Leidenfrost Self-Rewetting Drops - The Journal of Physical Chemistry

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Leidenfrost Self-Rewetting Drops Safouene Ouenzerfi, Souad Harmand, and Jesse Schiffler J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b11944 • Publication Date (Web): 19 Apr 2018 Downloaded from http://pubs.acs.org on April 20, 2018

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The Journal of Physical Chemistry

Leidenfrost Self-Rewetting Drops Safouene Ouenzerfi1, a), Souad Harmand 1, b*) and Jesse Schiffler 1, c) 1

University of Valenciennes and Hainaut-Cambrésis, LAMIH, UMR CNRS 8201, Valenciennes, France.

Abstract

As discovered by Leidenfrost, liquids placed on very hot solids levitate on a cushion of their own vapour. This is called also calefaction phenomenon, a dynamical and transient effect, as vapour is injected below the liquid and pressed by the drop weigh. To account the film vapor, we consider the surface tension magnitude as well as the Marangoni effect (in particular the thermal one) which arise with imbalance of surface tension forces. For standard liquids, these forces contribute to amplify the thickness of film layer and the levitation of the droplet. Our findings imply the ability of recent binary mixture liquids, called self-rewetting fluids to reduce the vapour film thickness and demonstrate the powerful influence exerted by different binary mixture to enhance the heat transfer at high temperature. Such self-rewetting fluids are presenting high value of surface tension at high temperature, and in which the Marangoni forces are inversed as from critical temperature. We consider our assay to be a way for improvement in the high temperature mass cooling applications.

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1. INTRODUCTION: Calefaction is the phenomenon occurring when liquid droplets roll over a very hot surface, due to the presence of a steam layer caused by the sudden vaporization of the drop. This phenomenon, called also Leidenfrost phenomena, is observed when the solid temperature is much higher than the boiling point1. Thus, the drop is not anymore in contact with the solid, but levitates above its own vapor. The film of vapor acts also as an insulator for the liquid above it, thereby slowing the evaporation process. Recently, Queré2 examined the effect of the step material, liquid properties and the step height on the jumping process during Leidenfrost phenomena. He presented also an overview about theoretical and experimental existing works. The existence and the characterization of the Leidenfrost point have been widely investigated3-5. It depends on the solid roughness

6-8

on the purity of the liquid 9, which

can also affect the lifetime of the drop10 and even on the way the liquid is deposited. Theoretically, numerous studies 11-13 have been performed to understand and prevent the thickness of vapour layer. In particular, Sobac et al.

13

obtain new scaling generalizing classical ones derived by Biance et al.4 by

taking in account the case when the shape of the vapor film underneath a Leidenfrost drop is not flat. Contact between the liquid and solid is crucial for cooling applications such as fire-fighting, hot-mill steel rolling, thermal power plants and microprocessor cooling 14. Methods to increase the Leidenfrost temperature, or delay the onset of the film boiling regime are therefore of great interest for such applications. Lately, surfaces covered with nanofibers were shown to effectively enhance the heat transfer from the surface to a liquid in contact with it 15, 16. Vakarelski et al. 16 report on increasing the Leidenfrost temperature by surface textures that can promote droplet wetting at high superheat via capillary wicking. The aim of our work is to demonstrate that using self-rewetting fluids (characterized by a surface tension that increases with increasing temperature) can leads to the reduction of the thickness of film layer as well. This reduction leads to an enhancement of the heat transfer between the droplet and the substrate. _____________________________ a) Electronic mail: [email protected] b*) Electronic mail: [email protected] c) Electronic mail: [email protected]


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2. Experimental setup: The experimental setup consists of a copper polished block substrate, a heater related to an autotransformer and a dropper (as shown in Fig. 1).The working fluids were pure Water and aqueous solutions diluted with different alcohols at different volumes’ concentrations (Water-7.15% Ethanol, Water-7.15% Propanol, Water-3% Butanol, and Water-1.5% Pentanol). K type thermocouple was installed on top of the copper surface in order to determine its temperature. Regulated electrical energy was supplied to the heater by using a variac, connected to the 220-volt laboratory power. A syringe (with tips needles from EFD, Inc with inner diameter of 2 mm and outer diameter of 3 mm) was used to drop the liquid droplets on the substrate. The syringe was held perpendicular to the horizontal surface and droplets were released from about four mm from the surface. The injected droplet is permanently nourished and fed by a syringe pump. The vapor layer under the droplet was measured with a high-speed Keyence microscope camera VHX-5000 setup (VH-Z2 Macro lens X 100 Observation range 18 mm x 6 mm). An automatically setup software was used to determine the distance’s gap with precision of 20 µm. First, we record a video using partial ring light option that make observation in partial dark field possible to emphasize height differences such as scratches. The VH-M100E XY measurement system allows us to measure a target while moving the stage to expand the field of view. Hence, we select manually the area to measure the distance. The system is already compared to reference line. Since a Leidenfrost drop evaporates, the film thickness is likely to vary with time. We first characterize and fix stationary states. Thus, we looked at the situation where the drop was constantly fed with the liquid, at a prescribed rate. The protocol measurement consist on establishing an equilibrium state by changing the flow pump rate. So, a specific rate and position determinate the stationary state.



FIG. 1: Experimental setup for film vapor measurements

•

Refrence’s measurement

Here we present a reference test in which we identify the diameter of a known needle in order to optimize the measurement setting by microscope. Hence we set up the video processing for the needle calibration subsystem. As a reference, we measure the diameter of a 400 µm NE27 needle. The values set is 412 µm with accuracy of 10 µm. a) Principle and description In this study, we present the calibration method used to measure the vapor thickness. The method allows accurate identification and quantification of changes in size of particular surfaces using digital optical microscopy approach. Performing the Keyence equipment, the horizontality is guaranteed by an adjustable support. We place the needle tip in front of the camera and we change the illumination option in order to find the best contrast then we perform a series of measurements as presented in figure 2. Measurements were analysed using a digital VHX-9000 microscope with a maximum resolution of 32 megapixels powered by microscope controller unit with integrated 23" LED monitor and Keyence software. The microscope had built-in LED lights and magnification adjustable from 20 to 200×, thus allowing accurate measurements of surface viewed in real time depth composition. The microscope was equipped with a versatile stand and stage that allowed 360 degree views of an object. Upper surface


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was lit by a high brightness LED lamp and then documented by a camera with CMOS image sensor and software resulting in a digital photograph file. Each measurement was documented by recording a digital image. The images were of high-resolution quality thanks to a short wavelength light used for illumination, and the HDR (high dynamic range) function that captures high-color gradation images at different exposures and then compiles them into a single image (figure 2). The images were stored in a VHX integrated system that enabled observing, capturing and measuring of morphometrical parameters of the experimental droplet. In this preliminary study, we used different images and measured thickness using tools for micrometrical measurements in the Keyence software in order to choose the image adequate mode. Knowing the focal distance and setting the magnification, the VH-M100E XY measurement system allows the automatic measurement of selected target. The camera under test shall target a uniformly illuminated white chart with even daylight illumination. The illumination to the chart shall be between 400-800 cd/m2. A back illuminated uniform chart may also be used for the evaluation. Illumination mode enable identify edge by intensity graphs, then choose proper setting by displaying edges detected for each segment and outputs the results separately (example in figure 3).

FIG. 2: Different image modes by VH-M100E XY measurement system



FIG. 3: Detecting edges by identifying levels of intensity. b) Comparison To compare and calibrate the measurement’s method, we measure the needle diameter with an electronic digital Schut-micrometer with 1 m resolution as presented in figure 4. Hence the setup used correspond to lens VH-Z2 Macro X 100 - Observation range 18 mm x 6 mm and partial ring light as illumination mode. We estimated an error of 10 µm.


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Moy = 402.45 µm Sigma = 4.43

420 415 410

Diameter (µm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


405 400 395 390 385 380 375 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18

Sample number

Micrometer measurement’s

VH-M100E measurement’s

FIG. 4: Micrometer reference measurement's with VH-M100E value

•

Liquids surface tension

In this study, we use pure water and several mixtures water-alcohol. Figure 5 present the variation of the surface tension with temperature for the several aqueous solutions mixtures tested in this work as well as water. If the surface data of Water-Ethanol and Water-Propanol solutions were investigated from 10, the rest of surface tensions measurements have been performed in this work using the pendant droplet method using Kruss DSA 100 equipment. Following the pendant drop method, the surface tension or interfacial tension is calculated from the shadow image of a pendant drop using drop shape analysis18, 19. The pendant drop is a drop suspended from a needle in a bulk liquid or gaseous phase. The shape of the drop results from the relationship between the interfacial tension and gravity. When making a measurement, the scale of the video image is measured first in order to give access to the actual drop dimensions. The shape of the drop is then determined from the video image of the dosed drop using greyscale analysis. The error in measurement is estimated to be less than 10%.



100 Pure Water

90

Surface tension (mN/m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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80

Water-3% Butanol

70 Water- 7.15% Ethanol

60

Water-7.15% Propanol

50 40

Water- 1.5% Pentanol

30 20 10

30

50

70

90

110

130

Temperature (˚C)

FIG. 5: Surface tension-temperature behavior for pure and a water-alcohol mixtures In particular, the mixture Water-3% Butanol and Water-1.5% Pentanol are called self-rewetting fluids in which the dependency of the surface tension with temperature is inversed in some ranges and the Marangoni forces are inversed as well

20

. This means that the surface tension values increase for

highest temperature assuming the surface tension forces are dominants. We notice that the main change proprieties between water and self-rewetting fluids (water + very small quantity of alcohol) consist in surface tension behaviour 20.

3. Theory:

For a given radius R of drop, the vapor film “e” has a defined thickness at a steady state regime. In order to determine this thickness we can establish the equilibrium of local mass in the vapor [4]. In fact, the steam is, at the same time, brought into the layer by evaporation of the liquid and driven out of by Laplace pressing forces (figure 6):

= . .

∆ .

=

.

∆


(1)

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Where λv is the vapor conductivity,

∆Tp is the difference between the plate temperature and the

boiling temperature of the liquid, L the heat latent, ηv the vapor viscosity, ρv the vapor density and Sc is the contact surface depending on the droplet shape. In this model we assume that the film vapor has a flat shape according to our experimental results (Fig. 6).

FIG. 6: Equilibrium mass for a droplet under calefaction

considering ∆P=2γ/R, where γ is the surface tension and Sc=2/3 .π.R4/k-2 with “k” the capillary length, we can establish the model for the vapor thickness 17:

e = /

∆ / $ ! " #

(2)

As the model presented, we assume the coexistence of deforming inertial forces and stabilizing cohesive forces for liquids. 4. Results and discussion: Figure 7 shows clearly that the air gap (vapour film) is reduced in the case of 3% Butanol aqueous solution compared to the same for pure Water (In table 1 we present a summarized of measured gap size value). In fact, pure Water as well as Water–7.15 % Ethanol and Water–7.15% Propanol solution exhibits a decrease in surface tension with increasing temperature; from one side the surface tension value for such liquids is low for higher temperature, in the other side if a temperature difference is established over a liquid-air interface, the liquid layer near the interface moves towards the cold side, where the higher surface tension generates a pulling action (figure 8). In order to explain our observation, we hypothesize that the Marangoni flow generates this action, which affects the droplet’s vapour layer. Furthermore, we believe that when a droplet hits the edge of the step, parts of the droplet



are cooled. We propose that this causes the temperature gradient on the droplet and as a result a

Pure water

Thickness ( μm)

Marangoni flow on the droplet surface in the radial direction.

Thickness (μm)

Diameter coordinate (mm)

Self-rewetting fluids

Thickness (μm)


Diameter coordiante ( mm)


Standard aqueous alcohol mixtures solutions


Thickness (μm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Thickness (μm)

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Diameter coordiante (mm)

FIG. 7: Film thickness measurements for 3%-Butanol aqueous solution,1.5%Pentanol aqueous solution, pure water, 7.15% Ethanol aqueous solution and 7.15% Propanol aqueous solution (R=2.2 mm and Ts= 200 ˚C)

FIG. 8: Inversed Marangoni effect in self-rewetting liquids

Fluids

Gap size

Water

380 µm ± 15%

Water-3% Butanol

140 µm ± 15%



Water- 1.5% Pentanol

81 µm ± 15%

Water-7.15% Ethanol

310 µm ± 15%

Water-7.15% Propanol

340 µm ± 15%

Table 1: Summarizing film vapor thickness measurements for different fluids (R=2.2mm).

The exact temperature determination at a non stable multiphase interface is not evident. We determined the temperature gradient at the surface of the droplets by using an infrared thermography camera from FLIR sc7000 S systems with a resolution of 30 µm per pitch. Focusing in the droplet edges, the film layer and the substrate in the same time consist a hard task. Hence, we try to have the profile of edge of the droplet at a specific section. At a given temperature, the maximum radiation is achieved when the object has an emissivity of 1. The mixture emissivity is about 0.94 in our case: mixture (as water) being mostly opaque to infrared, we expect to be able to read the surface temperature of the drop during evaporation.

The temperature profile at the droplets surfaces are given in figure 9. There is a significant temperature difference between the base (warm) and the top surface (cool since it is connected to the syringe system) of the surface levitated drop, indicating a possible thermal Marangoni effect and, hence, a Marangoni force which can affect the vapor layer stability. In addition we calculate the thermal Marangoni numbers using the data from figure 4 and 6 : %& =

'( ) ∆ . ' *.+

(where , is the length height of the droplet in m, ∆- is the maximum temperature

difference across the system in K, is the dynamic viscosity in kg/s/m, and . is the thermal diffusivity in m2/s ). In our case we consider the ∆- as the temperature difference between the measurement at the colder point in contact with syringe and the base warm temperature. In table 2, we compare the thermal number for several aqueous solutions at T=100 ˚C versus vapor film thickness : While Water-


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3% Butanol solution represent a self-rewetting liquids , Water and Water-7.15 Ethanol solutions represent a conventional fluids on which the surface tension20 falls down for highest temperatures. It is clear from the calculated data that the thermal Marangoni number is greater for self-rewetting fluids, which correspond to the dominating surface tension forces (see table 2). The thermal Marngoni number is regarded as proportional to surface tension forces divided by viscous forces.

Liquids

%&

Vapor Film Thickness (μm)

Water

494

380

Water_butanol3%

861

140

Water_Ethanol7.15%

382

310

Table 2: Thermal Marangoni number for different water mixture solutions (R =2.2mm, Ts =200 ˚C)

Especially for pure Water and Water-3% Butanol, we can notice a significant difference between the Marongoni numbers:

(%& //01 = 494 ; %& //015%7809:; = 861$. In the case of self-

rewetting fluids, the flow arise to the bottom of the droplet from colder to heater regions, compressing the vapor layer. In parallel with high value of surface tension, this may be the reason for the droplet’s vapor layer reduction.



120 110 100

Temperature (°C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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90 80 70 60 50 40

Water-3%but

30

Pure Water

20

0

1

2

3

4

5

Length (mm)

FIG. 9: Infrared camera snapshots for pure Water and Water-3% Butanol

Self-rewetting fluids (dilute aqueous solutions of high carbon alcohols), present a particular characteristic showing an increase in the surface tension with increasing temperature at a specific critical temperature. In such cases, the Marangoni effect can be inversed, and the liquid interface layer is closer to hot side following driving-in forces. In the other side, contrary to conventional fluids, selfrewetting fluids present a high value of surface tension at higher temperatures, which can reduce the film thickness following eq. 2. In fact, the surface tension values at Leidenfrost temperature are important [Table 3].


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Surface tension

Water–3%

Water–1.5%

Water–7.15

Water–7.15%

Butanol

Pentanol

%Ethanol

Propanol

58.17

71.22

25.72

21.51

Pure Water

52.16

(mN/m) at T=100˚C

Table 3: Surface tension values for high temperature 19.

This explains the reduced film thickness for the 3% Butanol aqueous solution and therefore why the droplet lifetime of a pure Water is longer (figure 10). To measure the lifetime, the droplet was released after getting a steady state and then followed by camera until the end of evaporation process. Water1.5% Pentanol solution is another self-rewetting mixture presenting higher surface tension than Water3% Butanol 20. The film thickness is the smallest one while the theoretical thickness is calculated to be about 50 µm for 2 mm droplet diameter. These results are a further evidence of Leidenfrost improvement by inverted Marangoni effect fluids and high surface tension value of self-rewetting fluids. As a consequence, the heat transfer to the liquid is enhanced in the case of self-rewetting fluid and the evaporation rate is shown in figure 11 to be more important 21. For R > @, capillary forces are not to be considered, the gravity dominates and the evaporation rate for both 3% Butanol aqueous solution and pure water, merge.



100

@

90

Droplet lfe time (s)

80 70 60 50 Pure water

40

Water- 3% Butanol

30 20 1

3

5

7

9

11

Droplet Radius (mm)

FIG. 10: Droplet lifetime function of radius (Ts= 200 ˚C)

7

Evaporation rate (µl/min)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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6 5 4 3 Pure water

2

Water-3% Butanol

1 1

2

3

Droplet radius (mm)

4

5

FIG. 11: Evaporation rate for each radius (Ts =200 ˚C)

In water, σ = 52.16 × 105 N/m at 100°C. The capillary length is thus within the range of 2 to 3 mm for water. This provides a good estimation for the diameter of a water droplet that is simply at rest on a table. Above this dimension, gravity becomes more predominant. Below this dimension, Marangoni forces occur and are effectives. In figure 12, we investigate the stability of Leidenfrost droplet upon drop diameter. For D > 3 mm, the difference between film thicknesses is reduced between water and self-rewetting fluids since we believe that the Marangoni forces are less present at this scale. This


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consideration is also noticed in the droplet life time behavior in which the difference between water and self-rewetting is diminished. For much bigger droplet, bubbles of vapor rise at the center and bursts at the upper interface due to a Rayleigh-Taylor instability at the lower interface 4, 23 like shown in figure 13. Likewise in figure 10 the life time of the droplet is reduced for bigger droplet due to instability and formation of bubbles 4.

FIG. 12: Vapor film thickness for different droplet sizes and several solutions (Ts =200 ˚C)



FIG. 13: Water-3%Butanol droplet behavior for different sizes and instability behavior when D> 10 mm (Ts =200 ˚C)

We studied in figure 14 the influence of Butanol concentration on the film thickness. In similar conditions (droplet radius and -C ), the film thickness D depends on the amplitude of the surface tension (see equation 2) . Ono

20

performed experiments proving that the higher the concentration of Butanol

is, the lower the surface tension will be. Thus, for the lowest Butanol concentration (1.5%), the film thickness is smallest corresponding to the highest surface tension value. We note that the thickness is measured in the zone where the steam is recognized graphically.


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Thickness (µm)

Thickness (μm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Thickness (µm)

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Diameter coordinate (mm )



FIG. 14: Comparison between vapor gap for different Water-Butanol concentration (Ts=200 ˚C , R=1.5 mm )

We present in figure 15, the calculated and experimental data for different concentration of Butanol 22

. Actually, we estimate the theoretical film thickness by two ways; the first one directly based on

equation 2 and the second based on equation 1 integrating the evaporation rate measured for each measurement: D = . .

E

∆ FG I . FH JK

and

e = /

∆ / $ ! " #

(3)

We can see clearly the difference between water (0% Butanol concentration) and the rest selfrewetting solutions. The film thickness decreases dramatically once the Butanol take presence. This is due mainly to the surface tension evolution presented in figure 4 and in agreement with film thickness model surface tension relationship (equation 3). However, the model do not take in account the reversed assumed Marangoni forces, which can explain the state of error with experimental data. The



results from the model-rate calculation are closer since the Marangoni effect is expressed in the change of evaporation rate.

200

Film thickness (µm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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150

100

50

0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

%butanol concentration

FIG. 15: Film thickness calculation from experimental and theoretical data (R=1.5mm)

Conclusion

In this paper, we have demonstrated the utility of self-rewetting fluid droplet in reducing the vapour thickness in Leidenfrost phenomena. We extent the experiments with water-Butanol solution to WaterPentanol solution in order to enhance the thermal contact performance. The thickness e of the vapor film was observed to depend on the surface tension characteristic of the fluid. As a consequence, the evaporation rate for self-rewetting fluid (such as Water-3% Butanol) exceeds the pure water one since the thermal contact is enhanced. The same, the lifetime of self-rewetting fluid droplet is smaller than the pure water one confirming the decreasing of heat transfer barrier. In the other hand, increasing the percentage of Butanol in aqueous water-Butanol solutions (reducing the level of surface tension) seems to increase the vapour gap.


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We studied as well, the standard water-alcohol mixture for instance, Water-ethanol and WaterPropanol solution (carbon composition less than five). We examined that, at the same measurements conditions as self-rewetting mixture, the vapour film still high and the droplet cooling is ineffective. This suppose that the enhancement of thermal performance come from the surface tension-temperature particularities of self-rewetting presenting inversed thermal Marangoni forces at high temperatures as well high surface tension value for such range of temperature , contributing in the reduction of vapour film.

These insights can be used to enhance the heat transfer performance in various cooling applications, including cooling of nuclear fuel rods under transient and accident conditions, fire suppression, electronics cooling, and metallurgy.



Supporting Information Camera video showing the vapor Leidenfrost film for both pure water and water_3%_butanol solution. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgements This work has been achieved within the framework of CE2I project (Convertisseur d’Énergie Intégré Intelligent). CE2I is co-financed by European Union with the financial support of European Regional Development Fund (ERDF), French State and the French Region of Hauts-de-France


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References

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Leidenfrost Self-Rewetting Drops - The Journal of Physical Chemistry

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