Fish-like three-dimensional swimming with an autonomous, multi-fin, and biomimetic robot.

Fish migrate across considerable distances and exhibit remarkable agility to avoid predators and feed. Fish swimming performance and maneuverability remain unparalleled when compared to robotic systems, partly because previous work has focused on robots and flapping foil systems that are either big and complex, or tethered to external actuators and power sources. By contrast, we present a robot-the Finbot-that combines high degrees of autonomy, maneuverability, and biomimicry with miniature size (160 cm3). Thus, it is well-suited for controlled three-dimensional experiments on fish swimming in confined laboratory test beds. Finbot uses four independently controllable fins and sensory feedback for precise closed-loop underwater locomotion. Different caudal fins can be attached magnetically to reconfigure Finbot for swimming at top speed (122 mm s-1≡ 1 BL s-1) or minimal cost of transport (CoT = 8.2) at Strouhal numbers as low as 0.53. We conducted more than 150 experiments with 12 different caudal fins to measure three key characteristics of swimming fish: (i) linear speed-frequency relationships, (ii) U-shaped CoT, and (iii) reverse Kármán wakes (visualized with particle image velocimetry). More fish-like wakes appeared where the CoT was low. By replicating autonomous multi-fin fish-like swimming, Finbot narrows the gap between fish and fish-like robots and can address open questions in aquatic locomotion, such as optimized propulsion for new fish robots, or the hydrodynamic principles governing the energy savings in fish schools.

Stability of the Shape of a Viscous Drop under Buoyancy-Driven Translation in a Hele-Shaw Cell.

It has been shown (N. R. Gupta, A. Nadim, H. Haj-Hariri, and A. Borhan, J. Colloid Interface Sci. 218, 338 1999) that a circular drop translating in a Hele-Shaw cell under the action of gravity is linearly stable for nonzero interfacial tension. In this paper, we use the boundary integral method to examine the nonlinear evolution of the shape of initially noncircular drops translating in a Hele-Shaw cell. For prolate initial deformations, it is found that the drop reverts to a circular shape for all finite Bond numbers considered. Initially oblate drops, on the other hand, are found to become unstable and break up if the initial shape perturbation is of sufficiently large magnitude. The critical conditions for the onset of drop breakup are examined in terms of the magnitude of the initial deformation as a function of Bond number. Two branches of marginal stability are identified and the effects of viscosity ratio and asymmetric initial perturbations on the stability diagram are discussed. Copyright 2000 Academic Press.

On the Linear Stability of a Circular Drop Translating in a Hele-Shaw Cell.

For the buoyancy-driven motion of a drop in a Hele-Shaw cell, a circle is an exact solution for the shape of the drop. The stability of the shape of a circular drop translating in a Hele-Shaw cell under the action of gravity is investigated. It is shown that for nonzero interfacial tension, the circular shape is linearly stable. Copyright 1999 Academic Press.