal rowing, we combine laboratory experiments and reduced-order analytical modeling. We measure beat kinematics and generated flows in two species of lobate ctenophores across a range of body sizes, from 7 to 40 mm in length. We observe characteristically different flows in ctenophores of differing body size and Reynolds number, and a general decrease in spatial asymmetry and increase in temporal asymmetry with increasing Reynolds number. We also construct a one-dimensional mathematical model consisting of a row of oscillating flat plates whose flow-normal areas change with time, and use it to explore the propulsive forces generated across a range of Reynolds numbers and kinematic parameters. The model results show that while both types of asymmetry increase force production, they have different effects in different regions of the parameter space. These results may have strong biological implications, as temporal asymmetry can be actively controlled while spatial asymmetry is likely to be partially or entirely driven by passive fluid-structure interaction.

Metachronal Motion across Scales: Current Challenges and Future Directions.

Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Finally, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers.

Turbulent flow reduces oxygen consumption in the labriform swimming shiner perch, Cymatogaster aggregata.

Fish swimming energetics are often measured in laboratory environments which attempt to minimize turbulence, though turbulent flows are common in the natural environment. To test whether the swimming energetics and kinematics of shiner perch, Cymatogaster aggregata (a labriform swimmer), were affected by turbulence, two flow conditions were constructed in a swim-tunnel respirometer. A low-turbulence flow was created using a common swim-tunnel respirometry setup with a flow straightener and fine-mesh grid to minimize velocity fluctuations. A high-turbulence flow condition was created by allowing large velocity fluctuations to persist without a flow straightener or fine grid. The two conditions were tested with particle image velocimetry to confirm significantly different turbulence properties throughout a range of mean flow speeds. Oxygen consumption rate of the swimming fish increased with swimming speed and pectoral fin beat frequency in both flow conditions. Higher turbulence also caused a greater positional variability in swimming individuals (versus low-turbulence flow) at medium and high speeds. Surprisingly, fish used less oxygen in high-turbulence compared with low-turbulence flow at medium and high swimming speeds. Simultaneous measurements of swimming kinematics indicated that these reductions in oxygen consumption could not be explained by specific known flow-adaptive behaviours such as Kármán gaiting or entraining. Therefore, fish in high-turbulence flow may take advantage of the high variability in turbulent energy through time. These results suggest that swimming behaviour and energetics measured in the lab in straightened flow, typical of standard swimming respirometers, might differ from that of more turbulent, semi-natural flow conditions.