Self-Rotation-Induced Propulsion of a Leidenfrost Drop on a Ratchet

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Self-rotation Induced Propulsion of a Leidenfrost Drop on a Ratchet Manjarik Mrinal, Xiang Wang, and Cheng Luo Langmuir, Just Accepted Manuscript • Publication Date (Web): 05 Jun 2017 Downloaded from http://pubs.acs.org on June 8, 2017

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Self-rotation Induced Propulsion of a Leidenfrost Drop on a Ratchet *Manjarik Mrinal, *Xiang Wang, and **Cheng Luo Department of Mechanical and Aerospace Engineering, University of Texas at Arlington 500 W. First Street, Woolf Hall 226, Arlington, TX 76019, USA; *: equal contribution; **email: [email protected]

Abstract. A Leidenfrost drop is capable of self-propelling on a ratchet, which consists of asymmetric teeth. In this work, the corresponding movements were first experimentally investigated. Since the detected motion could not be interpreted using existing propulsive mechanisms, a new propulsive mechanism was then developed, followed by force analysis using a scaling law.

1. INTRODUCTION After a liquid drop is placed on a solid that is pre-heated to a temperature significantly above boiling point of the liquid, the drop levitates on a film of its own vapor, which is so-called Leidenfrost phenomenon1-3. This temperature may also be reduced by covering the solid with specifically designed microstructures4 or a superhydrophobic material5. One of main future directions in Leidenfrost research is to control these ultra-mobile Leidenfrost drops, particularly when these drops are applied to remove heat from hot surfaces.6 Ratchets are the only devices that have been reported so far to have this capability. The ratchets consist of asymmetric toothlike structures, e.g., saw-teeth and tilted pillars.7-13

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Based on effects of viscous stress,7,9,10 rocket (jet thrust),8 and thermal creep,14 different propulsive mechanisms have been proposed to explain why Leidenfrost solids8,13 or fluids7,9-14 have directional movements on ratchets. On the other hand, there is no direct experimental evidence to support these proposed mechanisms, except the viscous mechanism in the case of a Leidenfrost solid9. Set up a rectangular xy coordinate system, as defined in Fig. 1(a). In ref. 9, vapor flow underneath a Leidenfrost solid has been traced using glass microbeads. The tested sample was a platelet of dry ice that was subliming on a heated ratchet. As illustrated in Fig. 1(a), due to rectification of the asymmetric teeth of the ratchet, the vapor was found to flow in the direction of descending slopes along each tooth.9 This flow created a viscous stress to entrain the dry ice along the positive direction of x-axis. The in-situ observation of vapor flow showed that the viscous mechanism might be the most plausible one for a Leidenfrost solid on a ratchet.6 However, due to lack of similar observation in the case of a Leidenfrost fluid, it was still unclear about whether the same mechanism also applied to the Leidenfrost fluid. The corresponding applicability was explored in this work.

2. EXPERIMENTAL SECTION Water and Isopropyl alcohol (IPA) drops were tested on two Al ratchets, which were manufactured using electrical discharge machining. As shown in Fig. 1(b), these two ratchets differed in geometric shapes and dimensions of their teeth, and were called “Ratchet I” and “Ratchet II”, respectively. Leidenfrost points of water and IPA were measured on these ratchets to be 220 ± 5 oC and 120 ± 5 oC, respectively. The ratchet temperatures in the tests were fixed to be 240 ± 5oC and 130 ± 5oC, separately, for water and IPA. Hence, both liquids were in their


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corresponding Leidenfrost states. The motions of Leidenfrost drops with volumes of 100 to 300 µL were recorded using a high-speed camera (Fastec TS3 with rates of 1000 to 1250 frames per second in recording our videos). Due to limit of resolution, our experimental equipment did not allow us to watch motions of microparticles as clear as in the case of ref. 9. To solve this problem, rectangular Al flakes with mm-scaled widths and lengths were adopted as tracers, instead. They were manually cut out of a 20-µm–thick Al foil. The flakes were classified into three groups: short, long, and longer flakes. The short and longer ones were, respectively, more than 0.2 mm shorter and longer than their underlying sidewalls of ratchet grooves. The long flakes have in-between lengths. The vapor film between a Leidenfrost drop and its substrate usually had a thickness of 0.1 to 0.2 mm.6 Consequently, the short flakes might not have direct contact with the bottom surface of a moving drop, while the longer ones should have. Meanwhile, long flakes might contact either a drop or its underneath vapor film.

3. RESULTS AND DISCUSSIONS 3.1. Detected motion Representative experimental results were given in Figs. 2-5, as well as in five supplementary videos that corresponded to Figs. 2(a), 2(b), 4(a), 4(b) and 5, respectively. As illustrated in Fig. 1(c), water and IPA drops were both found to have a combined motion of translation and self-rotation on the two ratchets. As reported by other researchers,7,9-14 a Leidenfrost drop was moving along the positive direction of x-axis (Fig. 1c). On the tested ratchets, the centers of water and IPA drops had translational speeds in the ranges of 3.3-10.3 cm/s and 2.2-12.2 cm/s, respectively. These speeds were close to what other researchers found


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on ratchets that also had mm-scaled teeth. The reported speeds were 5 cm/s 7 or ranged from 5 to 15 cm/s 8. In our case, when the drops were made of different liquids, had varied volumes, or moved on the two ratchets, the corresponding speeds did not show significant difference, i.e., the speeds had the same order. With the aid of the flakes, the moving direction of a drop’s bottom surface was detected. Due to lack of direct contact with a drop, short flakes remained almost stationary, when the drop ran over them. Examples are flakes “1” and “5” in Fig. 2(a), and flakes “1” and “3” in Fig. 2(b). Because of viscous stress applied by a drop, some long flakes were dragged into the drop, when they had much contact with it. The same applied to longer flakes. Flakes “3” and “4” in Fig. 2(a) gave two examples of this case. On the other hand, if long flakes just had slight contact with a drop, then they were not dragged into the drop. Instead, they were pushed by the drop’s bottom surface from the steep sidewalls to the slant ones. Examples include flake “2” in Fig. 2(a) and flake “2” in Fig. 2(b). In our tests, this pushing phenomenon has been found 62 times. In contrast, no matter what lengths the flakes had, none of them was seen to be pushed from slant to steep sidewalls by a drop’s bottom surface. They were either dragged into a drop or still remained on the slant sidewalls. Figure 3 gives tip speeds of the pushed flakes, which ranged from 4.0 to 21.0 cm/s and had an order of 10 cm/s. Since the tips of these flakes were found to have direct contact with drops’ bottom surfaces, the corresponding surfaces were considered to have the same moving directions and speeds as these tips. In addition, when a flake was placed on the tips of two neighboring teeth, it was tugged by a drop’s bottom surface to move along the direction opposite to that of the drop center (Fig. 2c). The moving directions of the pushed or tugged flakes indicate that a drop’s bottom surface


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actually moved along the negative direction of x-axis, which was opposite to the moving direction of the drop center (Fig. 1c). Furthermore, receding and advancing edges of a drop were found to roll up and down, respectively. As shown in Fig. 4(a), when a flake had contact with receding edge of a water drop, it was pulled up from a groove by the drop. Subsequently, it moved up, together with the receding edge, till it was thrown away from the drop due to centrifugal force. The moving trajectory of the flake shows that the receding edge was rolling up. Meanwhile, after two flakes had been hit by advancing edge of a water drop, these flakes were seen to rotate on tooth tips, implying that this advancing edge was rolling down (Fig. 4b). The moving directions of the receding and advancing edges, together with that of the drop’s bottom surface, indicated that, in addition to a translational movement, a drop also had self-rotation. The angular speed of this self-rotation, ω, was also estimated using ω=(Vc+Vb)/R1, where R1 denoted half thickness of a drop, and Vc and Vb represented the speeds of the drop’s center and bottom surface, respectively (Fig. 1c). When drops were large enough such that they had a pancake-like shape, their thicknesses were fixed.15 This applied to our case, in which drops had volumes ranging from 100 to 300 µL. In our tests, the values of R1 did not vary much with the volume of a drop or the liquids and ratchets that were tested. These values were measured to be 1.8 ± 0.4 mm. Typical value of ω was estimated to be 80 rad/s. In the calculation, Vc and Vb were set to be 5 and 10 cm/s, respectively, and R1 was 1.8 mm. Some long flakes were found to be pushed from steep sidewalls to slant ones, even if they did not have direct contact with a drop (Fig. 5). Accordingly, their motions should be caused by vapor flow underneath the drop. This phenomenon has been found 10 times in our experiment. The tips of the corresponding flakes on these 10 occasions had speeds in the range of 2.3-10.0


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cm/s. Due to small mass of the flakes, the vapor flows were considered to have the same moving directions and speeds as the tips of these flakes. The speeds of vapor flows have been previously theoretically estimated and experimentally measured in Refs. 6 and 9, respectively. The determined speeds were both in the order of 10 cm/s. Our measured ones were at the low end of these reported speeds. The moving directions and speeds of drops’ bottom surfaces imply that the viscous mechanism of Leidenfrost solids does not apply to Leidenfrost fluids. If this mechanism still holds true, then the viscous stress generated by vapor flow should drag the drop’s bottom surface to move along the same direction as the drop center, which, however, contradicts our experimental result. The same conclusion also applies to the thermal creep-based mechanism14. Also, given that surrounding vapors in our case have a typical speed of 5 cm/s, if a drop’s bottom surface moves solely due to the drag of these vapors, then it should have a speed of 0.5 cm/s.6 This speed is at least one order lower than detected, further indicating that the vapor flow is not the main cause of the movement at the drop’s bottom surface. In addition, the mass of vapors is much smaller than a drop, and the detected vapor speed is in the same order as the translational speed of the drop center. Consequently, according to the balance law of linear momentum, rocket effect8 should not be the main cause of the drop motion, either.

3.2. New propulsive mechanism Based on the observed motion, a new propulsive mechanism is proposed for selfpropulsion of a Leidenfrost drop on a ratchet. The self-rotation of the drop is considered to be the origin of the motion. It is a Marangoni thermocapillary flow, which is often found in a Leidenfrost drop.16-18 The temperature of the drop’s bottom surface equals boiling point of the


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corresponding liquid.6 It is a few degrees higher than that of the drop’s top surface.16 This temperature difference generates the Marangoni flow.16,18 The flow speed scales as6 V ~

∆γ , µ

(1)

where ∆γ is the difference in surface tension caused by a temperature difference between the bottom and top surfaces of the drop, and µ is dynamic viscosity of the liquid. ∆γ has an order of 0.1 mN/m for the temperature difference of a few degrees for both water19 and IPA20. The values of µ for water21 and IPA20 are about 0.6 and 0.3 mPa S, respectively, at temperatures close to their respective boiling points. Hence, by Relation (1), typical speeds of Marangoni flows for Leidenfrost drops of water and IPA are both in the order of 10 cm/s. They match the speeds of drops’ bottom surfaces measured in our tests (Fig. 3), as well as theoretical prediction of Ref. 6. In principle, there should be a symmetric Marangoni flow inside a Leidenfrost drop on a smooth substrate.17,18 As illustrated in Fig. 6(a), due to surface tension gradient that is induced by the temperature difference between A and B, there is a flow that goes from B to A, where A and B, as well as other symbols that will be seen in this paragraph, are defined in Fig. 6. Likewise, there is a flow from C to A. When the two flows meet at the middle plane of the drop, because of symmetry, their horizontal speeds are cancelled out. As a result, they move downwards, forming flows AD and AE, respectively. Temperature is considered to have a uniform distribution at the drop’s bottom surface. Therefore, there is no surface tension-driven flow on this surface. On the other hand, because of viscous stress, flows AD and AE drag the part of liquid, which is located at the drop’s bottom surface, to move along the directions of FB and FC, respectively. When the substrate surface is structured with asymmetric teeth, initially flows at the drop’s bottom surface may be still along the directions of FB and FC, and they hit slant and steep sides of teeth, respectively. The steep sides give more resistance. Hence, flow FB should have a higher speed 7 ACS Paragon Plus Environment

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than its counterpart FC. Consequently, flow BA has a higher speed than CA as well. As such, when the two flows meet at A again, the resulting flow moves along the direction AC instead (Fig. 6b). The corresponding flow at drop’s bottom surface also changes. It should only move towards the slant sidewalls, which was what we detected in the experiment. Furthermore, due to viscous stress, the inner part of the drop also goes along the direction of BAC, resulting in selfrotation of this drop. Two reaction forces of a ratchet play important roles in the motion of a drop (Fig. 1d). The first reaction force, Fdriving, is induced when a drop’s bottom surface hits the underneath teeth. This force propels the drop center to move along the positive direction of x-axis. The second reaction, Ffriction, is generated when the advancing edge of the drop rolls down to hit a tooth. It slows down the drop. Our propulsive mechanism is similar to that of a running car wheel. As a car transports on a road, its wheels also have a combined motion of translation and self-rotation. The self-rotation is also the origin of the motion. It is induced by engine and transmission system of the car. Once a self-rotated wheel contacts ground, the ground generates a friction to reduce the self-rotation. This friction also serves as a driving force to propel the wheel forward. As in our case, the wheel’s center translates along a direction, which is also opposite to its self-rotating direction at its bottom surface. Next, as what was done in ref. 8, both Fdriving and Ffriction are evaluated using a scaling law. Use d and w, respectively, to represent groove depth and width in a ratchet (Fig. 1a). Let ρ denote the mass density of a Leidenfrost liquid. As a drop moves, rolls of liquid hit the teeth along the negative direction of x-axis. The mass of a roll has an order of ρdwR2, where R2 denotes equatorial radius of a Leidenfrost drop (Fig. 1c). This mass is decelerating by Vb 2 / w. The number of rolls is R2 /w. Hence, Fdriving is scaled as


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2

2

(2)

Fdriving ~ ρVb R 2 d / w,

which is equivalent to friction force derived in ref. 8 (see its relation (7)). At the temperatures close to the boiling points, the values of ρ are, respectively, 960 and 728 kg/m3 for water19 and IPA20. The values of R2 were found to mainly depend on the volume of a drop, and did not vary much with the liquids and ratchets that were tested. As the drop volumes were, respectively, 100, 200 and 300 µL, the values of R2 were measured to be 3.5, 4.3, and 5.1 mm with an error of 0.4 mm. Ffriction is considered to be main friction. Surrounding vapors may also drag the drop. However, for a Leidenfrost drop on a ratchet, the magnitude of this drag force was estimated in ref. 8 to be one order lower than that of Fdriving. Thus, the vapor-induced drag force is just minor friction. As observed from Fig. 4(b), the advancing edge of the drop is modeled as a single roll of 2

2

mass. Its speed is scaled as (Vc + ω 2 R2 ). Following the same line of reasoning used to derive relation (2), we have 2

2

Ffriction ~ ρR2 d (Vc + ω 2 R2 ).

(3)

In our case, due to the following two facts, Ffriction is considered to have the same order of 2

2

2

magnitude as Fdriving. First, (Vc + ω 2 R2 )1 / 2 has the same order as Vb R2 / w . Set Vc=5 cm/s, ω = 80 rad/s, R2 = 4 mm, Vb=10 cm/s, and w=1 mm. Their ratio is in the order of 1. Second,

after traveling a few centimeters, a drop reached its terminal speed,7,8 indicating that Fdriving and Ffriction could be balanced. To validate relation (2), the driving force was detected using a setup shown in Fig. 7(a), which was similar to the one used in ref. 8 for the same purpose. A drop was pinned on a ratchet using a copper wire. The driving force was determined using the relation Fdriving=kδ, where k was


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spring constant of the copper wire and δ was the deflection of wire tip (supplementary gives the details about k and δ). Two points were observed from experimental results (Fig. 7b). First, the detected driving forces ranged from 11.6 to 170.3 µN. They were in the same range as what was detected by other researchers on ratchets that also had mm-scaled teeth.8 Second, the detected forces increased with the volume of a drop, mass density and ratio between height and width of a ratchet groove. The second point agreed with what was observed from relation (2). Relation (2) could also be written as 2

2

Fdriving = c ρ V b R 2 d / w ,

(4)

where c was a numerical factor. To determine c, four sets of data points (Fdriving, ρVb 2 R 2 2 d / w ) were plotted in Fig. 7(c). The values of Fdriving, R2, d and w were the measured ones, and V b was set to be 10 cm/s. As observed from Fig. 7(c), Fdriving and ρV b 2 R 2 2 d / w approximately had a linear relation, which matched what was predicted using relation (2). The values of c were curvefitted to be 0.60 and 0.71, respectively, for water drops on Ratchets I and II. For IPA, these values were 0.27 and 0.25. In deriving relation (2), a roll of liquid that hit teeth was scaled in the way that it fully filled a ratchet groove. In practice, the groove was just partially filled. Accordingly, the mass of a roll should be less than ρdwR2, giving a reason why c is less than 1.

4. Summary and conclusions A Leidenfrost drop is capable of self-propelling on a ratchet, which consists of asymmetric teeth. In this work, the corresponding movements were first experimentally investigated. A drop was found to have a combined motion of translation and self-rotation. In particular, the drop’s bottom surface was detected to move along a direction opposite to that of the translating drop center, which could not be interpreted using existing propulsive mechanisms. 10 ACS Paragon Plus Environment

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Subsequently, a new propulsive mechanism was developed, followed by force analysis using a scaling law. Self-rotation of a drop was considered to be origin of the motion. This mechanism was similar to that of a car wheel running on a road.

Supporting Information I. Method used to measure driving force; II. Illustration of this method (Figure S1); and III. Five videos, which correspond to Figs. 2(a), 2(b), 4(a), 4(b) and 5, respectively. This material is available free of charge via the Internet at http://pubs.acs.org.

References (1)

J. G. Leidenfrost. On the fixation of water in diverse fire e (Duisburg, 1756). Int. J. Heat Mass Trans. 9, 1153–1166 (1966) reprint.

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B. S. Gottfried, C. J. Lee, and K. J. Bell. Leidenfrost phenomenon: film boiling of liquid droplets on a flat plate. Int. J. Heat Mass Trans. 9, 1167-1172 (1966).

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R. S. Hall, S. J. Board, A. J. Clare, R. B. Duffey, T. S. Playle and D. H. Poole. Inverse Leidenfrost Phenomenon. Nature, 224, 266– 267 (1969).

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D. A. del Cerro, Á. G. Marín, G. Römer, B. Pathiraj, D. Lohse, and A. J. Huis in ’t Veld. Leidenfrost Point Reduction on Micropatterned Metallic Surfaces. Langmuir, 28, 15106– 15110 (2012).

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(6)

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Figures and legends

Figure 1: (a) Illustration of viscous mechanism to propel a platelet of dry ice on a heated ratchet9. Dimensions of teeth in Ratchets (b1) I and (b2) II, and the units are mm. (c) Sketch of a Leidenfrost drop’s motion observed on a ratchet: the drop center has a translational movement, while the drop also self-rotates simultaneously. (d) Forces that the drop suffers along x-axis. (a)(d) are all cross-sectional views. Figure 2: (a1)-(a6) When a water drop ran over flakes on Ratchet II, short flakes “1” and “5” remained stationary, long flakes “3” and “4” were pulled into a drop, and long flake “2” was pushed from its underlying steep sidewall towards the slant one by the drop’s bottom surface with an average speed of 10.4 cm/s, which was calculated using the groove width and elapsed time. The moving direction of long flake “2” was opposite to that of drop center. (b1)-(b3) As a water drop transported over flakes on Ratchet I, short flakes “1” and “3” remained stationary, while long flake “2” was pushed by the drop’s bottom surface from its underneath steep sidewall towards the slant one with an average speed of 12.0 cm/s. The moving direction of long flake “2” was also opposite to that of drop center. (c1)-(c3) A flake bridging two teeth of Ratchet I was dragged by a drop’s bottom surface along the direction opposite to that of drop center. For clarification, the flakes are marked with dotted lines. The thick, long arrows in (a)-(c) denote moving directions of drop centers, while the thick, short ones represent those of flakes. The same also applies to Figs. 4 and 5. Figure 3: Tip speeds of flakes that were pushed by (a) water and (b) IPA drops with three different volumes. “o” and “+” indicate tip speeds on Ratchets I and II, respectively.


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Figure 4: (a1)-(a5) Receding edge of a water drop rolled up a flake from Ratchet I. (b1)-(b3) Advancing edge of a drop rolled down and hit two flakes located on Ratchet II, and both flakes were subsequently pulled into the drop. Figure 5: On Ratchet I, a flake, which did not have direct contact with a water drop, was pushed backwards by vapor flow underneath the drop. The tip of this flake had an average speed of 7.5 cm/s. Figure 6: Marangoni flows inside Lendenfrost drops on (a) a smooth substrate, and (b) a ratchet (cross-sectional illustrations). Figure 7: (a1) On Ratchet II, a copper wire was put in front of a Leidenfrost drop, and (a2) the wire tip was in touch with advancing edge of the drop with a deflection of 3.2 mm, which corresponds to position “5” of Fig. S1. (b) Measured force-volume relationships, and (c) plot of Fdriving versus ρV b 2 R 2 2 d / w for validating relation (2) and curve-fitting relation (3). For a liquid drop with a specific volume on a ratchet, four measurements were done to determine the corresponding driving force. The mean value of the four was the vertical coordinate of a data point in (b) and (c), while the error bar around this data point in (b) denoted standard deviation.


Langmuir

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y 1.20 Moving direction of dry ice Dry ice

1.65 1.30 60

x w

o

O

0.75

0.70

30

O

1.21

d 1 mm

Moving direction of vapor

Ratchet

(b)

(a) Leidenfrost drop

Self-rotational direction

Moving direction of drop center

Vc

R2

ω R1

Fdriving Ffriction Vb

Moving direction Moving direction of drop’s bottom of vapor flow surface

(d)

(c)

Figure 1: (a) Illustration of viscous mechanism to propel a platelet of dry ice on a heated ratchet9. Dimensions of teeth in Ratchets (b1) I and (b2) II, and the units are mm. (c) Sketch of a Leidenfrost drop’s motion observed on a ratchet: the drop center has a translational movement, while the drop also self-rotates simultaneously. (d) Forces that the drop suffers along x-axis. (a)-(d) are all cross-sectional views.


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Langmuir

0 ms

(a1)

1

2

(a4)

3

4

(a2)

1

2

1

5

90.0 ms

0 ms

2

3

4

1

2

81.0 ms

(a3)

1

5

5 157.0 ms

1

5

(b2)

2

(a6)

97.0 ms

(a5)

5

(b1)

57.0 ms

4.0 ms

5 2 mm

2

8.8 ms

(b3)

3

1 (c1)

2

3 0 ms

2

1 (c2)

1

3 1.6 ms

Flake

(c3)

2

1 mm 7.2 ms

2 mm

Figure 2: (a1)-(a6) When a water drop ran over flakes on Ratchet II, short flakes “1” and “5” remained stationary, long flakes “3” and “4” were pulled into a drop, and long flake “2” was pushed from its underlying steep sidewall towards the slant one by the drop’s bottom surface with an average speed of 10.4 cm/s, which was calculated using the groove width and elapsed time. The moving direction of long flake “2” was opposite to that of drop center. (b1)-(b3) As a water drop transported over flakes on Ratchet I, short flakes “1” and “3” remained stationary, while long flake “2” was pushed by the drop’s bottom surface from its underneath steep sidewall towards the slant one with an average speed of 12.0 cm/s. The moving direction of long flake “2” was also opposite to that of drop center. (c1)-(c3) A flake bridging two teeth of Ratchet I was dragged by a drop’s bottom surface along the direction opposite to that of drop center. For clarification, the flakes are marked with dotted lines. The thick, long arrows in (a)-(c) denote moving directions of drop centers, while the thick, short ones represent those of flakes. The same also applies to Figs. 4 and 5. 17 ACS Paragon Plus Environment

Langmuir

Tip speed (cm/s)

1 Tip speed (cm/s)

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Water volume (µL) (µL (a)

IPA volume (µL) (µL (b)

Figure 3: Tip speeds of flakes that were pushed by (a) water and (b) IPA drops with three different volumes. “o” and “+” indicate tip speeds on Ratchets I and II, respectively.


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Langmuir

(a1)

0 ms

12.8 ms

(a2)

19.2 ms

(a3)

24.0 ms

(a4)

(a5)

50.4 ms

Fallen flake

1 mm

Flake

(b1)

0s

(b2)

0.8 ms

1.6 ms

(b3)

1 1

2

2

2

2 mm

Figure 4: (a1)-(a5) Receding edge of a water drop rolled up a flake from Ratchet I. (b1)-(b3) Advancing edge of a drop rolled down and hit two flakes located on Ratchet II, and both flakes were subsequently pulled into the drop.


Langmuir

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(a)

0 ms

(b)

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9.0 ms

(c)

16.0 ms

1 mm Figure 5: On Ratchet I, a flake, which did not have direct contact with a water drop, was pushed backwards by vapor flow underneath the drop. The tip of this flake had an average speed of 7.5 cm/s.


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Langmuir

A

Lendenfrost drop

E

D B

A

Lendenfrost drop

F

C

B

Vapor film

F

C

Ratchet

Substrate (a)

(b)

Figure 6: Marangoni flows inside Lendenfrost drops on (a) a smooth substrate, and (b) a ratchet (cross-sectional illustrations).


Langmuir

(a1)

Initial configuration of wire

Initial and deformed configurations

(a2)

δ

2 mm

Water on Ratchet I

Water on Ratchet II IPA on Ratchet I

Deflection Force (µN)

Water on Ratchet I Deflection Force (µN)

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Water on Ratchet II

IPA on Ratchet I IPA on Ratchet II

IPA on Ratchet II

Volume (µL)

ρVb2R22d/w (µN)

(b)

(c)

Figure 7: (a1) On Ratchet II, a copper wire was put in front of a Leidenfrost drop, and (a2) the wire tip was in touch with advancing edge of the drop with a deflection of 3.2 mm, which corresponds to position “5” of Fig. S1. (b) Measured force-volume relationships, and (c) plot of Fdriving versus ρVb 2 R 2 2 d / w for validating relation (2) and curve-fitting relation (3). For a liquid drop with a specific volume on a ratchet, four measurements were done to determine the corresponding driving force. The mean value of the four was the vertical coordinate of a data point in (b) and (c), while the error bar around this data point in (b) denoted standard deviation.


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Langmuir

Table of Content Graphic

(a)

0 ms

(b)

9.0 ms

(c)

16.0 ms

1 mm


Self-Rotation-Induced Propulsion of a Leidenfrost Drop on a Ratchet

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