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| Abstract: In Rayleigh Benard convection, it has been found that the amount of heat passing through the fluid has a power-law dependence on the imposed temperature difference. Modifying this dependence, either enhancing or reducing the heat transfer capability of fluids, is important in many scientific and practical applications. Here, we present a simple means to control the vertical heat transfer in Rayleigh Benard convection by injecting heat through one lateral side of the fluid domain and extracting the same amount of heat from the opposite side. This horizontal heat flux regulates the large-scale circulation, and increases the heat transfer rate in the vertical direction. Our numerical and theoretical studies demonstrate how a classical Rayleigh Benard convection responds to such a perturbation when the system is near or well above the onset of convection. |
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| Abstract: While classic hydrodynamic models predict ordered formations for fish schools, observations show that schools are seemingly disordered. Our experiments on robotic swimmers may help to reconcile this discrepancy by showing that many different formations all emerge spontaneously and are stabilized due to flow interactions. Surprisingly, these locked states extend almost twice as far downstream for laterally displaced swimmers as for those in line. We also observe significant boosts in swimming speed, up to 60% faster than an isolated swimmer, for side-by-side formations. These findings demonstrate that benefits such as group cohesion and speed enhancement arise naturally via flow interactions and for the diverse relative arrangements seen in schools. |
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| Abstract: A single flexible filament can be actuated to escape from the scallop theorem and generate net propulsion at low Reynolds number. In this work, we study the dynamics of a simple boundary-driven multi-filament swimmer, a two-arm clamshell actuated at the hinged point, using a nonlocal slender body approximation with hydrodynamic interactions. We first consider an elastic clamshell consisted of flexible filaments with intrinsic curvature, and then build segmental models consisted of rigid segments connected by different mechanical joints with different forms of response torques. The simplicity of the system allows us to fully explore the effect of various parameters on the swimming performance. Optimal included angles and elastoviscous numbers are identified. The segmental models capture the characteristic dynamics of the elastic clamshell. We further demonstrate how the swimming performance can be significantly enhanced by the asymmetric beating patterns induced by biased torques. |
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| Abstract: Flow in the inverted U-shaped tube of a conventional siphon can be established and maintained only if the tube is filled and closed, so that air does not enter. We report on siphons that operate entirely open to the atmosphere by exploiting surface tension effects. Such capillary siphoning is demonstrated by paper tissue that bridges two containers and conveys water from the upper to the lower. We introduce a more controlled system consisting of grooves in a wetting solid, formed here by pressing together hook-shaped metallic rods. The dependence of flux on siphon geometry is systematically measured, revealing behaviour different from the conventional siphon. The flux saturates when the height difference between the two container’s free surfaces is large; it also has a strong dependence on the climbing height from the source container’s free surface to the apex. A one-dimensional theoretical model is developed, taking into account the capillary pressure due to surface tension, pressure loss due to viscous friction, and driving by gravity. Numerical solutions are in good agreement with experiments, and the model suggests hydraulic interpretations for the observed flux dependence on geometrical parameters. The operating principle and characteristics of capillary siphoning revealed here can inform biological phenomena and engineering applications related to directional fluid transport. |
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| Abstract: Thermal convection of fluid is a more efficient way than diffusion to carry heat from hot sources to cold places. Here, we experimentally study the Rayleigh-Benard convection of aqueous glycerol solution in a cubic cell with suspensions of rod-like particles made of polydimethylsiloxane (PDMS). The particles are inertial due to their large thermal expansion coefficient and finite sizes. The thermal expansion coefficient of the particles is three times larger than that of the background fluid. This contrast makes the suspended particles lighter than the local fluid in hot regions and heavier in cold regions. The heat transport is enhanced at relatively large Rayleigh number (Ra) but reduced at small Ra. We demonstrate that the increase of Nusselt number arises from the particle-boundary layer interactions: the particles act as "active" mixers of the flow and temperature fields across the boundary layers. |
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| Abstract: In cellular vortical flows, namely arrays of counterrotating vortices, short but flexible filaments can show simple random walks through their stretch-coil interactions with flow stagnation points. Here, we study the dynamics of semirigid filaments long enough to broadly sample the vortical field. Using simulation, we find a surprising variety of long-time transport behavior—random walks, ballistic transport, and trapping— depending upon the filament’s relative length and effective flexibility. Moreover, we find that filaments execute L´evy walks whose diffusion exponents generally decrease with increasing filament length, until transitioning to Brownian walks. Lyapunov exponents likewise increase with length. Even completely rigid filaments, whose dynamics is finite dimensional, show a surprising variety of transport states and chaos. Fast filament dispersal is related to an underlying geometry of “conveyor belts.” Evidence for these various transport states is found in experiments using arrays of counterrotating rollers, immersed in a fluid and transporting a flexible ribbon. |
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| Abstract: Experiments on autophoretic bimetallic nanorods propelling within a fuel of hydrogen peroxide show that tail-heavy swimmers preferentially orient upwards and ascend along inclined planes. We show that such gravitaxis is strongly facilitated by interactions with solid boundaries, allowing even ultraheavy microswimmers to climb nearly vertical surfaces. Theory and simulations show that the buoyancy or gravitational torque that tends to align the rods is reinforced by a fore-aft drag asymmetry induced by hydrodynamic interactions with the wall. |
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| Abstract: Surface waves called meniscus waves often appear in systems that are close to the capillary length scale. Since the meniscus shape determines the form of the meniscus waves, the resulting streaming circulation has features distinct from those caused by other capillary–gravity waves recently reported in the literature. In the present study, we produce symmetric and antisymmetric meniscus shapes by controlling boundary wettability and excite meniscus waves by oscillating the meniscus vertically. The symmetric and antisymmetric configurations produce different surface capillary–gravity wave modes and streaming flow structures. The root-mean-square speed of the streaming circulation increases with the second power of the forcing amplitude in both configurations. The flow symmetry of streaming circulation is retained under the symmetric meniscus, while it is lost under the antisymmetric meniscus. The streaming circulation pattern beneath the meniscus observed in our experiments is qualitatively explained using the method introduced by Nicolás & Vega and Gordillo & Mujica. |
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| Abstract: We explore the behavior of micron-scale autophoretic Janus (Au/Pt) rods, having various Au/Pt length ratios, swimming near a wall in an imposed background flow. We find that their ability to robustly orient and move upstream, i.e., to rheotax, depends strongly on the Au/Pt ratio, which is easily tunable in synthesis. Numerical simulations of swimming rods actuated by a surface slip show a similar rheotactic tunability when varying the location of the surface slip versus surface drag. The slip location determines whether swimmers are pushers (rear actuated), pullers (front actuated), or in between. Our simulations and modeling show that pullers rheotax most robustly due to their larger tilt angle to the wall, which makes them responsive to flow gradients. Thus, rheotactic response infers the nature of difficult to measure flow fields of an active particle, establishes its dependence on swimmer type, and shows how Janus rods can be tuned for flow responsiveness. [*Editor's Suggestion; *Featured in Physics] |
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| Abstract: The atmospheric ablation of meteoroids is a striking example of the reshaping of a solid object due to its motion through a fluid. Motivated by meteorite samples collected on Earth that suggest fixed orientation during flight—most notably the conical shape of so-called oriented meteorites—we hypothesize that such forms result from an aerodynamic stabilization of posture that may be achieved only by specific shapes. Here, we investigate this issue of flight stability in the parallel context of fluid mechanical erosion of clay bodies in flowing water, which yields shapes resembling oriented meteorites.We conduct laboratory experiments on conical objects freely moving through water and fixed within imposed flows to determine the dependence of orientational stability on shape. During free motion, slender cones undergo postural instabilities, such as inversion and tumbling, and broad or dull forms exhibit oscillatory modes, such as rocking and fluttering. Only intermediate shapes, including the stereotypical form carved by erosion, achieve stable orientation and straight flight with apex leading. We corroborate these findings with systematic measurements of torque and stability potentials across cones of varying apex angle, which furnish a complete map of equilibrium postures and their stability. By showing that the particular conical form carved in unidirectional flows is also posturally stable as a free body in flight, these results suggest a self-consistent picture for the origin of oriented meteorites. |
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| Abstract: Continents exert a thermal blanket effect to the mantle underneath by locally accumulating heat and modifying the flow structures, which in turn affects continent motion. This dynamic feedback is studied numerically with a simplified model of an insulating plate over a thermally convecting fluid with infinite Prandtl number at Rayleigh numbers of the order of 10^6. Several plate–fluid coupling modes are revealed as the plate size varies. In particular, small plates show long durations of stagnancy over cold downwellings. Between long stagnancies, bursts of velocity are observed when the plate rides on a single convection cell. As plate size increases, the coupled system transitions to another type of short-lived stagnancy, in which case hot plumes develop underneath. For an even larger plate, a unidirectional moving mode emerges as the plate modifies impeding flow structures it encounters while maintaining a single convection cell underneath. These identified modes are reminiscent of some real cases of continent–mantle coupling. Results show that the capability of a plate to overcome impeding flow structures increases with plate size, Rayleigh number and intensity of internal heating. Compared to cases with a fixed plate, cases with a freely drifting plate are associated with higher Nusselt number and more convection cells within the flow domain.. |
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| Abstract: Many species of fish and birds travel in groups, yet the role of fluid-mediated interactions in schools and flocks is not fully understood. Previous fluid dynamical models of these collective behaviors assume that all individuals flap identically, whereas animal groups involve variations across members as well as active modifications of wing or fin motions. To study the roles of flapping kinematics and flow interactions, we design a minimal robotic “school” of two hydrofoils swimming in tandem. The flapping kinematics of each foil are independently prescribed and systematically varied, while the forward swimming motions are free and result from the fluid forces. Surprisingly, a pair of uncoordinated foils with dissimilar kinematics can swim together cohesively—without separating or colliding—due to the interaction of the follower with the wake left by the leader. For equal flapping frequencies, the follower experiences stable positions in the leader’s wake, with locations that can be controlled by flapping amplitude and phase. Further, a follower with lower flapping speed can defy expectation and keep up with the leader, whereas a faster-flapping follower can be buffered from collision and oscillate in the leader’s wake. We formulate a reduced-order model which produces remarkable agreement with all experimentally observed modes by relating the follower’s thrust to its flapping speed relative to the wake flow. These results show how flapping kinematics can be used to control locomotion within wakes, and that flow interactions provide a mechanism which promotes group cohesion. |
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| Abstract: The motion of a free-moving plate atop turbulent thermal convection exhibits diverse dynamics that displays characteristics of both deterministic and chaotic motions. Early experiments performed by Zhong and Zhang found two states existing for a plate floating on convective fluid in a rectangular tank. They proposed a piecewise smooth physical model (ZZ model) that successfully captures this transition of states. However, their model was deterministic and therefore could not describe the stochastic behaviors. In this study, we combine the ZZ model with a novel approach that models the stochastic aspects through a variational inequality structure. With the powerful mathematical tools for stochastic variational inequalities, the properties of the Markov process and corresponding Kolmogorov equations could be studied both numerically and analytically. Moreover, this framework also allows one to compute the transition probabilities. Our present work captures the stochastic aspects of the two aforementioned boundary-fluid coupling states, predicts the stochastic behaviors and shows excellent qualitative and quantitative agreement with the experimental data. |
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| Abstract: The swimming direction of biological or artificial microscale swimmers tends to be randomised over long time-scales by thermal fluctuations. Bacteria use various strategies to bias swimming behaviour and achieve directed motion against a flow, maintain alignment with gravity or travel up a chemical gradient. Herein, we explore a purely geometric means of biasing the motion of artificial nanorod swimmers. These artificial swimmers are bimetallic rods, powered by a chemical fuel, which swim on a substrate printed with teardrop-shaped posts. The artificial swimmers are hydrodynamically attracted to the posts, swimming alongside the post perimeter for long times before leaving. The rods experience a higher rate of departure from the higher curvature end of the teardrop shape, thereby introducing a bias into their motion. This bias increases with swimming speed and can be translated into a macroscopic directional motion over long times by using arrays of teardrop-shaped posts aligned along a single direction. This method provides a protocol for concentrating swimmers, sorting swimmers according to different speeds, and could enable artificial swimmers to transport cargo to desired locations. [* Featured on the cover of Soft Matter, 13(27) 2017] |
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| Abstract: Birds have to flap their wings to generate the needed thrust force, which powers them through the air. But how exactly do flapping wings create such force, and at what amplitude and frequency should they operate? These questions have been asked by many researchers. It turns out that much of the secret is hidden in the wake left behind the flapping wing. Exemplified by the study of Andersen et al. (J. Fluid Mech., vol. 812, 2017, R4), close examination of the flow pattern behind a flapping wing will inform us whether the wing is towed by an external force or able to generate a net thrust force by itself. Such studies are much like looking at the footprints of terrestrial animals as we infer their size and weight, figuring out their walking and running gaits. A map that displays the collection of flow patterns after a flapping wing, using flapping frequency and amplitude as the coordinates, offers a full picture of its flying ‘gaits’. |
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| Abstract: Classic models of fish schools and flying formations of birds are built on the hypothesis that the preferred locations of an individual are determined by the flow left by its upstream neighbor. Lighthill posited that arrangements may in fact emerge passively from hydro- or aerodynamic interactions, drawing an analogy to the formation of crystals by intermolecular forces. Here, we carry out physical experiments aimed at testing the Lighthill conjecture and find that self-propelled flapping wings spontaneously assume one of multiple arrangements due to flow interactions.Wings in a tandem pair select the same forward speed, which tends to be faster than a single wing, while maintaining a separation distance that is an integer multiple of the wavelength traced out by each body. When perturbed, these locomotors robustly return to the same arrangement, and direct hydrodynamic force measurements reveal springlike restoring forces that maintain group cohesion. We also use these data to construct an interaction potential, showing how the observed positions of the follower correspond to stable wells in an energy landscape. Flow visualization and vortex-based theoretical models reveal coherent interactions in which the follower surfs on the periodic wake left by the leader. These results indicate that, for the high-Reynolds-number flows characteristic of schools and flocks, collective locomotion at enhanced speed and in orderly formations can emerge from flow interactions alone. If true for larger groups, then the view of collectives as ordered states of matter may prove to be a useful analogy. |
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| Abstract: An object immersed in a fast flow typically experiences fluid forces that increase with the square of speed. Here we explore how this high-Reynolds-number force-speed relationship is affected by unsteady motions of a body. Experiments on disks that are driven to oscillate while progressing through air reveal two distinct regimes: a conventional quadratic relationship for slow oscillations and an anomalous scaling for fast flapping in which the time-averaged drag increases linearly with flow speed. In the linear regime, flow visualization shows that a pair of counterrotating vortices is shed with each oscillation and a model that views a train of such dipoles as a momentum jet reproduces the linearity.We also show that appropriate scaling variables collapse the experimental data from both regimes and for different oscillatory motions into a single drag-speed relationship. These results could provide insight into the aerodynamic resistance incurred by oscillating wings in flight and they suggest that vibrations can be an effective means to actively control the drag on an object. |
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| Abstract: Biological systems often involve the self-assembly of basic components into complex and functioning structures. Artificial systems that mimic such processes can provide a well-controlled setting to explore the principles involved and also synthesize useful micromachines. Our experiments show that immotile, but active, components self-assemble into two types of structure that exhibit the fundamental forms of motility: translation and rotation. Specifically, micron-scale metallic rods are designed to induce extensile surface flows in the presence of a chemical fuel; these rods interact with each other and pair up to form either a swimmer or a rotor. Such pairs can transition reversibly between these two configurations, leading to kinetics reminiscent of bacterial run-and-tumble motion. |
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| Abstract: Enhancing heat transport across a fluid layer is of fundamental interest as well as of great technological importance. For decades, Rayleigh-B\'{e}nard convection has been a paradigm for the study of convective heat transport, and how to improve its overall heat-transfer efficiency is still an open question. Here we report an experimental and numerical study that reveals a novel mechanism that leads to much enhanced heat transport. When vertical partitions are inserted into a convection cell with thin gaps left open between partition walls and the cooling/heating plates, it is found that the convective flow becomes self-organized and more coherent, leading to an unprecedented heat-transport enhancement. In particular, our experiments show that with 6 partition walls inserted the heat flux can be increased by about $30\%$. Numerical simulations show a remarkable heat-flux enhancement of up to 2.3 times (with 28 partition walls) that without any partitions. |
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| Abstract: On flow visualization of around a flapped disk. This publication follows the competition -- the Galley of Fluid Motion -- at the APS/DFD meeting 2014. |
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| Abstract: We investigate a mechanism that effectively transports fluids using vibrational motion imposed onto fluid boundary with anisotropy. In our experiment, two asymmetric, sawtooth-like structures are placed facing each other and form a corrugated fluid channel. This channel is then forced to open and close periodically. Under reciprocal motion, fluid fills in the gap during the expansion phase of the channel and is then forced out during contraction. Since the fluid experiences different impedence when flowing in different directions, the stagnation point that separates flows of two directions changes within each driving period. As a result, fluid is transported unidirectionally. This ratcheting effect of fluid is demonstrated through our measurements and its working principle discussed in some detail. |
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| Abstract: The lateral line of fish includes the canal subsystem that detects hydrodynamic pressure gradients and is thought to be important in swimming behaviors such as rheotaxis and prey tracking. Here, we explore the hypothesis that this sensory system is concentrated at locations where changes in pressure are greatest during motion through water. Using high-fidelity models of rainbow trout, we mimic the flows encountered during swimming while measuring pressure with fine spatial and temporal resolution. The variations in pressure for perturbations in body orientation and for disturbances to the incoming stream are seen to correlate with the sensory network. These findings support a view of the lateral line as a “hydrodynamic antenna” that is configured to retrieve flow signals and also suggest a physical explanation for the nearly universal sensory layout across diverse species. |
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| Abstract: Self-propelled particles can exhibit surprising non-equilibrium behaviors, and how they interact with obstacles or boundaries remains an important open problem. Here we show that chemically propelled micro-rods can be captured, with little change in their speed, into close orbits around solid spheres resting on or near a horizontal plane. We show that this interaction between sphere and particle is short-range, occurring even for spheres smaller than the particle length, and for a variety of sphere materials. We consider a simple model, based on lubrication theory, of a force- and torque-free swimmer driven by a surface slip (the phoretic propulsion mechanism) and moving near a solid surface. The model demonstrates capture, or movement towards the surface, and yields speeds independent of distance. This study reveals the crucial aspects of activity-driven interactions of self-propelled particles with passive objects, and brings into question the use of colloidal tracers as probes of active matter. |
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| Abstract: Erosion of solid material by flowing fluids plays an important role in shaping landforms, and in this natural context is often dictated by processes of high complexity. Here, we examine the coupled evolution of solid shape and fluid flow within the idealized setting of a cylindrical body held against a fast, unidirectional flow, and eroding under the action of fluid shear stress. Experiments and simulations both show self-similar evolution of the body, with an emerging quasi-triangular geometry that is an attractor of the shape dynamics. Our fluid erosion model, based on Prandtl boundary layer theory, yields a scaling law that accurately predicts the body's vanishing rate. Further, a class of exact solutions provides a partial prediction for the body's terminal form as one with a leading surface of uniform shear stress. Our simulations show this predicted geometry to emerge robustly from a range of different initial conditions, and allow us to explore its local stability. The sharp, faceted features of the terminal geometry defy the intuition of erosion as a globally smoothing process. |
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| Abstract: Synthetic microswimmers may someday perform medical and technological tasks, but predicting their motion and dispersion is challenging. Here we show that chemically propelled rods tend to move on a surface along large circles but curiously show stochastic changes in the sign of the orbit curvature. By accounting for fluctuation-driven flipping of slightly curved rods, we obtain analytical predictions for the ensemble behavior in good agreement with our experiments. This shows that minor defects in swimmer shape can yield major long-term effects on macroscopic dispersion. |
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| Abstract: The Applied Mathematics Laboratory is a research laboratory within the Mathematics Department of the Courant Institute. It was established to carry out physical experiments, modeling, and associated numerical studies in a variety of problems of interest to Courant faculty, postdocs, and graduate and undergraduate students. Most of the research to date has involved fluid mechanics, and we focus in this paper on the work that relates to the interaction of fluids with rigid, movable, or flexible bodies. |
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| Abstract: Erosion by flowing fluids carves striking landforms on Earth and also provides important clues to the past and present environments of other worlds. In these processes, solid boundaries both influence and are shaped by the surrounding fluid, but the emergence of morphology as a result of this interaction is not well understood. We study the coevolution of shape and flow in the context of erodible bodies molded from clay and immersed in a fast, unidirectional water flow. Although commonly viewed as a smoothing process,wefind that erosion sculpts pointed and cornerlike features that persist as the solid shrinks.Weexplain these observations using flow visualization and a fluid mechanical model in which the surface shear stress dictates the rate of material removal. Experiments and simulations show that this interaction ultimately leads to selfsimilarly receding boundaries and a unique front surface characterized by nearly uniform shear stress. This tendency toward conformity of stress offers a principle for understanding erosion in more complex geometries and flows, such as those present in nature. |
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| Abstract: In this paper, we present the design of a wireless powering system for ionic polymer metal composites (IPMCs). The system design is motivated by the need for enabling technologies to replicate hovering flight and swimming in biological systems. IPMC wireless powering is achieved by using radio frequency magnetically coupled coils and in-house designed power electronics for low-frequency IPMC actuation. Parameters of the circuit components describing the resonantly coupled coils and the IPMC are experimentally identified. The power transfer from the external power source to the receiver at the IPMC is experimentally analyzed for a broad range of system parameters. Flow visualization and particle image velocimetry are used to ascertain the system capabilities. Moreover, the IPMC vibration in the wireless and wired configurations is compared. |
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| Abstract: Undulatory locomotion of micro-organisms through geometrically complex, fluidic environments is ubiquitous in nature and requires the organism to negotiate both hydrodynamic effects and geometrical constraints. To understand locomotion through such media, we experimentally investigate swimming of the nematode Caenorhabditis elegans through fluid-filled arrays of micro-pillars and conduct numerical simulations based on a mechanical model of the worm that incorporates hydrodynamic and contact interactions with the lattice. We show that the nematode's path, speed and gait are significantly altered by the presence of the obstacles and depend strongly on lattice spacing. These changes and their dependence on lattice spacing are captured, both qualitatively and quantitatively, by our purely mechanical model. Using the model, we demonstrate that purely mechanical interactions between the swimmer and obstacles can produce complex trajectories, gait changes and velocity fluctuations, yielding some of the life-like dynamics exhibited by the real nematode. Our results show that mechanics, rather than biological sensing and behaviour, can explain some of the observed changes in the worm's locomotory dynamics. |
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| Abstract: We study the dynamics of a layer of viscoelastic fluid, in the Stokesian regime, that is driven from below by a 4 x 4 checkerboard pattern of rotating and counter-rotating disks. At low disk rotation rate (low Weissenberg number) the fluid flow response is slaved to the geometry of this forcing and divides into many steadily rotating cells, each contained within invariant manifolds issuing from hyperbolic stagnation points. As the rotation rate increases these fluid cells begin to oscillate periodically in a synchronized fashion. At a yet higher rotation rate, this temporally periodic flow disappears and is replaced by a richer, "turbulent" dynamics where the flow is delocalized from the forcing and has fluid cells that are continuously destroyed and reformed. |
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| Abstract: We explore the stability of flapping flight in a model system that consists of a pyramid-shaped object hovering in a vertically oscillating airflow. Such a flyer not only generates sufficient aerodynamic force to keep aloft but also robustly maintains balance during free flight. Flow visualization reveals that both weight support and orientational stability result from the periodic shedding of vortices. We explain these findings with a model of the flight dynamics, predict increasing stability for higher center of mass, and verify this counterintuitive fact by comparing top- and bottom-heavy flyers. |
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| Abstract: The flapping or bending of a flexible planar structure in a surrounding fluid flow, which includes the flapping of flags and the self-streamlining of flexible bodies, constitutes a central problem in the field of fluid-body interactions. Here we review recent, highly detailed experiments that reveal new nonlinear phenomena in these systems, as well advances in theoretical understanding, resulting in large part from the rapid development of new simulation methods that fully capture the mutual coupling of fluids and flexible solids |
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| Abstract: We investigate force transmission through a layer of shear-thickening fluid, here a concentrated aqueous cornstarch suspension. When a solid body is pushed through this complex fluid and approaches its containing wall, a hardened volume of the suspension is observed that adds to the leading side of the body. This volume leads to an imprint on the wall which is made of molding clay. By studying the geometry of the hardened volume, inferred by the imprint shapes, we find that its geometry is determined by the size and speed of the body. By characterizing the response of the clay to deformation we show that the force transmitted through the suspension to the wall is localized. We also study other aspects of this dynamical hardening of the suspension, such as the effect of the substrate and body shape, and its relaxation as the imposed straining is stopped. This work was highlighted on the cover of Physical Review Letters. |
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| Abstract: To better understand the role of wing and fin flexibility in flapping locomotion, we study through experiment and numerical simulation a freely moving wing that can "pitch" passively as it is actively heaved in a fluid. We observe a range of flapping frequencies corresponding to large horizontal velocities, a regime of underperformance relative to a clamped nonpitching flapping wing, and a surprising, hysteretic regime in which the flapping wing can move horizontally in either direction !despite left/right symmetry being broken by the specific mode of pitching. The horizontal velocity is shown to peak when the flapping frequency is near the immersed system's resonant frequency. Unlike for the clamped wing, we find that locomotion is achieved by vertically flapped symmetric wings with even the slightest pitching flexibility, and the system exhibits a continuous departure from the Stokesian regime. The phase difference between the vertical heaving motion and consequent pitching changes continuously with the flapping frequency, and the direction reversal is found to correspond to a critical phase relationship. Finally, we show a transition from coherent to chaotic motion by increasing the wing's aspect ratio, and then a return to coherence for flapping bodies with circular cross section. |
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| Abstract: We investigate the dynamics of rigid bodies (hollow 'pyramids') placed within a background airflow, oscillating with zero mean. The asymmetry of the body introduces a net upward force. We find that when the amplitude of the airflow is above a threshold, the net lift exceeds the weight and the object starts to hover. Our results show that the objects hover at far smaller air amplitudes than would be required by a quasi-steady theory, although this theory accounts qualitatively for the behaviour of the system as the body mass becomes small. |
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| Note: This work was selected by Physics Today and published in the section "Back Scatter." |
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| Abstract: In aggregates of objects moving through a fluid, bodies downstream of a leader generally experience reduced drag force. This conventional drafting holds for objects of fixed shape, but interactions of deformable bodies in a flow are poorly understood, as in schools of fish. In our experiments on ``schooling" flapping flags we find that it is the leader of a group who enjoys a significant drag reduction (of up to 50 %), while the downstream flag suffers a drag increase. This counterintuitive inverted drag relationship is rationalized by dissecting the mutual influence of shape and flow in determining drag. Inverted drafting has never been observed with rigid bodies, apparently due to the inability to deform in response to the altered flow field of neighbors. This work was highlighted on the cover of Phys. Rev. Lett. (Nov. 7, 2008), on the backcover of Physics Today's "Back Scatter" (Nov. 2008), in the "Research Highlights" of journal Nature (London, v456, p284, 2008) and in Economist (London, Nov.27). |
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| Abstract: We investigate the dynamics of a thermally convecting fluid as it interacts with freely moving solid objects. This is a previously unexplored paradigm of many-body interactions mediated by thermal convection, which gives rise to surprising robust oscillations between di erent large-scale circulations. Once begun, this process repeats cyclically, with the collection of spheres entrained and packed from one side of the convection cell to the other. The frequency of the cycle is highest when the spheres occupy about half of the cell bottom and their size coincides with the thickness of the thermal boundary layer. This phenomenon shows that a deformable mass can stimulate a turbulent, thermally convecting fluid into oscillation, a collective behavior that may be found in nature. This work was highlighted by Phys. Rev. Focus, New Scientist, and a few other sci-news sources. |
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| Abstract: We construct a valveless pump consisting of a section of elastic tube and a section of rigid tube connected in a closed loop and filled with water. Periodically squeezing the elastic tube at an asymmetric location generates a flow of water around the tubes. This effect, called the Liebau phenomenon or valveless pumping, has been known for some time, but is still poorly understood. We study the flow rates for various squeezing locations, frequencies, and elastic tube rigidities. To understand how valveless pumping works, we formulate a simple model that can be described by coupled ordinary differential equations. The time series of flow velocities generated by the model are qualitatively and quantitatively similar to those seen in the experiment. The model provides a physical explanation of valveless pumping, and it allows us to identify the essential pumping mechanisms. * In memory of Dr. Tom Bringley (1981-2008), who fought cancer for three years with great courage and dignity. It was our privilege to work with this optimistic, original, strong and very friendly young man. |
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| Abstract: Motivated by the swimming and flying locomotion found in the biological world, we perform laboratory experiments aimed to understand the basic thrust-generation mechanism through the flapping of thin structures. We first focus on the passive dynamics of flexible bodies that interact with the surrounding high speed flows. The emerging dynamical states are compared with the swimming modes of fish. We further investigate the self-sustained forward motion of a flat plate -- a prototypical wing or fin -- that is flapped up and down in a fluid. Its forward locomoting speed is sensitively determined by its geometry and flapping frequency. A scaling analysis is proposed to explain such dependences. Moreover, we also explore possible scenarios to increase the forward speed by incorporating wing flexibility, passive pitching and asymmetry in the design of our prototypical wings. The ultimate goal of our investigation is to find the minimum wing design that still ensures efficient thrust generation. Insights gained from this study would help us further appreciate and understand the subtle differences among all the modes and controls used in animal locomotion. |
a free boundary interacts with a thermally convecting fluid, click to view pdf Jun Zhang and Jin-Qiang Zhong submitted as an entry for "Gallery of Fluid Motion" to the APS/DFD meeting, nov., (2007) |
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| Abstract: Based on our previous experimental study, we present a one-dimensional, phenomenological model of a thermal blanket floating on the upper surface of a thermally convecting fluid. The model captures the most important interactions between the floating solid and the fluid underneath. By the thermal blanketing effect, the presence of the solid plate modifies the flow structure below; in turn, the flow exerts a viscous drag that causes the floating boundary to move. An oscillatory state and a trapped state are found in this model, which is in excellent agreement with experimental observations. The model also offers details on the transition between the states, and gives useful insights on this coupled system without the need for full-scale simulations. |
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| Abstract: We study experimentally the dynamical states of a freely-moving, floating heat blanket that couples with a thermally convective fluid. The floating boundary modifies the large-scale flow pattern in the bulk and destabilizes the coupled system, leading to spontaneous oscillations. The system makes a transition from the oscillatory state to a weakly confined state as the moving boundary exceeds a critical size. In the latter state, the moving boundary roams about the center of the convection cell and executes random excursions due to nearby passing thermal plumes. To understand the observed states and the transition, we provide a low-dimensional model that appears to capture the underlying mechanism of the coupled system. |
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| Abstract: We study the nature of surface waves on a semi-toroidal ring of water. We create this specific fluid shape by patterning a glass plate with a hydrophobic film, which confines the fluid to a precise geometric region. To excite the system, the supporting plate is vibrated up and down, thus accelerating/decelerating the fluid ring along its toroidal axis. When the amplitude of the driving acceleration is sufficiently large, the semi-toroidal surface becomes unstable to azimuthal and radial waves. We investigate the dependence of the diverent surface wave patterns on both driving amplitude and frequency. |
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| Abstract: In a rotational geometry, we study the unidirectional forward motion of a symmetric wing that is flapped vertically at frequency f and amplitude a. We find that, a combined dimensionless parameter from the wing geometry (length L, thickness \delta and chord c) and flapping amplitude, \alpha, uniquely determines the forward flight speed. This scaling relationship is explained by our quasi-steady and quasi-two-dimensional model. We then apply our results from the rotational geometry to a translational forward flight and compare the outcome with biological locomotion. In particular, the Strouhal number (St = af/U) for a load-free wing is found in the range of 0.30. We further investigate the so-called ground effect, as the wing flaps close to the horizontal boundaries, which increases the forward flight speed. |
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| Abstract: Small flexible bodies are observed to hover in an oscillating air column. The air is driven by a large speaker at frequencies in the range 1065 Hz at amplitudes 15 cm. The bodies are made of stiffened tissue paper, bent to form an array of four wings, symmetric about a vertical axis. The flapping of the wings, driven by the oscillating flow, leads to stable hovering. The hovering position of the body is unstable under free fall in the absence of the airflow. Measurements of the minimum flow amplitude as a function of flow frequency were performed for a range of self-similar bodies of the same material. The optimal frequency for hovering is found to vary inversely with the size. We suggest, on the basis of flow visualization, that hovering of such bodies in an oscillating flow depends upon a process of vortex shedding closely analogous to that of an active flapper in otherwise still air. A simple inviscid model is developed illustrating some of the observed properties of flexible passive hoverers at high Reynolds number. |
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| Abstract: We study the behavior of an elastic loop in a fast flowing soap film. The loop is wetted into the film and is held fixed at a single point against the oncoming flow. We interpret this system as a 2D closed flexible body moving in a 2D viscous flow. The loop is distended by the flow, and above a velocity threshold of the soap film it begins to oscillate. The horizontal motion of the loop centroid can be accounted for as a simple harmonic oscillator driven by the drag force on the loop, with frequency linearly proportional to the flow velocity. We also investigate the morphology of the elastic loop under fluid drag and compare the result with other instances of flexible bodies moving in a laminar fluid. |
the dynamics of a flexible loop in a quasi-2d flow, click to view pdf K. Mareck, S. Jung, M. Shelley and Jun Zhang Physics of Fluids, 18, 091112 (2006) |
| No abstract for this work: it was selected by a panel of judges and published in the "Gallery of Fluid Motion" |
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| Abstract: We study the dynamics of a rigid, symmetric wing that is flapped vertically in a fluid. The motion of the wing in the horizontal direction is not constrained. Above a critical flapping frequency, forward flight arises as the wing accelerates to a terminal state of constant speed. We describe a number of measurements which supplement our previous work. These include (a) a study of the initial transition to forward flight near the onset of the instability, (b) the separate effects of flapping amplitude and frequency, (c) the effect of wing thickness, (d) the effect of asymmetry of the wing planform, and (e) the response of the wing to an added resistance. Our results emphasize the robustness of the mechanisms determining the forward flight speed as observed in our previous study. |
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| Abstract: In thermal convection, coherent flow structures emerge at high Rayleigh numbers as a result of intrinsic hydrodynamic instability and self-organization. They range from small-scale thermal plumes that are produced near both the top and the bottom boundaries to large-scale circulations across the entire convective volume. These flow structures exert viscous forces upon any boundary. Such forces will affect a boundary which is free to deform or change position. In our experiment, we study the dynamics of a free boundary that floats on the upper surface of a convective fluid. This seemingly passive boundary is subjected solely to viscous stress underneath. However, the boundary thermally insulates the fluid, modifying the bulk flow. As a consequence, the interaction between the free boundary and the convective flows results in a regular oscillation. We report here some aspects of the fluid dynamics and discuss possible links between our experiment and continental drift. |
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| Abstract: We study the dynamics of heavy flexible sheets in a water flow, both to understand flapping of flags, and for its relevance to underwater animal locomotion. We find that the sheet can sharply transition from a straight state aligned with the flow, to a periodic flapping state, with bending waves traveling down the flag. We use a simple analytical model to understand the effect of fluid and structure inertia and elasticity. The model predicts a bifurcation with increasing flow speed, agreeing well with previous experiments in air and soap-films, but showing quantitative differences with our particular experiment. This work was highlighted by New Scientist. |
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| Abstract: The locomotion of most fish and birds is effected by flapping wings or fins transverse to the direction of travel. According to classical inviscid aerodynamic theory, a flapping wing translating at fixed speed can generate a propulsive force. In steady forward flight, this thrust is balanced by drag. But when the Reynolds number is small, viscous forces dominate, reciprocal flapping motions are ineffective, and the translating wing can only experience a net drag. Our experimental study bridges the two realms of large and small Reynolds number and examines the transition to forward flapping flight. at intermediate Reynolds numbers, the range relevant to swimming and flying of small organisms. We study experimentally the dynamics of a wing that is .flapped. up and down but is free to move either forwards or backwards. We show that flapping flight occurs abruptly at a critical flapping frequency as a symmetry-breaking bifurcation. Beyond this bifurcation, the speed of the wing increases linearly with the flapping frequency. The experiment establishes a clear demarcation between the different strategies of locomotion at large and small Reynolds number. Commentary on this work by Michael Hopkin that appeared in Nature: Nature, 429, 147 (2004) |
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| Abstract: Recent work in bio-fluid dynamics has studied the relation of fluid drag to flow speed for flexible organic structures, such as tree leaves, seaweed, and coral beds, and found a reduction in drag growth due to body reconfiguration with increasing flow speed. Our theoretical and experimental work isolates the role of elastic bending in this process. Using a flexible glass fibre wetted into a vertical soap-film tunnel, we identify a transition in flow speed beyond which fluid forces dominate the elastic response, and yield large deformation of the fibre that greatly reduce drag. We construct free-streamline models that couple fluid and elastic forces and solve them in an efficient numerical scheme. Shape self-similarity emerges, with a scaling set by the balance of forces in a small "tip region" about the flow's stagnation point. The result is a transition from the classical U^2 drag scaling of rigid bodies to a U^4/3 drag law. The drag scaling is derived from an asymptotic expansion in the length scale of similarity, and it is found that the tip region induces the far-field behavior. The drag law persists, with a simple modification, under variations of the model suggested by the experiment, such as the addition of flow tunnel walls, and a back pressure in the wake. |
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| Abstract: The classical theory of high-speed flow predicts that a moving rigid object experiences a drag proportional to the square of its speed. However, this reasoning does not apply if the object in the flow is flexible, because its shape then becomes a function of its speed -- for example, the rolling up of broad tree leaves in a stiff wind. The reconfiguration of bodies by fluid forces is common in nature, and can result in a substantial drag reduction that is beneficial for many organisms. Experimental studies of such flow structure interactions generally lack a theoretical interpretation that unifies the body and flow mechanics. Here we use a flexible fibre immersed in a flowing soap film to measure the drag reduction that arises from bending of the fibre by the flow. Using a model that couples hydrodynamics to bending, we predict a reduced drag growth compared to the classical theory. The fibre undergoes a bending transition, producing shapes that are self-similar; for such configurations, the drag scales with the length of self-similarity, rather than the fibre profile width. These predictions are supported by our experimental data. Commentary article on this work by Victor Steinberg that appeared in Nature: Bend and survive, Nature, 420, 479 (2002). It was also highlighted in New York Times. |
flexible threads in a flowing soap film, click to view pdf Jun Zhang Physics of Fluids, 13(9), S15 (2001) |
| No abstract for this work: published as an entry in session "Gallery of Fluid Motion" |
flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind, click to view pdf Jun Zhang, Stephen Childress, Albert Libchaber, and Michael Shelley Nature, 408, 835 (2000) |
| Abstract: The dynamics of swimming fish and flapping flags involves a complicated interaction of their deformable shapes with the surrounding fluid flow. Even in the passive case of a flag, the flag exerts forces on the fluid through its own inertia, elastic responses, and is likewise acted on by hydrodynamic pressure and drag. But such couplings are not well understood. Here we study these interactions experimentally, using an analogous system of flexible filaments in flowing soap films. We find that, for a single filament (or 'flag') held at its upstream end and otherwise unconstrained, there are two distinct, stable dynamical states. The first is a stretched-straight state: the filament is immobile and aligned in the flow direction. The existence of this state seems to refute the common belief that a flag is always unstable and will flap. The second is the flapping state: the filament executes a sinuous motion in a manner akin to the flapping of a flag in the wind. We study further the hydrodynamically coupled interaction between two such filaments, and demonstrate the existence of four different dynamical states. Commentary article on this work by Greg Huber that appeared in Nature: Swimming in flatsea, Nature 408, 777 (2000). It was also highlighted by a few popular science magzines. |
periodic boundary motion in thermal turbulence, click to view pdf Jun Zhang, Albert Libchaber Phys. Rev. Lett., 84, 4361 (2000) |
| Abstract: A free-floating plate is introduced in a Bnard convection cell with an open surface. It partially covers the cell and distorts the local heat flux, inducing a coherent flow that in turn moves the plate. Remarkably, the plate can be driven to a periodic motion even under the action of a turbulent fluid. The period of the oscillation depends on the coverage ratio, and on the Rayleigh number of the convective system. The plate oscillatory behavior observed in this experiment may be related to a geological model, in which continents drift in a quasiperiodic fashion. |
non-Boussinesq effect: asymmetric velocity profiles in thermal convection, click to view pdf Jun Zhang, S. Childress, and A. Libchaber Physics of Fluids 10, 1534 (1998) |
| Abstract: In thermal convection at high Rayleigh numbers, in the hard turbulent regime, a large scale flew is present. When the viscosity of the fluid strongly depends on temperature, the top-bottom symmetry is broken. In addition to the asymmetric temperature profile across the convection cell, the velocity profiles near the plate boundaries show dramatic difference from the symmetric case. We report here that the second derivative of the velocity profiles are of opposite signs in the thermal sublayers, through measurements derived from the power spectrum of temperature time-series. As a result, the stress rate applied at the plates is maintained constant within a factor of 3, while the viscosity changes by a factor of 53, in qualitative agreement with previous theory. |
non-Boussinesq effect: thermal convection with broken symmetry, click to view pdf Jun Zhang, S. Childress, and A. Libchaber Physics of Fluids 9, 1034 (1997) |
| Abstract: We investigate large Rayleigh number (106-109) and large Prandtl number (102-103) thermal convection in glycerol in an aspect ratio one cubic cell. The kinematic viscosity of the fluid strongly depends upon the temperature. The symmetry between the top and bottom boundary layers is thus broken, the so-called non-Boussinesq regime. In a previous paper Wu and Libchaber have proposed that in such a state the two thermal boundary layers adjust their length scales so that the mean hot and cold temperature fluctuations are equal in the center of the cell. We confirm this equality. A simplified two-dimensional model for the mean center temperature based on an equation for the thermal boundary layer is presented and compared with the experimental results. The conclusion is that the central temperature adjusts itself so that the heat fluxes from the boundary layers are equal, temperature fluctuations at the center symmetrical, at a cost of very different temperature drops and Rayleigh number for each boundary. |
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