Optimal concentrations in transport systems

Many biological and man-made systems rely on transport systems for the distribution of material, for example matter and energy. Material transfer in these systems is determined by the flow rate and the concentration of material. While the most concentrated solutions offer the greatest potential in terms of material transfer, impedance typically increases with concentration, thus making them the most difficult to transport. We develop a general framework for describing systems for which impedance increases with concentration, and consider material flow in four different natural systems: blood flow in vertebrates, sugar transport in vascular plants and two modes of nectar drinking in birds and insects. The model provides a simple method for determining the optimum concentration in these systems. Comparing the model predictions with experimental data from more than 100 animal and plant species, we find that the simple model rationalizes the observed concentrations and impedances. The model provides a universal framework for studying flows impeded by concentration, and yields insight into optimization in engineered systems, such as traffic flow.

See paper:  Jensen, Kim, Holbrook and Bush (2013)

The dynamics of coughing and sneezing


Respiratory events such as exhalations or  more violent coughs and sneezes are key in transferring respiratory diseases between infectious and susceptible individuals. We present the results of a combined experimental and theoretical investigation of the fluid dynamics of such violent expiratory events. Direct observation reveals that such flows are multiphase turbulent buoyant clouds with suspended droplets of various sizes. Our observations guide the development of an accompanying theoretical model in which pathogen-bearing droplets interact with a turbulent buoyant momentum puff. The  range of validity of our theoretical model is explored experimentally. Our study highlights the importance of the multiphase nature of respiratory clouds in extending the range of respiratory pathogens.
See Press and amusing video.  MIT News piece here.

Cocktail boats: on bugs and beverages

A fleet of cocktail boats (right) in dry dock, being prepared for launch.

A water-walking bug propels itself with a chemically-induced surface tension gradient.

Cocktail boats take their inspiration from water-walking insects that employ Marangoni propulsion. As an emergency escape mechanism, certain water-walking insects propel  themselves across the surface by generating chemically-induced surface-tension gradients (left).

The cocktail boat (right) floats at the surface of one’s drink, propelled forward by the surface stress generated by alcohol leaking out of its trailing edge. Their utility as a drink accessory in high-end restaurants is currently being explored.

See paper: Burton, Cheng, Vega, Andres and Bush (2013)

PRESS:  Prism Magazine , Wired

Below: a cocktail boats sets sail in a Martini glass.

Can flexibility help you float?

We consider the role of flexibility in the weight-bearing characteristics of bodies floating at an interface. Specifically, we develop a theoretical model for a two- dimensional thin floating plate that yields the maximum stable plate load and optimal stiffness for weight support. Plates small relative to the capillary length are primarily supported by surface tension, and their weight-bearing potential does not benefit from flexibility. Above a critical size comparable to the capillary length, flexibility assists interfacial flotation. For plates on the order of and larger than the capillary length, deflection from an initially flat shape increases the force resulting from hydrostatic pressure, allowing the plate to support a greater load. In this large plate limit, the shape that bears the most weight is a semicircle, which displaces the most fluid above the plate for a fixed plate length. Exact results for maximum weight-bearing plate shapes are compared to analytic approximations made in the limits of large and small plate sizes. The value of flexibility for floating to a number of biological organisms is discussed in light of our study.

See paper here:  Burton & Bush (2012)

Nectar loading by hummingbirds

We present the results of a combined experimental and theoretical investigation of the dynamics of drinking in ruby-throated hummingbirds. In vivo observations reveal elastocapillary deformation of the hummingbird’s tongue and capillary suction along its length. By developing a theoretical model for the hummingbird’s drinking process, we investigate how the elastocapillarity affects the energy intake rate of the bird and how its open tongue geometry reduces resistance to nectar uptake. We note that the tongue flexibility is beneficial for accessing, transporting and unloading the nectar. We demonstrate that the hummingbird can attain the fastest nectar uptake when its tongue is roughly semicircular. Finally, we assess the relative importance of capillary suction and a recently proposed fluid trapping mechanism, and conclude that the former is important in many natural settings.

See paper: Kim, Peaudecerf, Baldwin & Bush, Proc Roy Soc B (2012) .

Drinking strategies in nature


In this special edition of the Journal of Fluid Mechanics dedicated to Tim Pedley on the occasion of his 70th birthday, we examine the fluid mechanics of drinking in nature. We classify the drinking strategies of a broad range of creatures according to the principal forces involved, and present physical pictures for each style. Simple scaling arguments are developed and tested against existing data. While suction is the most common drinking strategy, various alternative styles have evolved among creatures whose morphological, physiological and environmental constraints preclude it. Particular attention is given to creatures small relative to the capillary length, whose drinking styles rely on relatively subtle interfacial effects. We also discuss attempts to rationalize various drinking strategies through consideration of constrained optimization problems. Some biomimetic applications are discussed.

See paper:  Kim & Bush, JFM (2012).



A number of different drinking styles arising in the natural world.

Optimal concentrations in nectar feeding

Nectar drinkers must feed quickly and efficiently due to the threat of predation. While the sweetest nectar offers the greatest energetic rewards, the sharp increase of viscosity with sugar concentration makes it the most difficult to transport. We here demonstrate that the sugar concentration that optimizes energy transport depends exclusively on the drinking technique employed. We identify three nectar drinking techniques: active suction, capillary suction, and viscous dipping. For each, we deduce the dependence of the volume intake rate on the nectar viscosity and thus infer an optimal sugar concentration consistent with laboratory measurements. Our results provide the first rationale for why suction feeders typically pollinate flowers with lower sugar concentration nectar than their counterparts that use viscous dipping.

See paper:  Kim, Gilet and Bush (2011).

PRESS:  MIT News ,  BBC News


Propulsion by directional adhesion

The rough integument of water-walking arthropods is well-known to be responsible for their water- repellency; however, water-repellent surfaces generally experience reduced traction at an air– water interface. A conundrum then arises as to how such creatures generate significant propulsive forces while retaining their water-repellency. We here demonstrate through a series of experiments that they do so by virtue of the detailed form of their integument; specifically, their tilted, flexible hairs interact with the free surface to generate directionally anisotropic adhesive forces that facilitate locomotion. We thus provide new rationale for the fundamental topological difference in the roughness on plants and water-walking arthropods, and suggest new directions for the design and fabrication of unidirectional superhydrophobic surfaces. Indeed, the ingenious methods employed by insects and spiders to move across a water surface rely on microphysics that is of little use to larger water walkers but of considerable interest to the microfluidics community.

See paper: Prakash & Bush (2011) .


Grabbing water: the elastocapillary pipette

Floating flowers inspired the elastocapillary pipette.

Grabbing water with an edible flower.

We introduce a novel technique for grabbing water with a flexible solid. This new passive pipetting mechanism was inspired by floating flowers and relies purely on the coupling of the elasticity of thin plates and the hydrodynamic forces at the liquid interface. Developing a theoretical model has enabled us to design petal-shaped objects with maximum grabbing capacity.

See: Reis, Hure, Jung, Bush & Clanet (2010)

The folding of flowers represents an example of capillary origami in nature, a few examples of which are discussed in Reis, Jung, James, Clanet and Bush (2009) .


The elastocapillary pipette is being adapted for use in the culinary arts, as a means of serving small volumes of liqueurs with flowers composed of edible gels (right).

PRESS:  Highlights in Chemical Technology

Can flexibility help you fly?

The influence of flexibility on the flight of autorotating winged seedpods is examined through an experimental investigation of tumbling rectangular paper strips freely falling in air. Our results suggest the existence of a critical length above which the wing bends. We develop a theoretical model that demonstrates that this buckling is prompted by inertial forces associated with the tumbling motion, and yields a buckling criterion consistent with that observed. We further develop a reduced model for the flight dynamics of flexible tumbling wings that illustrates the effect of aeroelastic coupling on flight characteristics and rationalizes experimentally observed variations in the wing’s falling speed and range.

See paper here: Tam, Bush, Robitaille and Kudrolli (2010)

Biomimetic water-walking robots

Robostrider, the first water-walking robot, confronts his natural counterpart.

We report recent efforts in the design and construction of water-walking machines inspired by insects and spiders. The fundamental physical constraints on the size, proportion and dynamics of natural water-walkers are enumerated and used as design criteria for analogous mechanical devices. We report devices capable of rowing along the surface, leaping off the surface and climbing menisci by deforming the free surface. The most critical design constraint is that the devices be lightweight and non-wetting. Microscale manufacturing techniques and new man-made materials such as hydrophobic coatings and thermally actuated wires are implemented. Using high-speed cinematography and flow visualization, we compare the functionality and dynamics of our devices with those of their natural counterparts.

See Hu, Prakash,_Chan and_Bush (2010)

PRESS:  Wikipedia ,  BBC News

The hydrodynamics of water-walking arthropods

We present the results of a combined experimental and theoretical investigation of the dynamics of water-walking insects and spiders. Using high-speed videography, we describe their numerous gaits, some analogous to those of their terrestrial counterparts, others specialized for life at the interface. The critical role of the rough surface of these water walkers in both floatation and propulsion is demonstrated. Their waxy, hairy surface ensures that their legs remain in a water-repellent state, that the bulk of their leg is not wetted, but rather contact with the water arises exclusively through individual hairs. Maintaining this water-repellent state requires that the speed of their driving legs does not exceed a critical wetting speed. Flow visualization reveals that the wakes of most water walkers are characterized by a series of coherent subsurface vortices shed by the driving stroke. A theoretical framework is developed in order to describe the propulsion in terms of the transfer of forces and momentum between the creature and its environment. The application of the conservation of momentum to biolocomotion at the interface confirms that the propulsion of water walkers may be rationalized in terms of the subsurface flows generated by their driving stroke. The two principal modes of propulsion available to small water walkers are elucidated. At driving leg speeds in excess of the capillary wave speed, macroscopic curvature forces are generated by deforming the meniscus, and the surface behaves effectively as a trampoline. For slower speeds, the drivinglegs need not substantially deform the surface but may instead simply brush it: the resulting contact or viscous forces acting on the leg hairs crossing the interface serve to propel the creature forward.

See paper here: Hu & Bush (2010)



Capillary feeding in shorebirds

The Phalarope seeks its prey at the water surface. PHOTO CREDIT: Rainey Shuler

The phalarope captures its prey in a droplet, then transports it mouthwards by a series of tweezer-like beak motions. PHOTO CREDIT: Rainey Schuler

A certain class of shorebirds have an extremely clever feeding mechanism. By swimming in a circle, the phalarope generates a vortex that sweeps its prey towards the surface, like tea leaves in a stirred tea cup (see video below). Then, by dipping its beak into the water and withdrawing it, the bird captures its prey inside a droplet pinned between its upper and lower bills. By moving its beak in a tweezer -like succession of openings and closings, the phalarope transports the drop and the desired prey from its beak tip to its mouth. The ability to transport fluid in this fashion was demonstrated in a series of analogue experiments (see second video below).


We here present the results of a combined experimental and theoretical investigation of this subtle feeding mechanism.  Our study provides a simple physical rationalization for the observation of multiple mandibular spreading cycles in feeding, and highlights the critical role of contact angle resistance. We also find a unique geometrical optima in beak opening and closing angles for the most efficient drop transport. This mechanism would seem to be a unique natural example of directed drop transport via contact angle history. This capillary ratchet mechanism may also find applications in microscale fluid transport, such as valveless pumping of fluid drops.

REFERENCE [1] Surface Tension Transport of Prey by Feeding Shorebirds: The Capillary Ratchet, M. Prakash, D. Quere and J. W. M. Bush, Science, Vol. 320 (5878), 931-934, 16 May 2008. pdf

[2] BIOPHYSICS COMMENTARY: The Intrigue of the Interface, Mark Denny, Science, Vol. 320 (5878), pp. 886, 16 May. 2008 pdf

[3] Bush, J.W.M., Peaudecerf, F., Prakash, M., and Quere, D., 2010. On a tweezer for droplets. Advances in Colloid and Interface Science, 161, 10-14. pdf

[4] POUR NOS AMIS FRANCAIS: Quere, D., Prakash, M., Bush, J.W.M., 2011. Prises de bec chez les phalaropes. Reflets de la Physique, Vol. 15, 11-14. pdf

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Water-repellency in biology

Inverted microscope image reveals the nature of the contact between the insect and the interface.

We develop a coherent view of the form and function of the integument of water-walking insects and spiders by reviewing biological work on the subject in light of recent advances in surface science. Particular attention is given to understanding the complex nature of the interaction between water-walking arthropods and the air–water surface. We begin with a discussion of the fundamental principles of surface tension and the wetting of a solid by a fluid. These basic concepts are applied to rationalize the form of various body parts of water-walking arthropods according to their function. Particular attention is given to the influence of surface roughness on water-repellency, a critical feature of water-walkers that enables them to avoid entrapment at the interface, survive the impact of raindrops and breathe if submerged. The dynamic roles of specific surface features in thrust generation, drag reduction and anchoring on the free surface are considered. New imaging techniques that promise important insights into this class of problems are discussed. Finally, we highlight the interplay between the biology, physics and engineering communities responsible for the rapid recent advances in the biomimetic design of smart, water- repellent surfaces.

See paper:  Bush, Hu & Prakash (2008).


Water snail locomotion: underwater crawling


Land snails move via adhesive locomotion. Through muscular contraction and expansion of their foot, they transmit waves of shear stress through a thin layer of mucus onto a solid substrate. Since a free surface cannot support shear stress, adhesive locomotion is not a viable propulsion mechanism for water snails that travel inverted beneath the free surface. Nevertheless, the motion of the freshwater snail, Sorbeoconcha physidae, is reminiscent of that of its terrestrial counterparts, being generated by the undulation of the snail foot that is separated from the free surface by a thin layer of mucus. Here, a lubrication model is used to describe the mucus flow in the limit of small-amplitude interfacial deformations. By assuming the shape of the snail foot to be a traveling sine wave and the mucus to be Newtonian, an evolution equation for the interface shape is obtained and the resulting propulsive force on the snail is calculated. This propulsive force is found to be nonzero for moderate values of the capillary number but vanishes in the limits of high and low capillary number. Physically, this force arises because the snail’s foot deforms the free surface, thereby generating curvature pressures and lubrication flows inside the mucus layer that couple to the topography of the foot.

See paper here: Lee, Bush, Hosoi & Lauga (2008).

SELECT PRESS:  NBC News , Nature News


Flow visualization with TMV

The wakes of swimming fish are revealed through the flow visualization technique developed herein.

TMV visualization of the flow around an idling fish. Note the signature of intake into its mouth.

A flow visualization technique using dilute solutions of tobacco mosaic virus (TMV) is described. Rod-shaped TMV-particles align with shear, an effect that produces a luminous interference pattern when the TMV solution is viewed between crossed polarizers. Attractive features of this technique are that it is both transparent to the naked eye and benign to fish. We use it here to visualize the evolution and decay of the flows that they produce. We also report that dilute solutions of Kalliroscope are moderately birefringent and so may similarly be used for qualitative in situ flow visualizations.

Images presented here:  Hu, Goreau & Bush, Gallery of Fluid Motion (2005) .

See paper here: Hu, Goreau and Bush (2008)

Walking on water: Interfacial biolocomotion

We consider the hydrodynamics of creatures capable of sustaining themselves on the water surface by means other than flotation. Particular attention is given to classifying water walkers according to their principal means of weight support and lateral propulsion. The various propulsion mechanisms are rationalized through consideration of energetics, hydrodynamic forces applied, or momentum transferred by the driving stroke. We review previous research in this area and suggest directions for future work. Special attention is given to introductory discussions of problems not previously treated in the fluid mechanics literature, with hopes of attracting physicists, applied mathematicians, and engineers to this relatively unexplored area of fluid mechanics.

See papers:  Bush & Hu, Ann. Rev. Fluid Dynamics (2006) and  Bush & Hu, Physics Today (2010) .

This work has prompted the development of a class of water-walking robots.

PRESS:  Life’s Little Mysteries


Underwater breathing via plastron respiration


“Errors like straws upon the surface flow: Who would search for pearls must dive below.”    –  John Dryden

The rough, hairy surfaces of many insects and spiders serve to render them water-repellent, allowing them to walk on water and survive in case of accidental submergence. Most such creatures take in oxygen through spiracles on their body cavity. We explore here the manner in which some creatures have adapted to life below the interface, surviving by virtue of a thin air layer trapped along their exteriors. The diffusion of dissolved oxygen from the ambient water may allow this layer to function as a respiratory bubble or ‘plastron’, and so enable certain species to remain underwater indefinitely. Images of plastrons on a submerged waterboatman and spider are provided below. By coupling the bubble mechanics, surface and gas-phase chemistry, we enumerate criteria for plastron viability and thereby deduce the range of environmental conditions and dive depths over which plastron breathers can survive. The results of our study are reported in  Flynn & Bush (2008).

SELECTED PRESS:  New York Times , National Geographic , Science News , Boston Globe




A bug uprising: meniscus-climbing insects


“I was stunned by the perfection of the insects”.   – Pablo Neruda

1 - Meniscus at the surface of a pond


Wetting climbers

From our perspective, the surface of a pond appears to be flat; however, there is millimetric topography in the form of menisci that  arise where the water surface meets land, floating objects or emergent vegetation (1). To millimetric water-walking creatures, these menisci can appear as frictionless mountains that they may be unable to climb using their ordinary means of propulsion.

The waterlily leaf beetle Pyrrhalta feeds upon the plant for which it is named (2).  The larva is a poor swimmer, making  travel between lily pads difficult.  It uses a special meniscus-climbing technique to close in on emerging (left) and overhanging (right) vegetation.

2 - Waterlily leaf beetle


3 ) The larva of Pyrrhalta is circumscribed by a contact line with the water surface.  To climb the meniscus, the larva arches its back pulling up on the free surface with its head and tail.

3 - Meniscus-climbing larva


4 ) The deformation of the water surface near the head and tail of the larva is clearly visible.  In these images, it approaches an emerging wetted leaf.

4 - Deformation of water surface

Surface deformation



Non-wetting climbers

Water-walking insects are generally covered by a dense mat of hair that renders them hydrophobic.  Learning to climb the meniscus was a necessary adaptation for their terrestrial ancestors as they colonized the water surface.  Modern water walking insects ascend to land in order to escape aquatic predators and lay their eggs.

5 ) The border between land and water may appear flat to us, but to water-walking insects, there may be significant topography.  Here the water measurer Hydrometra treads carefully atop slippery rocks protruding from below the water surface.

5 - Hydrometra walking on rocks

6 ) Meniscus-climbing by the water treader Mesovelia.  The water treader approaches a meniscus, from right to left. The deformation of the free surface is evident near its front and hind tarsi.  While covered entirely with non-wetting hairs, the treader uses specialized wetting claws to pull up on the water surface.

6 - Meniscus-climbing by the water treader Mesovelia.

7 ) To climb the slippery meniscus, water-walking insects need to get a running start.  Only by running up the meniscus and using their specialized climbing mechanism as they slide back down can they generate the speed to reach land.  Mesovelia (left) and the infant water strider (right) start their sprints at the bottom of the meniscus.

7 - Mesovelia (left) and the infant water strider (right) start their sprints at the bottom of the meniscus.

8 ) Floating weeds (left) are attracted to the meniscus, so on occasion, Mesovelia can hitch a ride to draw itself closer to land. On the right Mesovelia pauses before attempting a second climb.

8 - Mesovelia climbing

9 ) Left, Two water treaders making haste to climb the meniscus. Right, the water measurer prepares to climb the mensicus by drying its non-wetting claws.

9 - Water treaders


10 ) Water measurers Hydrometra known for their plodding speed on the water surface.  Left, Hydrometra next to a downward sloping meniscus at the edge of a glass of water.  Surface tension both supports Hydrometra‘s weight and keeps the water from spilling out the glass.  Right, an upward sloping meniscus generated by an overhanging plant.  To asend the plant, Hydrometra must ascend the slippery meniscus.

10 - Hydrometra managing the meniscus

11 ) Hydrometra  ascending the meniscus.  By assuming a static posture in which it pushes down with its middle legs and pulls up with its front and hind legs, the creature rises to the top of the meniscus.  Once at the top (right), it uses its claws to haul itself upward.

11 - Hydrometra ascending the meniscus

12 ) Meniscus-climbing postures assumed by insects.  Shaded spots indicate the sense of the surface deflection, light being upwards and dark downwards. a, Mesovelia. b, Microvelia. c, Hydrometra. d, Pyrrhalta. e, Anurida. Figures courtesy of Brian Chan.



13 ) Meniscus-climbing by Anurida maritima.  By pulling up on the water surface with its wetting ventral tube and pushing down with its nose and tail, Anurida can deform the water surface.  Assuming this static postures allows Anurida to ascend to land and to form colonies of 50-100 individuals.


14 ) To travel between two colonies, Anurida combines walking with meniscus-climbing.  Meniscus-climbing is recognized by the upward deformation of the free surface, as seen around the individual on the left.



See paper here:  Hu & Bush, Nature (2005)  



Andersen, N.M. (1976). A comparative study of locomotion on the water surface in semiaquatic bugs (Insecta, Hemiptera, Gerromorpha). Videnskabelige Meddelelser fra Dansk Naturhistorisk Forening, 139: 337-396.

Bush, J. W. M. & Hu, D. L., 2006. Walking on water: Biolocomotion at the interface. Ann. Rev. Fluid Mech. 38.

Chan, D. Y. C., Henry, J. D. J. & White, L. R. The interaction of colloidal particles collected at fluid interfaces. J. Coll. Int. Sci. 79, 410 418 (1981).

Kralchevsky, P. A. & Denkov, N. D. Capillary forces and structuring in layers of colloid particles. Curr. Opin. Coll. Interf. Sci. 6, 383 401 (2001)

Miyamoto, S. On a special mode of locomotion utilizing surface tension at the water-edge in some semiaquatic insects. Konty  23, 45 52 (1955).

Nicolson, M. The interaction between floating particles. Proc. Camb. Phil. Soc. 45, 288 295 (1949).

Whitesides, G. & Grzybowski, B. Self-assembly at all scales. Science 295, 2418 2421 (2002).


SELECTED PRESS:  MIT News ,  NY Times ,  National Geographic ,  PhysicsToday-Backscatter

ALBUM COVER:   Meniscus


Water strider locomotion: Paradox lost


“Like a long-legged fly upon the stream, his mind moves upon silence”.

– William Butler Yeats

Water striders Gerridae are insects of characteristic length 1 cm and weight 10 dynes that reside on the surface of ponds, rivers, and the open ocean. Their weight is supported by the surface tension force generated by curvature of the free surface5,6, and they propel themselves by driving their central pair of hydrophobic legs in a sculling motion. Previous investigators have assumed that the hydrodynamic propulsion of the water strider relies on momentum transfer by surface waves. This assumption leads to Denny’s paradox: infant water striders, whose legs are too slow to generate waves, should be incapable of propelling themselves along the surface. We here resolve this paradox through reporting the results of high-speed video and particle-tracking studies. Experiments reveal that the strider transfers momentum to the underlying fluid not primarily through capillary waves, but rather through hemispherical vortices shed by its driving legs. This insight guided us in constructing a self-contained mechanical water strider whose means of propulsion is analogous to that of its natural counterpart.

See paper: Hu, Chan and Bush, Nature (2003)    … and commentary Dickinson (2003)

SELECT PRESS:  The Economist ,  Nature , BBC News ,  SouthFlorida Sun-Sentinel , Science_Dong A , Ca m’interesse ,  Pour la Science , Biophotonics

Television:  BBC International

For an account of the project presented by David Hu, see the below video.


Some nice strider shots from Dr. Hu’s old webpage:








And some vortical flows, induced by sprinkling Thymol Blue on the water surface, and letting the striders paint…