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Many animals in nature travel in groups either for protection, survival, or endurance. Among these, certain species do so under the burden of aero/hydrodynamic loads, which incites questions as to the significance of the multibody fluid-mediated interactions that are inherent to collective flying/swimming. Prime examples of such creatures are fish, which are commonly seen traveling in highly organized groups of large numbers. Indeed, over the years, there have been numerous attempts to examine hydrodynamic interactions among self-propelled fish-like swimmers. Though many have studied this phenomenon, their motivations have varied from understanding animal behavior to extracting universal fluid dynamical principles and transplanting them into engineering applications. The approaches utilized to carry out these investigations include theoretical and computational analyses, field observations, and experiments using various abstractions of biological fish. Here, we compile representative investigations focused on the collective hydrodynamics of fish-like swimmers. The selected body of works are reviewed in the context of their methodologies and findings, so as to draw parallels, contrast differences, and highlight open questions. Overall, the results of the surveyed studies provide foundational insights into the conditions (such as the relative positioning and synchronization between the members, as well as their swimming kinematics and speed) under which hydrodynamic interactions can lead to efficiency gains and/or group cohesion in two- and three-dimensional scenarios. They also shed some light on the mechanisms responsible for such energetic and stability enhancements in the context of wake-body, wake-wake, and body-body interactions.

 

From insects to arachnids to bacteria, the surfaces of lakes and ponds are teaming with life. Many modes of locomotion are employed by these organisms to navigate along the air–water interface, including the use of lipid-laden excretions that can locally change the surface tension of the water and induce a Marangoni flow. In this paper, we improved the speed and maneuverability of a miniature remote-controlled robot that mimics insect locomotion using an onboard tank of isopropyl alcohol and a series of servomotors to control both the rate and location of alcohol release to both propel and steer the robot across the water. Here, we studied the effect of a series of design changes to the foam rubber footpads, which float the robot and are integral in efficiently converting the alcohol-induced surface tension gradients into propulsive forces and effective maneuvering. Two designs were studied: a two-footpad design and a single-footpad design. In the case of two footpads, the gap between the two footpads was varied to investigate its impact on straight-line speed, propulsion efficiency, and maneuverability. An optimal design was found with a small but finite gap between the two pads of 7.5 mm. In the second design, a single footpad without a central gap was studied. This footpad had a rectangular cut-out in the rear to capture the alcohol. Footpads with wider and shallower cut-outs were found to optimize efficiency. This observation was reinforced by the predictions of a simple theoretical mechanical model. Overall, the optimized single-footpad robot outperformed the two-footpad robot, producing a 30% improvement in speed and a 400% improvement in maneuverability.

 

Abstract Inspired by creatures that have naturally mastered locomotion on the air–water interface, we developed and built a self-powered, remotely controlled surfing robot capable of traversing this boundary by harnessing surface tension modification for both propulsion and steering through a controlled release of isopropyl alcohol. In this process, we devised and implemented novel release valve and steering mechanisms culminating in a surfer with distinct capabilities. Our robot measures about 110 mm in length and can travel as fast as 0.8 body length per second. Interestingly, we found that the linear speed of the robot follows a 1/3 power law with the release rate of the propellant. Additional maneuverability tests also revealed that the robot is able to withstand 20 mm s −2 in centripetal acceleration while turning. Here, we thoroughly discuss the design, development, performance, overall capabilities, and ultimate limitations of our robotic surfer. 

The Marangoni propulsion of spheres and elliptical disks floating on the air–water interface were studied to understand the effect of particle shape on its motion and its stability at moderate Reynolds numbers. Self-propulsion of the Marangoni surfer was achieved by coating half of the spheres and the elliptical disks with either a solution of soap or isopropyl alcohol (IPA). The presence of the soap or IPA resulted in a surface tension gradient across the particles which propelled the particles in the direction of increasing surface tension. Beyond a critical velocity, a transition was observed from a straight-line motion to a rotational motion. These vortices were observed to shed above a critical Reynolds number resulting in an unbalanced torque that caused the particles to rotate. Increasing the aspect ratio between the major and minor axes of the elliptical disks was found to decrease their stability and greatly enhance their rate of rotation. This was especially true for elliptical disks traveling in a direction parallel to their major axis. The interactions between the particles and the wall of a Petri dish were also studied. Repulsive, concave curvature was found to decrease stability and enhance rotational motion, while attractive, convex curvature was shown to stabilize the straight-line motion of the spheres. For the neutrally buoyant elliptical disks, the presence of the bounding wall was found to greatly stabilize the straight-line motion of the elliptical disks when they were traveling in a direction parallel to their minor axis. 

Abstract We theoretically study forced convection heat transfer from a single particle in uniform laminar flows. Asymptotic limits of small and large Peclet numbers Pe are considered. For Pe≪1 (diffusion-dominated regime) and a constant heat flux boundary condition on the surface of the particle, we derive a closed-form expression for the heat transfer coefficient that is valid for arbitrary particle shapes and Reynolds numbers, as long as the flow is incompressible. Remarkably, our formula for the average Nusselt number Nu has an identical form to the one obtained by Brenner for a uniform temperature boundary condition (Chem. Eng. Sci., vol. 18, 1963, pp. 109–122). We also present a framework for calculating the average Nu of axisymmetric and two-dimensional (2D) objects with a constant heat flux surface condition in the limits of Pe≫1 and small or moderate Reynolds numbers. Specific results are presented for the heat transfer from spheroidal particles in Stokes flow. 

In the study of fluid dynamics and transport phenomena, key quantities of interest are often the force and torque on objects and total rate of heat/mass transfer from them. Conventionally, these integrated quantities are determined by first solving the governing equations for the detailed distribution of the field variables (i.e. velocity, pressure, temperature, concentration, etc.) and then integrating the variables or their derivatives on the surface of the objects. On the other hand, the divergence form of the conservation equations opens the door for establishing integral identities that can be used for directly calculating the integrated quantities without requiring the detailed knowledge of the distribution of the primary variables. This shortcut approach constitutes the idea of the reciprocal theorem, whose closest relative is Green’s second identity, which readers may recall from studies of partial differential equations. Despite its importance and practicality, the theorem may not be so familiar to many in the research community. Ironically, some believe that the extreme simplicity and generality of the theorem are responsible for suppressing its application! In this Perspectives piece, we provide a pedagogical introduction to the concept and application of the reciprocal theorem, with the hope of facilitating its use. Specifically, a brief history on the development of the theorem is given as a background, followed by the discussion of the main ideas in the context of elementary boundary-value problems. After that, we demonstrate how the reciprocal theorem can be utilized to solve fundamental problems in low-Reynolds-number hydrodynamics, aerodynamics, acoustics and heat/mass transfer, including convection. Throughout the article, we strive to make the materials accessible to early career researchers while keeping it interesting for more experienced scientists and engineers.