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The Leidenfrost Effect

Presentation of practical work @ Physics of Fluids, University of Twente

Martin Klein Schaarsberg

on 19 April 2012

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Transcript of The Leidenfrost Effect

Lifetime of drops
Vapour height
Leidenfrost stars
The Leidenfrost Effect
Measuring the height of the vapour layer underneath the drop

Figure copied from: Ejs Open Source Single Slit Diffraction Model
Retrieved on 14 April 2012
the wavelength of the light
the thickness of the vapour layer
an integer, counting from the center
the angle between the fringe and the center of the pattern
We can now calculate the height of the vapour layer with:
We measured the vapour height for a range of different drop diameters.
We used a 532 nm green laser, a water drop on a 300 degree Celcius wafer and two syringes to keep the drop in place.

A remarkable observation is that besides the small diffraction pattern, also a much larger pattern appears.

In the measurements we could move this large pattern sideways by moving the drop sideways.

Presumably, the secondary pattern comes from the light rays that are deflected by the liquid of the drop.
The diffraction pattern was measured by analyzing photographs taken, using the dimensions of the whiteboard as reference. For each drop, we calculated the vapour height with the first four minima of the diffraction pattern.
Norah Hornsveld
Peter van der Linde
Martin Klein Schaarsberg
Henk-Willem Veltkamp

Figure copied from: A.L. Biance, C. Clanet & David Quéré, Leidenfrost drops, Physics of Fluids 15 (2003), 1632-1637
The drop width was determined by analyzing photographs taken, by making use of the diameter of the wafer as a reference width to calculate the drop width.
As a reference, we compared our data with the data from Biance et al. In their experiment, the drop was deposited on a duralumin plate at 300 degrees Celcius, and kept at constant radius by continuously feeding it with water.

The resulting vapour height we calculated shows the same increasing trend. However, the resulting vapour heights we calculated were up to two times as large as those from Biance et al. We presume that this discrepancy is due to either a difference in the setup or a systematic error. Biance et al. used a different plate material and kept the radius constant, while we took snapshots of the drops while they evaporated.
Biance et al.
our data, approximately
The vapour layer forms a slit between the liquid and the heated surface. Shining a laser on this slit results in a diffraction pattern. With this pattern, we calculated the height of the vapour layer for range of different droplet radii.

By projecting the diffraction pattern a certain distance away from the slit it is enlarged and the fringes can be easily be distinguished from each other.

Figure copied from [1].

The diffraction pattern occurs due to the wave properties of light [2]. If the slit is considerably larger than the wavelength of the light, the wavefront can be considered a series of point sources. Path length differences between these points and the screen will give constructive and destructive interference where light waves are in and out of phase. This creates a diffraction pattern of bright and dark fringes on a screen [3].
Measuring the vapour height
The drop starts to show self-sustained oscillations if the maximum radius is bigger than the capillary length of the drop:

They oscillate in a rapid motion due to the low friction between the drop and the heated surface and it lead sometimes to a morphological bifurcation of the drop, which takes the shape of a star [1-4].

Similar star-shaped drops have been reported in drops vertically vibrated on non-sticky surfaces, and is generally attributed to a parametric instability [5].

The instability of the drop increases if the radius of the drop is increased. The drop starts to produce vapour bubbles which are trapped below the curved and concave surface of the drop. These vapour drops rise due to buoyancy and burst if they reach the upper surface of the drop (so called chimneys).
1. N.J. Holter and W.R. Glasscock, J. Acoust. Soc. Am. 24, 682, (1952)

2. R. Takaki and K. Adachi, J. Phys. Soc. Jpn. 54, 2462, (1985)

3. D.E. Strier, A.A. Duarte, H. Ferrari, and G. Mindlin, Physica A, 283, 261 (2000)

4. A. Snezhko, E. Ben Jacob, and I. S. Aranson, New J. Phys. 10, 043034, (2008)

5. A.L. Biance, C. Clanet, and D. Quéré, Phys. Fluids, 15, 1632, (2003)

6. A.L. Biance, Ph.D. thesis, University of Paris VI (2003)

7. G.I. Taylor, Proc. R. Soc. London, Ser. A, 201, 192 (1950)
The precision of the setup could also be improved, most notably by increasing the distance from the slit to the screen. In the current setup, with the screen at about 3 m from the slit, the first minimum was sometimes barely discernible. In future measurements the focus of the camera on the drop could be improved resulting in higher quality analytical possiblities.
A drop consisting of ethanol and water absorbs the laser light.
Drops bouncing on the surface of the brass plate.
The making of...
would like to thank
for using their lab!
their assistance and
This happens if the radius of the bubble equals at least a few capillary lengths. The theoretical value for this critical radius is calculated by Biance et al.[5,6]:

This theoretical value corresponds with the measured value, also determined by Biance et al. [1,2]:

Biance et al. based these values on the fact that this effect suggests that the critical radius is related to the Rayleigh-Taylor instability of a heavy fluid (the drop) layered above a light fluid (the vapour layer). The vapour layer tends to rise because of Archimedes’ thrust, but this implies a deformation of the lower interface, which the surface tension opposes [7].

These chimneys start to occur if the radius of the water drop is roughly 1 cm [5].
The minima in intensity, positions of the dark fringes, can be found with:

The effect of a drop floating on a hot plate was first reported by the Dutch researcher
Herman Boerhaave
(1668-1738) in his "Elementa Chemiae" of 1732. He was surprised to observe that a drop of alcohol deposited on the hot plate did not ignite, but started hovering over the plate instead.

The effect was not investigated thoroughly until
Johann Gottlob Leidenfrost
(1715-1794), Professor at the University of Duisburg (Germany), published "De Aquae Communis Nonnullis Qualitatibus Tractatus" (A Tract About Some Qualities of Common Water) in 1756.

The "Tractatus" is a very detailed study of 175 pages in Latin, 39 of them deal with the experiment we now refer to as the "Leidenfrost effect" experiments of a waterdrop on a hot plate.

In the section "De Fixitate Aquae Diversa In Igne" (On the Fixation of Water in Diverse Fire) Leidenfrost describes the experiment: He performed the experiments with an iron spoon ("well polished and without rust") heated red-hot in a fireplace and carefully put a drop of water into the spoon and timed (with a pendulum) how long the drop survived.
When a drop of water is deposited on a sufficiently hot plate, it won’t vapourize instantly but it will hover over the plate for minutes instead.
What is the "Leidenfrost effect"?
The bottom layer of the drop is immediately vapourized at the moment of impacts on the hot plate. This vapour layer forms a cushion for the drop and prevents it from touching the hot surface. The cushion continues to exist, because it is constantly refuelled with water vapour from the drop. In this way no heat transfer can take place directly from the hot plate to the drop. Indirectly there is still heat transfer possible through the vapour layer, but water vapour is a poor thermal conductor.
So just a little heat can be transferred indirectly, which explains the long existence of the water drop on a very hot surface.

The drop is hovering over the plate on a vapour layer - like a hovercraft on a layer of air - which is only 0.1 mm thick at the edge and 0.2 mm in the middle of the drop. John Tyndall (1820-1893), Professor at the Royal Institution in London, performed the Leidenfrost experiments with a glowing filament (candle) behind the floating drop. He was able to see the light of the filament through the vapour layer and thereby confirmed the presence of a thin vapour layer beneath the drop keeping it afloat.
John Tyndall
The Leidenfrost principle
Johann Gottlob Leidenfrost
*November 27, 1715 (Rosperwenda, Germany)
†December 2, 1794 (Duisberg, Germany)
Son of the well-known minister, Johann Heinrich Leidenfrost
University of Gießen: Theology
University of Leipzig: Medicine
University of Halle: Medicine
1741: doctorate in medicine for his thesis:
"On the Harmonious Relationship of Movements
in the Human Body"
Spent some years travelling
1743: Professor (medicine, physics and chemistry) at the University of Duisberg
1745: Married with Anna Cornelia Kalckhoff (7 children)
Rector of the University of Duisberg
1756: Member of the Berlin Academy of Sciences
Published over 70 manuscripts, but the most famous is his "De Aquae Communis Nonnullis Qualitatibus Tractatus" (1756) ("A Tract About Some Qualities of Common Water"). The "Leidenfrost effect is first discussed in the section "De Fixitate Aquae Diversa In Igne" (On the Fixation of Water in Diverse Fire).
The error in the vapour height was estimated as two times the standard deviation of the four calculated heights

The error in the radius was approximated as 5% of the measured value
Vapour height vs. drop radius
J.G. Leidenfrost
Lifetime versus diameter
Lifetime versus temperature
Properties of water and ethanol

Comparing ethanol drops of different volumes
Comparing different fluids: 0.05 ml drops of water and ethanol
Comparing different fluids: water and ethanol

1. Ejs Open Source Single Slit Diffraction Model: http://weelookang.blogspot.com/2011/10/ejs-open-source-single-slit-diffraction.html
(Retrieved on 14 April 2012)

2. Information about diffraction: http://en.wikipedia.org/wiki/Diffraction
(Retrieved on 14 April 2012)

3. The Fresnel principle: http://en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle
(Retrieved on 14 April 2012)
The Leidenfrost effect occurs when a drop is deposited on a surface whose temperature is sufficiently high enough. The drop will form a protecting vapour layer underneath the drop at the first contact with the plate. Water vapour acts here as an insulator for the remaining water in the drop, hence there can be less energy transport from the plate to the drop. With further increase of the heat of the plate, the lifetime of the drop will slowly decrease.

The experimentally found data is shown in the graphs "Lifetime versus diameter" and "Lifetime versus temperature". The data presented in the graphs allowed us to make the following conclusions.
A multimeter connected to a thermo-coupler, that measures the temperature of the brass plate, displays the measured temperature.
A stopwatch has been used to keep track of the lifetimes of the drops deposited on the brass plate.
A photo camera is positioned above the center of the brass plate, to make photographs of the drops to allow calculation of the diameters of the drops.
With the pipette the drops are deposited.
Herman Boerhaave M.D.
For the lifetime measurements two liquids are used to form the drops with, water and ethanol. These liquids have different properties that will show different results in the performed measurements. Inthe table on the right, some of the properties that influence the measurement of the liquids are shown.

In the experimental setup the drops of the liquids are deposited on a heated brass (CuZn) plate. To measure the radii of drops deposited on the hot brass plate, the drops are photographed from above and the radii are measured by analyzing the photographs and calculate the actual size of the drop by using the fixed radius of the brass plate as a reference.

To measure the lifetime of the drops as a function of the diameter of the drops, the brass plate is kept at a constant temperature of 300°C, while drops with different radii are deposited on the plate one at a time. The lifetime of the drop is measured with a stopwatch and thus the radius of a drop can be related to the lifetime of the drop.

There are several aspects that need to be taken into consideration when it comes to measuring the lifetime of the drops. The capillary length (lc) is a characteristic length scale for fluid subject to a body force due to gravity and surface force due to the surface tension. It can be calculated with

Were γgamma is the surface tension of the liquid, ρrho is the density of the liquid and g is the acceleration by gravity. If the drop radius (R) is lower than the capillary effect the drop becomes almost spherical, with a flattened surface at the bottom. Thus the volume of the drop can be determined with

The larger the volume of a drop the longer the expected lifetime since more water needs to be evaporated for a drop to evaporate completely. It was shown that the size of the contact surface (lambdaλ) of the drop is given by a balance between gravity and surface tension. However if the radius of the drop is larger than the capillary length the drop becomes flattened by gravity [6]. And thus the contact surface becomes roughly equal to the radius of the drop. If the drop is smaller than the capillary length, the contact surface was found to be:[7]
Drop illuminated with laser shows internal reflection.
An unstable drop touches the surface of the brass plate.
On the spot where the drop had been, the spoon turned dull, but the surroundings were still red-hot.

After depositing the first drop, he noticed the lifetime of the next drops decreased rapidly and he wrote down:

"...as if the matter of light and fire from the glowing iron suddenly was snatched into the water. (..) it finishes its existence, and in the spoon it leaves a smal particle of earth."

Leidenfrost's observation of the "particle of earth" and the title of the section "On the Fixation of Water in Diverse Fire" fit the alchemical conception of his era. According to this alchemical conception the world is made of the 4 elements water, earth, air and fire, which by various means can be transformed into one antother. Leidenfrost therefore dismissed Boerhaave's suggestion that the dust, inevitably blowing around in the chemistry lab, gets into the water. He was convinced of the alchemical fixation of water into earth by the use of fire. This essentially was because he was at a point in time when the still prevalent Aristotlean approach was slowly, but surely, giving way to experimental exploration in science.

For both liquids used the capillary length has been calculated to determine whether the radius of a single drop exceeds the capillary length and gravity influences the evaporation rate which would show up in the measurements as nonlinearity in the relation between the size of the drop and the lifetime of the drop.
The capillary length for water is calculated at the boiling point of water, 99.98°C.

The capillary length for Ethanol is calculated at its boiling point of 78.1°C.

The capillary length of the fluids decreases with; a lower surface tension or high density. Therefore the capillary length is larger for water than it is for ethanol. This means that water can obtain a larger radius of the drop while it holds a spherical form. Also the boiling points of the liquids used determines the evaporation rate of that liquid, the different chemical and physical properties of the liquids determine the boiling points.

Water molecules however can form hydrogen bonds with other water molecules9 making water a less volatile fluid then ethanol and it has a higher boiling point. Ethanol is a volatile liquid thus it evaporates faster since it is easier to make the transition from liquid phase to gas phase. Water requires a higher energy to evaporate resulting in a lower evaporation rate compared to ethanol with similar conditions. Thus the lifetime of a drop placed upon the hot brass plate decreases with a lower boiling point. Both these claims should be reflected by the measured data.

To determine the influence of the temperature of the heated brass plate on the lifetime of the drops, the volume of the drops deposited on the plate are kept constant. The liquids; water and Ethanol; are used to form the drops with either a volume of 0.05 ml or 0.025 ml. The temperature of the plate is varied and the lifetime of the drop is measured with a stopwatch and thus the temperature of the plate can be related to the lifetime of the drop.
1) Surface tension data of ethanol: http://ddbonline.ddbst.de/EE/11%20SFT%20%28Surface%20Tension%29.shtml (Retrieved on 14 April 2012)
2) David R. Lide, ed., CRC Handbook of Chemistry and Physics, Internet Version 2007, (87th Edition), <http:/www.hbcpnetbase.com>, Taylor and Francis, Boca Raton, FL,2007.
3) Surface tension data of water: http://www.engineeringtoolbox.com/water-surface-tension-d_597.html (Retrieved on 14 April 2012)
4) Density and specific weight of water: http://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html (Retrieved on 14 April 2012)
5) Data sheet of ethanol: http://www.wolframalpha.com/entities/chemicals/ethanol/jg/qp/et/ (Retrieved on 14 April 2012)
6) L. Mahadevan and Y. Pomeau, Phys. Fluids, Vol. 11, 2449, (1999)
7) A.L. Biance, C. Clanet, and D. Quéré, Phys. Fluids, Vol. 15, 1632, (2003)
8) Dynamic and kinematic viscosity of water: http://www.engineeringtoolbox.com/water-dynamic-kinematic-viscosity-d_596.html (Retrieved on 11-04-2012)
9) O. Markovitch, N. Agmon, Mol. Phys. Vol. 106, 485, (2008)
10) Leidenfrost temperature on different surfaces: https://engineering.purdue.edu/BTPFL/BTPFL%20Publications/81.pdf
Lifetime versus diameter:
This experiment shows us that the lifetime of the drops experiencing the Leidenfrost effect increases with increase in diameter of the drop. The calculated capillary length of water at 100°C is 7.9 mm. This length is not approached in the measurement with water. Since the capillary length is not exceeded, the drops can be considered spherical while they evaporate.

The same experiment was performed with ethanol and these results are shown in the same graph. It is clearly visible that the increase in diameter resulted in a longer lifetime of the drop. However in this experiment the drop sizes does exceeds the limit of the capillary length. The calculated capillary length was found to be 4.9 mm for ethanol. Thus drops with a diameter larger than 4.9 mm can experience more deviation, inter-/extrapolation of the data beyond the diameter of 4.9 mm will likely have a reduced coefficient of determination.

It is shown that the lifetime of the ethanol drops is shorter than those of water drops with similar diameters. As explained in the theory, this is due to different chemical and physical properties of the two liquids. Ethanol is a volatile liquid, thus it evaporates faster since it is easier to make the transition from liquid phase to gas phase. Water molecules however can form stronger hydrogen bonds with other water molecules [1], making it less volatile and requires a higher energy to evaporate resulting in a lower evaporation rate compared to ethanol with similar conditions.

Lifetime versus temperature:
The temperature at which the drops first begin to float (the Leidenfrost temperature) for water is found to be about 210°C [10]. With a water drop of 0.025 ml, we measured a Leidenfrost temperature of 215°C. The temperature at which the ethanol drops first begin to float is found to be about 160°C. With a drop of 0.025 ml, we measured a Leidenfrost temperature of 170°C.

When the temperature of the plate is increased, the lifetime of the drop will slowly decrease. This effect can also be seen in the graphs of our measurements. In the first graph of "lifetime versus temperature", the lifetime of water and ethanol of 0.025 ml drops is shown as a function of the temperature. The lifetimes of the ethanol drops are shorter than those of the water drops. This is due to different chemical and physical properties of the two liquids as we already described in the theory.
Also it can be seen that the measurement of water is limited. This is due to the fact that water has a higher Leidenfrost temperature and also because at high temperatures (close to 300°C) the water started to evaporate again. We didn't expect this evaporation at high temperatures. More research is needed to explain this effect.
In the second graph the "lifetime versus temperature" for ethanol is shown for a volume of 0.05 and 0.025 ml. The drop with the greater diameter has a longer lifetime. This is due to the fact that there is more liquid to evaporate. This is also explained in the previous lifetime/diameter experiment.

With our experimental set-up it was not possible to control the temperature. It took at least 1 hour to achieve a stable temperature. Therefor we measured delta T to achieve our data. Also we had some difficulties because the plates where very rough.
To improve the experiments a better temperature controller is needed. Also the plate should be completely smooth.
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