University of LjubljanaFaculty of Mathematics and Physics

Department of Physics

Leidenfrost effectDrop on hot surfaces

Seminar

Jure Aplinc, dipl. fiz. (UN) Advisor:doc. dr. Primoz Ziherl

25th February 2012

Abstract

Drops deposited on the hot solids levitate on a layer of their own vapour, which causesdrop lifetime extension and extreme mobility. If surface is not flat but ratchet-like, waterdrops appear to propel themselves in a well-defined direction. Conversely, if the surface iscrenelated drops appear to decelerate across a distance of a few centimetres. Furthermore,these surfaces can even trap a drop at well-defined position. Here we explain these phenom-ena. We also introduce superhydrophobic materials and nanoratchets, which also propeldrops.

Contents

1 Introduction 2

2 Leidenfrost drops 22.1 Drop shape and stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Vapour layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Self-propelled Leidenfrost drops 53.1 Self-propelling force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Decelerating and trapping Leidenfrost drops 84.1 Friction on crenelated surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5 Hydrophobic materials and nanoscale ratchets 105.1 Nanoscale ratchets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

6 Conclusion 12

1

1 Introduction

The fact that a water drop is long-lived when deposited on solid that is much hotter thanthe boiling temperature of water was first reported by Herman Boerhaave in 1732. It was notinvestigated extensively until 1756 when doctor Johann Gottlob Leidenfrost published ”A TractAbout Some Qualities of Common Water” [1]. His work was not translated from Latin until1965, so it was not widely read. But his name is still associated with the phenomenon and suchfloating drops are called Leidenfrost drops.

Leidenfrost conducted his experiments with an iron spoon heated red-hot on the coals. Afterplacing the drop of water into the spoon he noticed that glowing iron around the drop is darkerthen the rest. He deduced that ”the matter of light and fire from the glowing iron is suddenlysnatched into the water” [1]. The first drop deposited in the spoon lasted for over 30 s while thenext drop lasted only for 10 s. An additional drop lasted for a few seconds only. Observationsof evaporating drops led him to a conclude that when drop vanishes ”it leaves a small particleof earth in the spoon” [1].

Leidenfrost misunderstood his experiments because he did not realize that the drops withshorter lifetime were actually boiling. His understanding of the phenomena was alchemicaland based on Aristotelian approach, which was still prevalent in his time. Here we discuss theLeidenfrost phenomena properly within a more modern physical approach.

2 Leidenfrost drops

When a drop of liquid is deposited on a hot solid surface of temperature around the boilingtemperature, drop spreads over the plate in a thin layer, boils and quickly vanishes. But if thesolid’s temperature is much higher the drop is no longer in contact with the solid but levitatesabove its own vapour. The temperature where the insulating vapour film forms is called theLeidenfrost temperature [2]. Because of the insulating properties of the film, evaporation israther slow and the lifetime τ of the drop is increased by up to 500 times [3]. This causes asharp maximum (Fig. 1) . For example, a millimetre-size droplet of water on a metallic surfaceat 200 oC is observed to float for more than a minute. In addition, the absence of contactbetween the liquid and the solid prevents the nucleation of bubbles so that the drop does notboil, it just evaporates [2]. Such floating drops are called Leidenfrost drops. If temperature Tof the plate is increased even more the drop’s lifetime begins to decrease, because conductionand radiation between the plate and the drop are enhanced.

The existence and the characterization of Leidenfrost temperature depends on the roughnessof the solid, on the purity of the liquid (which also affects the lifetime), and even on the way itis deposited.

2.1 Drop shape and stability

As we have seen, Leidenfrost drops float on a thin vapour layer, so they can be considered asnonwetting. We distinguish several types of drop shape.

An important parameter which determines drop shape is the capillary lenght defined by

a =

√γ

ρg(2.1.1)

where γ is the surface tension and ρ is the density of liquid. The capillary lenght correspondsto drops whose gravitational and surface energies are the same. If the drop radius R is smallerthan the capillary length the drop is nearly spherical, except at the bottom where is flattened.

2

Figure 1: Life-time τ of a millimetre water droplet as a function of the temperature T of theduralumin plate on which it is deposited. When temperature of the solid approaches certaintemperature much higher than the boiling temperature (in our case 150 oC) vapour film formsand insulates drop from the hot solid. Hence life-time increases and reaches maximmum at socalled Leidenfrost temperature [2].

Radius δ of the contact zone is given by a balance between surface tension and gravity, whichyields δ ≈ R2/a.

If the drop radius is bigger then the capillary length water forms puddles, which are flattenedby gravity as seen in Fig. 2. The size of the contact zone is of the order of drop radius δ ≈ R andthickness h is dominated by the balance between surface tension and gravity. These argumentsgive h ≈ 2a.

Figure 2: Large water droplet on hot surface. Radius of contact zone of the drop is similar toits radius [4].

2.2 Vapour layer

Vapour layer causes lifetime extension of Leidenfrost drops and here we investigate its properties.The thickness can be measured accurately by diffraction of He-Ne laser beam by the slit betweenthe drop and the solid [2]. From the diffraction pattern, the film thickness e typically in therange 10− 100µm is computed.

It was experimentaly discovered that thickness of the film increases with drop radius as seenin Fig. 3 [2]. For precise measurements it is very inconvenient if the film thickness varies withtime. Stationary drops are needed, so we supply water from outside in to the observed drop.By fixing the feeding rate we determine the drop radius. Moreover this experiment provides adirect measurement of evaporation rate for a given radius.

In the stationary regime, the vapour film is supplied by the evaporation of the drop, butflows because of the drop weight. Flow rates caused by evaporation and pressure imposed by

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Figure 3: Thickness of the vapour layer beneath the drop, deposited on duralumin plate at300 oC as a function of drop radius, which is varied by changing the feeding rate. The transitionbetween the small- and the large-drop regime takes place at the capilar length (in this casea = 2.5 mm) [2].

the drop mass can be both evaluated.First, the heat Q brought to the liquid per unit time is proportional to the surface of the

contact area πδ2, thermal conductivity of the vapour κ and the thermal gradient ∆T/e. Butin the stationary state where temperature of the liquid is equal to its boiling temperature, allof the incoming heat is used for evaporation. We find that the flow rate yields:

dm

dt=κ

L

∆T

eπδ2, (2.2.1)

where L is the latent heat of evaporation.Second, the drop weight induces a radial Poiseuille flow of the vapour outside the conduction

layer. We can calculate its rate from the Navier-Stokes equation and lubrication approximation,which can be used due to the small thickness of the vapour layer as shown in Fig. 3. The flow isradial and the boundary conditions are vr(r, z)|z=0 = vr(r, z)|z=e = 0 so that v(r, z) ∝ z(e−z).In the radial direction the flow rate must be constant and since the vapour is incompressiblev(r, z) ∝ 1/r. Velocity should also be proportional with ∆P , pressure imposed by the drop,vapour density ρv and inversely proportional to its viscosity η [5]. The flow rate reads:

dm

dt= ρv

2πe3

3η∆P. (2.2.2)

In the stationary regime, the mass of the vapour film remains constant. Thus we can deducefrom Eqs. (2.2.1) and (2.2.2) the film thickness. For puddles (R > a), the contact zone radiusis proportional to the drop radius (δ ∼ R) and the pressure acting on the film is 2ρga. Thisyields

e =

(3κ∆Tη

4Lρvρga

) 14

R12 . (2.2.3)

For small drops (R < a), vapour film plays a minor role in the process of evaporation.Evaporation take place over the whole drop surface (both top and bottom), and the gradientshould be of the order of ∆T/R. The pressure acting on the film is the Laplace pressure 2γ/R.The flow rate is given by the thickness of the film

e ≈(κ∆Tηρg

Lρvγ2

) 13

R43 . (2.2.4)

On the whole, the film thickness increases monotonically with the drop radius, but it scaling lawin the large drop regime is different from that in the small drop regime [2]. The correspondingscaling laws are obviously in good agreement with the observations represented in figure (3).

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3 Self-propelled Leidenfrost drops

In the previous section we investigated properties of the vapour layer, which is responsible forthe long lifetime of drops and their almost frictionless motion. Furthermore vapour flow propelsLeidenfrost drops when placed on a hot ratchet, as we will see below. We will also discuss thisdriving force and the special friction generated by the texture of the substrate.

In 2006 Linke and coworkers showed that levitating Leidenfrost drops self-propel if asym-metric teeth are present on the solid (as shown in Fig. 4) [6, 7]. If the solid is heated just abovethe Leidenfrost temperature the tips of the ratchet may induce boiling, which is unwanted, sowe assume that the ratchet temperature is much higher. We will only consider drops biggerthan the capilary length, for which the liquid is flattened by gravity.

Figure 4: Drop deposited on a hot ratchet (in this case made of brass) self propels in the directionindicated by the arrow [6]. The radius of the drop is R = 3 mm. The ratchet temperature(350 oC) is much higher than the Leidenfrost temperature of ethanol (200 oC). The length andthe height of the teeth are 1.5 mm and 300µm, respectively [6].

Propulsion may cause several phenomena:

1. A drop placed on the ratchet tends to curve concavely around the tops of the ridges,whereas elsewhere the shape is convex [6]. Using the variation in the curvature, theprofile pressure along the vapour layer can be estimated. Pressure in the vapour layer isapproximately given by the Laplace pressure ∆P = γ/R, where 1/R is the local curvature.A concave shape (near point A in Fig. 5) corresponds to a curvature radius RA < 0 andPA > Pi, if Pi is the drop internal pressure. On the other hand the convex curvature atpoints B1 and B2 implies PB < Pi, such that PA > PB. Therefore we expect net vapourflow from point A to points B1 and B2. Flow from A to B2 creates a viscous force in thesame direction, while flow from A to B1 can escape sideways along the grooves. So forcein this direction is relatively small. Therefore, drop is accelerated in the direction of theflow between A and B2.

2. A wave propagates from back to the front end of the drop. It makes the transport ofmatter possible in the direction of motion.

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Figure 5: Photograph of the solid-liquid-vapour contact of a drop of water deposited on a brassratchet. A drop placed on the ratchet tends to curve concavely around the tops of the ridges,whereas elsewhere the shape is convex. The scale bar is 1.5 mm long [6].

3. A Leidenfrost drop is likely to oscillate spontaneously in all directions. So the ratchetcould transfer a part of oscillating drop kinetic energy from the vertical to the horizontaldirection because of the slope of the teeth.

4. A drop placed on a hot ratchet is propelled by the vapour flow, which is distorted byasymmetric teeth.

The first three effects are related to the deformability of the moving body, that is, to itsliquid nature. Hence the question arises whether a motion is still possible if solid is used insteadof a liquid. To explore this possibility an experiment was performed by Quere and coworkers [8]who used dry ice (solid carbon dioxide), whose sublimation point is at −78 oC and atmosfericpressure.

Dry ice indeed levitates (Fig. 6) and moves in the same direction as Leidenfrost drops andis driven with a constant force. Hence, even Leidenfrost solids self-propel and we conclude thatthe motion is not necessarily related to deformability of the liquid, which suggests that vapourproduction is the primary cause of motion. If a drop is deposited on a flat surface vapourescapes isotropically but the presence of a ratchet breaks the symmetry of the substrate anddirects the vapour flow.

Figure 6: When a disk of dry ice is placed an a hot ratchet (T = 350 oC) it accelerates as seenin photographs above. The bar indicates 1 cm and the time interval between two successivephotos is 300 ms [6]. Since the ratchet is hot enought vapour from the air cannot condensebetween the ratchet and the disk.

Reynolds number for the vapour flow Re = ρue/η is of the order of 10, so that the flow isirreversible. As a consequence, this flow can be asymmetric.

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When the vapour moves towards the step, that is towards a sudden contraction in the fluidchannel, the flow resistance is higher than in the reverse direction. Consequently the vapourwill mainly escape along the smallest slopes of the ratchet, which propels the Leidenfrost bodyin the direction shown in Fig. 4. So the ratchet converts a uniform vapour flow into a jet thrust.

3.1 Self-propelling force

Let us now investigate the propelling force in more detail.If m is the mass ejected per unit time, the force propelling the object scales as m∆u where

∆u is the difference of gas velocity of the flow between two opposite directions [8, 9]. ∆uincreases with asymmetry and decreases with flow thickness e. It is also expected that ∆uincreases proportionally with u.

We need to evaluate both m and u to explain the propelling force quantitatively. We assumethat the Leidenfrost drops are larger than the capilary length and hence flattened by gravity.In this case, the drop radius R is almost the same as radius δ of the contact zone between theplate and the drop. Conservation of matter can be be written as

m = 2πeρvuR. (3.1.1)

We presume that the drop is in the stationary regime, which means that its temperature alreadyreached the boiling temperature. The transient regime is indeed very short (less than 1 s)compared with a lifetime of the drop. We have already discussed the flow rate, conduction,lubrication approximation and film thickness of the system in the stationary state section 2.2.

In the order to calculate the propelling force we combine Eqs. (2.2.2) and (2.2.3). Thisyields

dm

dt= ρv

µ32R

32

τ, (3.1.2)

where τ = (3η)/(2πρgh) is the characteristic viscous relaxation time of the film, and µ =√(3κ∆Tη)/(4Lρvρga) is constant for a given liquid and plate temperature. We can express

force Fp ≈ mu by combining Eqs. (3.1.1), (2.2.3) and (3.1.2). We find that

Fp ≈ F0

(R

µ

) 32

, (3.1.3)

where F0 = ρµ4/τ2.The propelling force is expected to be of the order of 10µN, and it rapidly increases with

drop size R. To determine the magnitude of the propelling force Linke and coworkers placeda long thin glass fibre in the path of the droplet [6]. The drop is caught by the fibre, which isdeflected and stops the drop. The drop propelling force is balanced by elastic force associatedwith the deflection, so quantitative values of the force can be measured (Fig. 7). The typicalvalue of the force Fp is 10µN for drops of size R = 3 mm, a relatively small value comparedwith other characteristic forces at this scale: The weight of the drop for the same volume is10 times larger. However, this force is large enough to induce fast motion because of the lowfriction provided by the vapour layer. So evaporation provides both levitation and propulsion,itself made possible by levitation alone.

3.2 Friction

Friction is generaly very week for Leidenfrost drops. The viscous friction in a thin vapour filmscales as (ηv/e)R2, where v is a velocity of the drop. On the other hand, the air drag force

7

Figure 7: Drop propelling force is balanced by elastic force of the bent glass fibre, so that theforce can be measured. This force is of the order of 10µN and increases with R

32 [8]. Error

bars at large F indicate the amplitude of the fluctuations of the force in the experiments; smalldrops are sensitive to discrete step length [8].

scales as ρv2R2. Both contributions are of the order of 0.1µN, which is 100 times smaller thanthe driving force Fp. In the stationary regime propulsion and friction balance each other (dropis moving with a terminal velocity), which implies that drop experiences an additional frictionmuch larger than usual. How is this possible?

If we look at Fig. 4 we see that the interface below the drop is distorted by the presenceof the teeth. As the drop moves, rolls of liquid hit the steps, which dissipates energy. We canevaluate the corresponding friction force. Let λ and ε be the length and the depth of eachtooth, respectively. The mass of a roll scales as ρλεR. Energy loss of the kinetic energy percrenelation scales as ρλεRv2, and must be multiplied by the number R/λ of bumps. The totalloss W1 is given by ρεR2v2, and it corresponds to the work Ff1λ of a friction force. This yieldsthe friction force

Ff1 ≈ ρv2R2 ε

λ. (3.2.1)

Ff1 is tipically of the order of 10µN as observed experimentally. If one would replace the liquidby a solid which does not deform on a ratchet (dry ice for instance) friction would be muchsmaller, hence the terminal velocity should be much higher.

Terminal velocity of the drop

v ≈ µ

τ

(ρvρ

)1/2(λε

)1/2 ( µR

)1/4(3.2.2)

can be calculated using the above equations. It is found to be almost insensitive to the dropradius, but strongly depends on the design of a ratchet. Indeed friction can be highly amplifiedusing a ratchet with larger period λ and larger height ε [8]. If a drop hits such a ratchet withsome initial velocity it would stop in a few centimetres, whereas drops on a flat surface maytraverse several metres before they come to a stop. What was once a good tool for acceleratingdrops is now ideal for decelerating and even trapping ultra-mobile Leidenfrost drops.

4 Decelerating and trapping Leidenfrost drops

The ratchet was equipped with asymmetrical teeth to induce propelling force of the drops.In order to decelerate or trap a drop, one may want to use a symmetric ratchet surface. Acrenelated surface (shallow bands of metal are removed, forming periodic pattern as in Fig. 8) ofthis type was tested by Dupeux and coworkers [10]. They fabricated crenelations of wavelength

8

λ = 3 mm and height ε = 480µm and heated it to 450 oC [10]. Drops were forced to collidewith it, moving with an initial speed v0. It was observed that drops decelerate much faster if

Figure 8: A drop of ethanol was forced to collide with crenelations of wavelength λ = 3 mmand height ε = 480µm made of aluminium, heated up to 450 oC. Such drops stop in a fewcentimetres, whereas drops on a flat surface may traverse several metres before they come to astop. Interface below the drop is distorted by the presence of textures [10].

the surface is textured than it does on a flat surface (Fig. 9). Two deceleration regimes wereobserved. Initially, the drop velocity decreases exponentially with the distance. When velocityreaches a certain value, the motion crosses over into the second regime where the velocity vdrastically falls to zero, showing that textured substrates also have the ability to trap the liquidat a well defined distance x∗. Friction force was found to vary between 20 and 300µN [10].

Figure 9: Velocities of two Leidenfrost drops, both with the same initial velocity and mass, asa function of coordinate x. The first drop (empty circles) moved over a smooth solid, while thesecond one over slided crenelated one. The velocity of the latter initially decreases exponentiallyand after passing certain distance sharply falls to zero. The first drop experiences almost nofriction [10].

4.1 Friction on crenelated surface

The experimental observations [10] can be interpreted in terms of the same mechanism proposedin Subsection 3.2. As seen in Fig. 8 the bottom side of the liquid gets into the grooves andreaches the bottom of the groove. Hence the volume of liquid trapped per groove is proportionalwith the volume of the groove section with length equal to the drop diameter R. So the bumpvolume scales as Rελ.

These bumps can generate friction in two ways. First, they hit the crenelation sides and losekinetic energy in these soft impacts. We have already calculated this contribution in Subsection

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3.2. Second, the sliding liquid has to pass through crenelations, this is to overcome potentialenergy barriers W2 ≈ ρgR2ε2. W2 is the energy of R/λ bumps of masses ρRελ, lifted for oneheight of the groove ε. This energy is lost when liquid falls into the groove, and must be sameas the work Ff2λ of the friction force Ff2 across one period λ. The total friction force is thesum of Eq. (3.2.1) and Ff2:

Ff = b1ρR2v2

ε

λ+ b2ρgR

2 ε2

λ, (4.1.1)

where b1 and b2 are constants which depend on the crenelation geometry. For shallow crenela-tions, the dominant term in Eq. (4.1.1) is the inertial one. In discussion about friction onthe ratchet (in Subsection 3.2) we consider only this contribution because ratches are indeedshallow. However, the friction on deeper crenelations is not described by the inertial term alone.The friction becomes higher than expected due to the gravitational correction.

This correction can also explain the trapping of the drop at a well defined position x∗. Todetermine x∗, we need to solve the equation of motion Ff = mv. The general solution is

v2 = (v20 + v∗2) exp

(−2x

L

)− v∗2. (4.1.2)

For drops faster than v∗ ≈ √gε, velocity is an exponential function of x because v∗ can beneglected. The parameter L ≈ aλ/ε is the characteristic distance of slowing down and onlydepends on crenelation design. As the drop velocity is smaller than v∗, it can no longer beneglected. When velocity finally falls to zero we get the trapping distance: x∗ ≈ L ln v0/v

∗.Remarkably, it only logarithmically depends on the initial velocity v0, and it appears to bemainly fixed by the design of the texture via L. Trapping occurs when the drop velocitybecomes of the order of v∗, because the liquid does not have enough kinetic energy to overcomethe next crenelation. As seen in Fig. 9, the transition to the trapped state is very sharp. Thedeceleration of drop and its final halt after a distance L can also be affected by other factors. Itis observed that the defects on the solid can generate local pining. Conversely, drop oscillationsor local boiling can provide enough energy to the drop to reach the next crenelation. Thereforeuncertainty of the trapping distance is around λ.

In Subsection 3.2 we discussed friction on asymmetric teeth. According to our scenariowhere the dissipation is due to the liquid hitting the crenel, these teeth should generate ananisotropic friction force [8]. Indeed measurements confirm these suggestions. Friction for droptravelling in direction 1 in Fig. 4 is found to be almost twice as big as friction in direction 2[10]. The loss of kinetic energy is larger when the drop hits the sharp edge of the crenel thanwhen it follows the smooth slope. Drops deposited on ratchet self-propel in the direction of thelarger friction, which seems counterintuitive and raises the question of the optimal teeth designfor fastest self-propulsion.

5 Hydrophobic materials and nanoscale ratchets

When a Leidenfrost drop floats upon a very hot solid on a thin layer of vapour, it glides almostwithout friction. But extreme mobility can also be achieved without heating the solid if itsmicrotexture is suitably modified.

When a drop of water is deposited on a solid we commonly observe that the liquid makescontact with the surface. If this surface is an incline, the drop generally remain stuck on it butgets deformed. Angle at the ”front” is larger than the angle at the ”rear” which generates acapillary force

F = πγR sin(θ)(cosθr − cosθa) (5.0.3)

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opposing the motion [11]. Here θa and θr are maximum and minimum possible contact anglesand θ is an average contact angle. So if we want to make drops of water mobile on a solidwe must minimize the contact angle hysteresis ∆θ = θa − θr or maximize contact angle θ (orboth) [12].

A Leidenfrost drop makes a contact angle of 180o, which corresponds to complete dryingfor which liquid-solid contact zone vanishes. Hence the liquid cannot pin anymore on the soliddefects, which also yields a zero contact angle hysteresis.

Several natural materials approach the Leidenfrost limit at room temperature. For instanceduck feathers or legs of water strider repel water, and contact angles are in the range 150o−170o.More than 200 plants are similarly superhydrophobic, the most famous one being the lotus whoseleaf does not retain raindrops (θ = 160o and ∆θ = 10o) [11].

Using electron microscope microtextures characterized by a lenghtscale of 10µm becomevisible (Fig. 10). Different designs are observed: bumps (lotus and many other plants), spikes(water strider leg) and microfibres (drosera and other plants). These microtextures all drastic-ally increase surface area (roughness) of the material. The design in Fig. 10c is found to beparticularly appealing because it is the simplest one and it can be quantitatively investigated.Drop deposited on such microtextured surface can adopt two types of configurations: conform-

Figure 10: Electron micrographs of four superhydrophobic surfaces. (a) bumps of magnolialeaf, (b) hair on a water strider leg, (c) synthetic microposts, (d) fibrous and spongy syntheticmaterial [11].

ing to the solid (Fig. 11a; the so-called Wentzel state) or sitting on the top of the posts (Fig.11b; the so-called Cassie state). A drop in the Wentzel state is very hard to remove irrespectiveof whether it is hydrophobic or hydrophylic in contrast to what we expect from a lotus-typematerial [11].

If the roughness of the surface in the Wentzel regime is increased, it is energetically betterfor the liquid to pass in Cassie state [11]. Drop in Cassie state is virtually sitting on air becauseits only contact with the solid is possible only on the tops of microposts. Leidenfrost limit canbe approached if the post ”density” vanishes. The cassie angle θ appears to be around 160o

[11]. The contact angle hysteresis is also very weak, since the liquid mainly sits on air on whichit cannot stick.

In the Cassie the state drop literally glides on air (as a Leidenfrost drop), owing to the largeviscous ratio between water and air. But its slip length cannot be infinite while a part of theliquid glides on posts. If post density is decreased, slippage is better.

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Figure 11: Two different states: (a) drop either follows the structures on the solid (Wentzelstate) or (b) sits at the top of the posts (Cassie state) [11].

5.1 Nanoscale ratchets

If all microposts (Fig. 10c) would be tipped by the same angle in the same direction we wouldcreate a surface ratchet which has unidirectional wetting properties [13, 14]. Drop depositedon such ratchet remains in the Cassie state and does not move. But if we introduce vibrationsin the vertical direction, droplets can be propelled on this surface in a single direction (thedirection of the asperities). It appears that the frequency required to move the water dropsdecreases with increasing size of the drop [13]. So only drops of equal sizes can be transportedat the same time.

6 Conclusion

All the properties of the Leidenfrost drop are caused by some 10µm thick vapour layer. Itseparates and thus insulates the drop from the hot solid, to increase its lifetime by up to 500times. Vapour prevents contact with the solid so it behaves as superhydrophobic drop. Whilethere is no contact, there is no pinning. Hence the only force acting on the drop is viscousfriction and air drag, which are both extremely small due to the low density of vapour and air.

If the solid is not flat but consists of numerus asymmetric teeth, vapour flow beneath thedrop is not uniform any more [6, 8]. This asymmetry causes a kind of jet thrust which propelsdrops in a very well defined direction. Ratchet-like topology not only propells drops, but alsocauses special friction due to deformability of the drop interface. Energy is dissipated evenbetter if we use symmetric rathet than asymmetric teeth [10].

Self-propelling fluidic devices are important because of their unique ability to displace liquidat small scales without an external force. These devices can be used to chemically treat a solid,to direct and concentrate liquid, for example in condensors or to drive chemical compoundsof small quantities. Despite the numerous potential applications, the domain of applicationof superhydrophobic materials still remains to be explored. Water repellency for syntheticmaterials is practically non-permanent owing to the pollution or fragility of the materials. Asa consequence, very few products based on the principles described in Section 5 exist today onthe market.

References

[1] J. G. Leidenfrost, On the Fixation of Water in Diverse Fire, Int. J. Heat Mass Transfer 9,1153 (1966).

[2] A. Blanche, C. Clanet, and D. Quere, Leidenfrost drops, Phys. Fluids 15, 1632 (2003).

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[3] http://darkwing.uoregon.edu/ linke/papers/Walker leidenfrost essay.pdf, (2011).

[4] http://www.flickr.com/photos/jmhuttun/4551184222/in/set-72157615262856419, (2011)

[5] http://www.physics.princeton.edu/ mcdonald/examples/radialflow.pdf, (2011).

[6] H. Linke, B. J. Aleman, L. D. Melling, M. J. Taormina, M. J. Francis, C. C. Dow-Hygelund,V. Narayanan, R. P. Taylor, and A. Stout, Self-Propelled Leidenfrost Droplets, Phys. Rev.Lett. 96, 154502 (2006).

[7] http://netserver.aip.org/epaps/phys rev lett/E-PRLTAO-96-022616/, (2011).

[8] G. Lagubeau, M. L. Merrer, C. Clanet, and D. Quere, Leidenfrost on a ratchet, Nat. Phys.7, 1925 (2011).

[9] J. Bico and D. Quere Self-propelling slugs, J. Fluid Mech. 467, 101 (2002).

[10] G. Dupeux, M. L. Merrer, C. Clanet, and D. Quere, Trapping Leidenfrost Drops withCrenelations, Phys. Rev. Lett. 107, 114503 (2011).

[11] D. Quere and M. Reyssat, Non-adhesive lotus and other hydrophobic materials, Phil. Trans.R. Soc. A 366, 1539 (2008).

[12] D. Quere, Non-sticking drops, Rep. Prog. Phys. 68, 2495 (2005).

[13] K. Sekeroglu, U. A. Gurkan, U. Demirci, and M. C. Demirel, Transport of a soft cargo ona nanoscale ratchet, Appl. Phys. Lett. 99, 063703 (2011).

[14] A. Buguin, L. Talini, and P. Silberzan, Ratchet-like topological structures for the control ofmicrodrops. Appl. Phys. Lett. 75, 207 (2002).

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