An experimental study of rupture dynamics of evaporating liquid films on different heater surfaces

International Journal of Heat and Mass Transfer 54 (2011) 1538–1547

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

An experimental study of rupture dynamics of evaporating liquid films on different heater surfaces Shengjie Gong, Weimin Ma ⇑, Truc-Nam Dinh 1 Department of Physics, Royal Institute of Technology (KTH), Roslagstullsbacken 21, 106 91 Stockholm, Sweden

a r t i c l e

i n f o

Article history: Received 19 February 2010 Received in revised form 15 November 2010 Accepted 16 November 2010 Available online 18 December 2010 Keywords: Liquid film Film evaporation Film dynamics Film rupture Film thickness measurement

a b s t r a c t Experimental data were obtained to reveal the complex dynamics of thin liquid films evaporating on heated horizontal surfaces, including formation and expansion of dry spots that occur after the liquid films decreased below critical thicknesses. The critical thickness of water film evaporating on various material surfaces is measured in the range of 60–150 lm, increasing with contact angle and heat flux while decreasing with thermal conductivity of the heater material. In the case of hexane evaporating on a titanium surface, the liquid film is found resilient to rupture, but starts oscillating as the averaged film thickness decreases below 15 lm. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction A thin liquid film spreading over and evaporating on a solid surface is encountered in many mechanical, nuclear and chemical engineering applications that involve processes such as cooling (e.g., condensation), heating (e.g., boiling), coating, cleaning and lubrication. A study on film dynamics is of special interest to understand boiling phenomena, for it has been well known that liquid film stability plays a key role in dryout of annular flow boiling. The film dynamics also finds its importance in pool boiling, since it is believed that the behavior of the near-wall liquid layer (so-called macro- and micro-layers) plays a key role in boiling heat transfer and boiling crisis. Noteworthily, recent experimental investigations [1,2] suggested a ‘‘scale separation’’ phenomenon in pool boiling which relates the dominant physics of boiling crisis to micro-hydrodynamics of the near-wall liquid layer. This provides rationale for the boiling experiment performed on a thin liquid film [3] so as to facilitate the diagnosis of the film dynamics. The other emerging application of liquid film is the cooling of high-power electronics where the space is constrained. In most cases, the liquid film stability and integrity are desired, since otherwise burnout (DNB for pool boiling or dryout for flow boiling) would occur as a threat to equipment performance and safety. Over the past three decades, a large number of experimental and theoretical studies have been carried out to investigate the ⇑ Corresponding author. Tel.: +46 8 5537 8821; fax: +46 8 5537 8830. 1

E-mail address: [email protected] (W. Ma). Present address: Idaho National Laboratory, Idaho Falls, ID-83415, USA.

0017-9310/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.11.036

film instability. Notably, the minimum thickness of liquid film flowing down a vertical or inclined adiabatic solid surface has been predicted theoretically on basis of force balance analysis or minimization of total energy criteria [4–9], resulting in a reasonable agreement with the limited experimental data under isothermal conditions. For a horizontal liquid film, Sharma et al. [10,11] developed a theory to predict the critical thickness at which liquid film rupture occurs by hole formation when the free energy of the film– solid system becomes equal to the free energy of the hole–liquid– solid system. The model predicted film rupture thickness is several hundred micrometers which are in good agreement with the experimental data on selected nonwetting solid surfaces (e.g., Teflon, polyethylene, PMMA, wax). In such thickness range the disjoining pressure cannot account for the film rupture since van der Waals intermolecular forces are negligible for films thicker than 0.1 lm [10]. The predictions also show that critical thickness of film rupture is strongly affected by fluid wettability which can be represented by contact angle; the smaller the contact angle is, the thinner the critical thickness. Orell and Bankoff [12] performed experiments to investigate the formation of a dry spot in a nonboiling thin film of ethanol creeping on a horizontal surface, and found the downstream film thickness around dry spot is 450– 660 lm in the heat flux range of 3–15 kW/m2. Benard-type convection cell pattern was found to appear prior to the dry spots. They also concluded that the threshold heat flux for formation of a dry spot at wall temperatures exceeding the saturation temperature was substantially lower than reported for incipience of pool boiling of ethanol. For a better wetting solid surface (the apparent contact angle is near zero), the film may be thinning to such an extent that

S. Gong et al. / International Journal of Heat and Mass Transfer 54 (2011) 1538–1547

1539

Nomenclature D h nw r RSD t k d

position of surface, lm height of, m refractive index of the liquid radius, m relative standard deviation time, s wave length, lm liquid film thickness, lm

the disjoining pressure can cause the film to rupture spontaneously. The film rupture is therefore determined by film-thinning disturbances such as drainage driven by gravity and spreading driven by surface tension gradients [13]. Narsimhan [14], Narsimhan and Wang [15] used numerical simulation to study the rupture of thin stagnant films on a solid surface due to random thermal and mechanical perturbations, generating insights for a basic understanding of the relations among rupture time, film thickness and perturbation amplitude. The film thickness in their study is less than 1 lm which is applicable to well wetting surfaces. Oron et al. [16] provided perhaps the most comprehensive review of the multifaceted subject of thin film dynamics modeling. They presented a unified mathematical system to predict the long-scale evolution of thin liquid films, based on the long wave theory. The set of mathematical evolution equations has its root in the work of Burelbach et al. [17], taking into account the influential factors such as van der Waal forces, surface tension, gravity, thermo-capillary, mass loss and vapor recoil force. In their review, Oron et al. [16] emphasized the importance of experimentally assessing and validating models derived from the long-wave theory. Noteworthy, Burelbach et al [18] investigated the steady thermo-capillary flow of the nonvolatile silicone oil with the thickness from 0.125 to 1.684 mm on a nonuniformly heated horizontal solid plate, and van Hook et al. [19] performed experiments on the onset of the long-wave instability in a thin layer of silicone oil of thickness ranging between 50 and 250 lm. Elbaum and Lipson [20] studied the thinning by evaporation of completely wetting water films on clean mica surfaces. It was observed that the thinning was unstable to nucleation and growth of dry patches in the film with thickness in the range from 10 to 100 nm, causing the liquid dewetting of the substrate. The initial process was described by a simple nucleation theory. Craster and Matar [21] presented a comprehensive review of the work carried out on thin films flows, focusing attention on the studies undertaken after the review by Oron et al. [16]. They pointed out that for the modeling of thin film dynamics, lubrication theory was still used to elucidate a wide variety of flows in which films have small aspect ratios. In general, our literature survey shows a good number of analytical models developed to simulate dynamics and rupture of liquid films on a wetting solid surface (apparent contact angle near zero) with the film thickness less than 1 lm for which longrange intermolecular interactions are pronounced. For non-wetting surfaces (apparent contact angle is much greater than zero), the film instability can be initiated at a significantly larger film thickness (say, hundreds of micrometers as shown in the abovementioned works) by external disturbances, and predicted by total free energy criteria. In both cases, high-fidelity experimental data are necessary for understanding of film rupture phenomenon and validation of the models. However, experimental characterization of film dynamics has been proven to be a challenging task due to difficulties in adapting traditional techniques to measure the micro-scale film thickness. Remarkably, there is no data for film rup-

dd/dt Dd h

evaporation rate, lm/s variation of film thickness, lm contact angle

Subscripts cr critical i ith monochromatic light

ture on a horizontal surface under diabatic (heating) conditions of importance to boiling heat transfer and boiling crisis. More recently, advances in micro (nano) fabrication and measurement techniques provide new capabilities to address the challenge. As a milestone in our research to study thin film dynamics under boiling conditions, we developed an innovative confocal optical sensor system to characterize the dynamic thickness of an evaporating water film [22]. Calibration and verification of the optical sensor were accomplished by comparative measurements between the optical sensor and a micro conductive probe. Various tests and measures were also carried out to identify and minimize the secondary effect of experimental conditions on measurement accuracy. The results prove the suitability and reliability of the confocal optical diagnostic system. In a further study on film instability using the optical sensor, we observed that at low heat flux (56 kW/m2) the water film evaporating on silicon wafer ruptures at the thickness of 84 lm, with a good reproducibility [22]. Since liquid film dynamics is affected by physicochemical properties of the liquid and surfaces as well as thermal-hydraulic conditions, the critical thickness at film rupture is expected to vary under different conditions. The present study aims to combine the optical diagnostic technique with a test program to produce a database that enables evaluation of factors and properties which govern film dynamics, stability and rupture. For heater substrate material effect, the experiment conducted on the silicon wafer is extended to various heater surfaces made of copper, aluminum, stainless steel and titanium. These materials are chosen because of their extensive usage in industrial applications. The titanium surfaces aged at different protocols are used to investigate the effect of wettability (contact angle) on film stability and rupture. The influence of heat flux on film rupture is also studied experimentally. Finally, ethanol and hexane are chosen for comparative tests with water, in order to establish the impact of liquid properties on film behavior and assess different analytical models.

2. Experimental method 2.1. Test rig A dedicated experimental platform was designed and constructed at the Royal Institute of Technology (KTH) to investigate liquid film dynamics and boiling physics at a microscopic level. Fig. 1 shows the test rig which consists of an optical table, liquid supply and temperature control system, power supply and heating system, stereo microscopic visual system, a confocal optical sensor system, two one-dimensional linear manipulators, a three-dimensional micro-manipulator and its control system, lighting system, and a test section for liquid film formation on solid surfaces. The optical table provides the required vibration isolation serving both for the test section and instrumentation mounted on the platform. Liquid is preheated in a stainless steel tank by a band heater to a

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Fig. 1. The schematic of the test rig.

desired temperature and the temperature level is maintained with a temperature controller; the hot liquid is then supplied to the test section through a micro pump capable of accurate flow rate control. The stereo microscope with magnification up to 300 is coupled with either a conventional digital camera or a special high-speed video camera. 2.2. Film thickness measurement system Techniques developed to measure the liquid film thickness can be divided into four groups: acoustic methods, nucleonic techniques, electrical methods and optical methods [23]. For the purpose of the present study, the optical methods are best suited for a dynamic liquid film for their non-intrusiveness and potential for high resolution in space and time. Specifically, we apply the confocal optical sensor, the latest breakthrough in optical methods. The similar technique was recently reported in [24] for thickness measurement of a vertical film. Fig. 2 shows the measuring principle of the confocal optical sensor. A beam of polychromatic (white) light is dispersed to a series of monochromatic light (denoted by wavelengths from k0 to kn) through an optical system of multiple lenses. Consequently, the white light source is imaged by the objective lenses on continuous points along the optical axis in the measurement space. When a measured object is placed in the measurement space, a single of the monochromatic point images (with wavelength of ki) is focalized on the object surface. Due to the confocal configuration, only the light of wavelength ki is reflected through the objective lenses and directed towards the spectrometer with high efficiency, all other wavelengths will be out of focus. The spatial peak on the spectrometer indicates the position at which the measured object

Fig. 2. Measurement principle of the confocal optical sensor.

surface intercepts with the optical axis. When a transparent object is placed in the measuring space, the reflections from the upper and the lower surfaces of the object will be detected by the spectrometer as two peak signals, and the thickness of the object is therefore deduced. For a liquid layer on a solid surface (e.g., heater), the variation of its thickness between time t1 and t2 can be expressed as

S. Gong et al. / International Journal of Heat and Mass Transfer 54 (2011) 1538–1547

Ddliquid ¼

Dt2  Dt1 ; 1  1=nw

ð1Þ

where nw is the refractive index of the liquid that has to be input as known parameter in the measurement, and Dt1 and Dt2 are the positions of the solid surface measured by the confocal optical sensor at time t1 and t2, respectively. This approach can continuously record film evaporation till dryout. The confocal optical sensors employed in the present study were made by Micro-Epsilon Company (see www.micro-epsilon.com) in Germany. As illustrated in Fig. 3, the sensor is incorporated with a controller which is also connected to a special Xenon light source. A single controller can support a number of sensors with different measuring ranges and accuracies. The controller optoNCDT2431 was chosen here, which is communicated with the computer through the software package provided by the company or a program further developed by the user depending on a specific application. So far two sensors IFS2431-3 and IFS24310.3 have been selected for different measuring ranges, as shown in Table 1. In principle, the sensors can be applied to a surface with curvature, and have the potential to measure a multilayer transparent system, with further software development for post-processing of the raw signal by users.

Fig. 3. Block diagram of the confocal optical sensor measuring system.

Table 1 The main parameters of the confocal optical sensors. Sensor

Measuring range (lm)

Spot diameter (lm)

Resolution (lm)

Max. tilt

IFS2431-3 IFS2431-0.3

0–3000 0–300

25 10

0.12 0.012

±22° ±28°

1541

The confocal optical sensor system employed here features a data acquisition rate up to 30 kHz and measuring range of 300 lm with nominal spatial resolution of 0.012 lm, which is the most suitable for a rapidly varied and evaporating liquid film of our interest. In a previous study [22], we reported a comprehensive test campaign for the verification and calibration of the optical system. The results showed a high accuracy (with the relative error of less than 1%) and reliability of the measurement under various experimental conditions. 2.3. Test section, its material and surface properties As shown in Fig. 4, the test section is a rectangular metallic sheet mounted on a heating system. The metal sheet is 30 mm long, 20 mm wide and 0.42 mm thick. The materials of the sheet selected in the present study are copper, aluminum, stainless steel and titanium. The test section and its surfaces on which the liquid film forms are prepared by a controlled procedure to ensure that the surface properties are reproducible. After flattening, all metal sheets are polished by #1200 emery paper and cleaned thoroughly by deionized water. The metal sheets are then glued to the copper block using silver epoxy to minimize thermal resistance. The heating zone of the surface is 10  15 mm. Cartridge heaters are embedded in the copper block and powered by the programmable DC power supply EA-PSI 9080-200 (EA Elektro-Automatik GmbH & Co., Germany), providing the controlled heating. Copper temperature is monitored by K-type thermocouples. Prior to experimentation, the positioning of the test section and the optical sensor are achieved by the high-precision manipulators. The procedure involves measuring the distances from the sensor to the test surface at selected points near the four corners and the center, using the sensor’s distance mode. The surface level adjustment is made until getting the greatest difference between the distances at the measured points below 5 lm. The deionized water is preheated and degassed prior to release to the test section. Microscopic bubbles of non-condensable gas are removed by both mechanical means and heating. The temperature measurements are recorded through a data acquisition system of PCI6035E plus SCXI-1102B of National Instruments. The stereo microscope is employed to visualize the process of film rupture. To characterize a test surface, the contact angle of a droplet of fluid formed on the surface is obtained using the method of droplet shape analysis. The test fluid is loaded in a plastic syringe which is then pressed to form a pendant droplet at the tip of its needle. The tip is lowered as closely as possible to the test surface where a new

Fig. 4. Test section of evaporating thin liquid film on a solid surface.

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S. Gong et al. / International Journal of Heat and Mass Transfer 54 (2011) 1538–1547 Table 2 Test matrix. Heater material

Surface condition

Liquid

Ti_20 Ti_200

Fresh Aged at 200 °C

Ti_400 Ti_800 Copper

Aged at 400 °C Aged at 800 °C Fresh Aged by 4 h boiling Fresh Fresh

Deionized Deionized Ethanol Hexane Deionized Deionized Deionized Deionized Deionized Deionized

Stainless steel Aluminum

Evaporation rate (lm/s) water water

water water water water water water

1.7–4.05 1.99–3.05 3.76–9.40 7.03–38.0 0.97–3.92 2.11–3.61 1.72–6.41 2.59–2.70 2.90–3.02

3.1. Water film thinning and rupture Fig. 5. Contact angle measurement.

droplet is formed when the growing pendant droplet falls due to its own weight. The photo of the droplet on the test surface is taken horizontally by a camera (Canon 450D with resolution of 12 million pixels) as shown in Fig. 5(a). For convenience of the analysis, the obtained picture can be transferred to a binary image via digital image processing, as illustrated in Fig. 5(b). The shape of the droplet is approximately of a spherical cap. If the variables r and h denote the radius of the base of the cap and the height of the cap, respectively, the contact angle can be expressed by the following equation:

h ¼ 2 arctan

  h : r

ð2Þ

For fluid/surface pairs with good wettability (e.g., ethanol or hexane on titanium), the droplet is spreading so thin that its height can only be estimated through its diameter and the volume discarded from the syringe. 3. Test results and discussion In order to gain insights into physical mechanism of film instability and rupture, the work reported in this paper focuses on quantification of the threshold thickness for film stability under various experimental conditions. The threshold film thickness (also called ‘‘critical thickness’’ in the paper) is corresponding to the thinnest film stably spreading over the surface. In other words, the film is considered to be unstable if its thickness is less than the critical value. The matrix of experimental conditions used in tests is as shown in Table 2. First, the test campaign covers different heater surface materials such as fresh titanium, copper, aluminum and stainless steel to examine the material effect. The working fluid is deionized water (ultrapure, HPLC grade). The heat fluxes were regulated from adiabatic condition to the initiation of boiling. Second, the study addresses the wettability (contact angle) effect by using the titanium sheets aged in a high-temperature resistance furnace. Three types of titanium surface (named as Ti_200, Ti_400 and Ti_800) were prepared by placing them in the furnace preheated and maintained over a duration of 1 h at the constant temperature of 200, 400 and 800 °C, respectively. Finally, fluids other than water, i.e., ethanol (90% anhydrous denatured HPLC grade, 5% methanol, 5% isopropanol) and hexane (95+% HPLC grade), were selected as working fluid and tested on aged titanium surfaces, to study the effect of fluids. All tests were conducted at atmospheric pressure.

As illustrated in Fig. 6, the thickness of a still water film on a Ti_400 surface is decreasing with time, because of heating from below with a heat flux no larger than that of boiling onset. Given a fixed heat flux, the thinning process is approximately characterized by a linear reduction of film thickness at the beginning. This is consistent to the constant evaporating rate at the heat flux. However, the thinning becomes non-linear and accelerated after the film thickness is decreased to a threshold value. A simultaneous observation of the microscopic imaging shows that following the thinning acceleration a hole (dry spot) is formed in the middle of the heating zone, and rapidly expands outward due to receding of the film, as shown in Fig. 7. Repeated runs indicate that the origin of the hole is within the circle of diameter 100 lm around the center of the heating zone. This implies that the optical senor should be situated near the centerline of the heating zone so that the dry spot can be caught as soon as it occurs. The thinning process can partially be explained by the principle of heat transfer at the liquid film surface and film instability. The evaporation rate is a function of heat flux and the film surface temperature. Initially, the liquid film is stable with its surface temperature being unchanged (e.g., at saturation). The evaporation rate is therefore constant due to quasi steady-state nature of the process. As the liquid film is thinning to such an extent imitating instability, the film rupture finally occurs, resulting in the steep variation of film thickness.

Fig. 6. Thinning process of a water film evaporating on a Ti_400 surface. Measuring point is at the center of the heater surface, and the critical thickness is 95.4 lm. The wall temperature is 105 °C, and heat flux is 36.8 kW/m2 over the heating zone.

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Fig. 8. Measuring points (A, at the center; B, C, D, E: 1, 3, 5 and 6.5 mm away from the center).

300 at Center

Thickness (µm)

To obtain the critical film thickness, a simplified approach is adopted in the data processing. As shown in Fig. 6, the black solid squares are the thickness data measured by the confocal optical sensor. The thickness variation within 0–300 lm can be represented by the pink dashed curve which is the polynomial fit of experimental data. The blue solid line is the linear fit of experimental data, whose slope indicates the evaporating rate of the film before rupture. The critical thickness for liquid film rupture is determined at the intersection of the linear fit line and the polynomial fit curve. In principle, the critical thickness should be corresponding to the minimum thickness of a liquid film spreading over the horizontal surface. The film is considered to be unstable (e.g., formation of a hole in the film) if its thickness is less than the critical value. This can be verified by the lateral profile of film thickness when the hole is formed. Since only one optical sensor is applied in each run of the tests, the lateral profile of film thickness cannot be obtained by simultaneous measurements at different locations. But this information can be derived from the thinning characteristics at different locations and the visual data. The methodology is described as follows. As shown in Fig. 8, five measuring points are chosen to obtain the respective thinning curves (see Fig. 9). The probing points A, B, C, D and E are 0, 1, 3, 5 and 6.5 mm away from the center of heating region, respectively. The experimental conditions are kept exactly the same for all the test runs performed for the measurements at the different locations. Based on the images of dry spot (hole) propagation, the time intervals for the hole to spread from the center to the other points are available. Given the time intervals as reference, the thinning curves of the liquid film at the five measuring points can be plotted on the same (relative) time coordinate, as shown in Fig. 9, which carries the information of liquid film profile as a function of time. If the time at the film rupture is assumed 0, the film profiles are as illustrated in Fig. 10 for earlier time points (minus means the time is before the film rupture). From Fig. 10, one can see that the film thickness at the position far away from the center is 93.5 lm when the film rupture occurs at the center. This is the minimum thickness for the film integrity, and comparable with the critical thickness (95.4 lm; Fig. 6) obtained from above-mention approach. Thus, the critical thickness defined as in Fig. 6 is suitable for identifying the onset of film instability. Interestingly, the critical thickness (96.1 lm;

250

1mm from Center 3mm from Center

200

5mm from Center 6.5mm from Center

150 100 50 0

0

20

40

60

80

100

120

Time (s) Fig. 9. Thinning curves of a water film at different locations on the Ti_400 surface.

140 120

Thickness (µm)

Fig. 7. Hole formation and expansion in an evaporating liquid film: the visual field is 12.5  12.5 mm with spatial resolution of 25 lm, and time interval between frames is 10 ms.

100 80 60 Time=0

40

Time= -1 Sec Time= -5 Sec

20 0

Time= -9 Sec

0

1

2

3

4

5

6

7

Distance from cenetrline (mm) Fig. 10. Lateral profiles of a water film evaporating on a Ti_400 surface.

Fig. 11) so-obtained from the thinning curve of a proximity position (say, 1 mm away from the center) is similar to the critical value. This means that the critical thickness is insensitive to the measuring position as long as the probe is located within a circle of diameter 1 mm around the center of the heating zone. Instead of addressing the physical mechanism of film instability and rupture, this paper is focused on quantification of the critical thickness for film stability under various experimental conditions. One can expect that the critical thickness is affected by the properties of both the surface and the fluid as well as contact angle and heat flux. An understanding of such impacts is the objective of the present study and reported in the following subsections.

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Critical thickness (µm)

150

130

110

Ti_20 Ti_200 Ti_400

90

Ti_800

70 0

1

2

3

4

5

Evaporation rate (µm/s) Fig. 12. Critical thicknesses of water film on titanium surfaces at varied evaporation rate.

Fig. 11. Thinning process of a water film evaporating on a Ti_400 surface. Measuring point is 1 mm away from the center, and the critical thickness is 96.1 lm.

dd þ 71:6; with RSD of 2:12%; dt for the surface Ti 400;

ð5Þ

dd þ 70:5; with RSD of 1:29%; dt for the surface Ti 800;

ð6Þ

dcr ¼ 14:3

dcr ¼ 14:2 3.2. Effect of surface aging on the critical thickness Contact angle, the scale of wettability of a liquid–solid system, is one of the key parameters affecting the instability of a liquid film [11,12]. In the present study, the titanium surfaces aged under different conditions are chosen to investigate the effect of contact angle on the film’s critical thickness. All aged surfaces (Ti_200, Ti_400 and Ti_800) together with the fresh surface (called Ti_20) are placed on the test platform for no less than one day prior to experiment, in order to avoid any change in their wettability due to photocatalytic activity [25,26]. The contact angles for the surfaces are as shown in Table 3, measured both before and after experiment. It can be seen that the variations of the contact angles before and after tests are marginal. This means change in surface properties is negligible during the experiment. Interestingly, the contact angle is elevated for the surface of Ti_200 aged at 200 °C, in comparison with the surface Ti_20 which does not take the aging procedure in the furnace. However, further increase in aging temperature results in a reduction in contact angle. Fig. 12 shows the critical thicknesses of water film on the titanium surfaces obtained at varied evaporation rates. The evaporation rate employed here is the linear value prior to the critical thickness (cf. Fig. 6), which is proportional to heat flux of each test. Based on the experimental data, the critical thickness can approximately be expressed as a linear function of the evaporation rate (see the solid lines in Fig. 12):

where RSD denotes relative standard deviation, while dcr and dd are dt the critical thickness (lm) and evaporation rate (lm/s), respectively. 3.3. Effect of surface material and operational time on the critical thickness In addition to silicon wafer [22] and titanium, other surfaces made of copper, aluminum, and stainless steel are employed in the current investigation. These materials are selected because of their applications available in heat transfer process. The critical thicknesses of the surfaces are plotted in Fig. 13, as a function of running time and material. The running time is the accumulative operational time (up to 4 h) on a test surface at the same heat flux. Liquid is refilled for the consecutive runs. It is actually a natural aging process of the test surfaces under the experimental conditions, which is reflected by Table 4 where the contact angles of water on the test surfaces are listed. The contact angles for the surfaces made of copper and aluminum decrease significantly during the experiment, while those of stainless steel and Ti_200 almost unchanged. This is because that stainless steel and Ti_200 are

140

dd þ 77:9; with RSD of  0:79%; dt for the surface Ti 20;

dcr ¼ 15:8

dd þ 82:9; with RSD of 1:61%; dt for the surface Ti 200;

dcr ¼ 13:9

ð4Þ

Table 3 Contact angle of titanium surfaces. Surface

Aging temperature (°C)

Contact angle before test (°)

Contact angle after test (°)

Ti_20 Ti_200 Ti_400 Ti_800

20 200 400 800

51.4 55.1 43.1 39.4

51.0 55.6 43.5 38.9

Critical thickness ( m)

120

ð3Þ

100 80 60 Copper Ti_200 Aluminum Stainless steel

40 20 0 0

50

100

150

200

250

300

Running time (min) Fig. 13. Critical thickness of water film on various metal surfaces (q = 36.8 kW/m2).

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S. Gong et al. / International Journal of Heat and Mass Transfer 54 (2011) 1538–1547 Table 4 Contact angle of water on surfaces made of different materials. Material of surface

Contact angle (°)

Copper Aluminum Stainless steel Ti_200

Before test

After test

55.2 61.4 62.1 55.1

35.5 40.2 59.8 55.6

much more stable and resilient to oxidation than copper and aluminum under the same conditions. This is why the critical thicknesses of the water film on the surfaces made of stainless steel and Ti_200 do not vary much during 4 h of running time, while those obtained on the copper and aluminum surfaces decrease with running time at the beginning, as shown in Fig. 13. However, a stable critical thickness is reached on the surfaces made of copper and aluminum after a sufficient running time (3 h). This implies that the surface properties no longer change from then on, and a stable contact angle is obtained. It appears that the material effect can also be explained by difference in contact angle. For instance, the surfaces made of stainless steel and Ti_200 have a similar critical thickness due to the similar contact angle. This applies to the aged copper and aluminum surfaces, although there is a slight difference between their measured contact angles. On the other hand, the critical thickness of stainless steel and Ti_200 is larger than that of copper and aluminum, since the contact angle of the former is greater than the latter. Nevertheless, the contact angle alone cannot account for all aspects of the material effect. This is manifested by the significant difference in the critical thickness (as shown in Fig. 14) of aged copper and Ti_800 surfaces, although they have comparable contact angles (see Tables 3 and 4). The critical thickness of the aged copper surface can be expressed as

dcr ¼ 8:1

dd þ 61:3; with RSD of 0:48%: dt

ð7Þ

Comparing Eq. (6) with Eq. (7), one point can be concluded: the influence of evaporation rate on the critical thickness of water film

on the Ti_800 surface is more pronounced than on the aged copper surface. This may be due to the superior thermal conduction of copper over titanium. A conjugate heat transfer analysis is needed to reveal the influence of thermal conductivity, which is beyond the scope of the paper. In general, it is clear that the critical thickness decreases with reducing contact angle of water on various surfaces (varied aging and materials) that have similar thermal properties. The film stability also benefits from a solid thermal conduction. The improved wettability and film stability due to aging process also help explain the significant gain in critical heat flux in boiling tests conducted on aged heater surfaces [2].

3.4. Ethanol film thinning and rupture To investigate the effect of fluids on the film instability, two organic fluids, ethanol and hexane, are employed in the present study. Table 5 shows physical properties of hexane and ethanol, compared with water. Ti_200 surface is chosen for the new tests with hexane and ethanol. With a contact angle of 12.8° when spreading on the Ti_200 surface, the wettability of ethanol is superior to that of water. However, ethanol is a volatile liquid with low latent heat, and its evaporation rate is therefore higher than water under the same heating conditions. For the tests conducted with heat flux in the range from 3.15 to 11.13 kW/m2, the critical thickness for ethanol film rupture obtained is illustrated in Fig. 15 as a function of evaporation rate and can be approximated by the following equation.

dcr ¼ 14:9

dd þ 93:7; with RSD of2:9%: dt

ð8Þ

It can be seen that under similar thermo-dynamic conditions ethanol exhibits a higher critical thickness than water. A thicker thermal boundary layer in the ethanol film may have been a contributing factor. Ethanol also has smaller thermal diffusivity, lower boiling point and latent heat, all of which may influence film instability. Although ethanol’s higher wettability enhances the film

300

150

Critical thickness (µm)

Critical thickness (µm)

Ti_400 Ti_800

130

Copper

110

90

250

200

150

100

70 0

1

2

3

4

5

2

6

4

6

8

10

12

Evaporation rate (µm/s)

Evaporation rate (µm/s) Fig. 14. Critical film thicknesses on aged copper and titanium surfaces.

Fig. 15. Critical thickness of ethanol film on Ti_200 surface.

Table 5 Properties of fluids (20 °C and 0.1 MPa). Fluid

Density kg/m3

Viscosity Pa.s

Surface tension N/m

Boiling point °C

Thermal conductivity W/(m.K)

Heat capacity kJ/(kg.K)

Latent heat kJ/kg

Water Hexane Ethanol

998 659.4 789

0.001 0.00031 0.0012

0.073 0.018 0.024

100 68.7 78.3

0.58 0.121 0.169

4.19 2.26 2.47

2257 365 896

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stability, other factors counteract it. The difference in critical thickness in water and ethanol is invaluable as a litmus test for validation of analytical models of thin film dynamics. 3.5. Hexane film thinning and rupture Hexane is a volatile liquid in room environment, while possessing a nearly perfect wettability on the titanium surface (with a contact angle of 2.7°). Fig. 16 shows the thinning processes of a hexane film on the Ti_200 surface under different heat fluxes. The linear thinning process (constant evaporation rate) prior to film rupture observed in water/ethanol tests is not the case for the hexane film. Instead, at a varied evaporation rate the film continues to decrease to a thickness less than 10 lm, and then become unstable; see the close-up views of Run A and Run B in

Fig. 17(a)–(b). If no heating from below is applied, the film thinning due to natural evaporation in atmosphere is approximately linear (Fig. 18a), and the oscillation phenomenon occurs at a film thickness of around 15 lm (Fig. 18b). As heat flux increases, the thinning process is accelerated, and oscillations are detected at a lower thickness. The oscillation frequency is within range of 20–35 Hz, and slightly elevated with increasing heat flux (evaporation rate). The oscillation was found to disappear when the heat flux is high enough, as in Run C in Fig. 16 which has the averaged evaporation rate of 38 lm/s. While mechanisms that suppress film oscillation at higher heat fluxes is subject to further study, it is noted that the hexane film behavior and measured data provide an unique window to understand a basic physics that govern film dynamics, instability and rupture. 4. Conclusions

Thickness (µm)

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This paper reports first-of-a-kind data on the thinning and rupture process of a thin liquid film on a horizontal surface heated from below. The focus was placed on the effects of the material’s and fluid’s properties, as well as surface (i.e.. aging) and operating conditions (e.g., heat flux). The micro-scale measurement was realized through the delicate experimental method developed in a previous study [22], which features a precise diagnostic system using confocal optical sensors. It is observed that a water film ruptures when thinning to a threshold thickness (called ‘‘critical’’ thickness in the paper). The film critical thickness in the tests performed was found to increase with increasing heat flux or evaporation rate, and within the range of 60–150 lm for water films and 150–250 lm for ethanol films. In addition to heat flux and fluids, the film instability is found to be greatly affected by the surface’s properties. Contact angle proves to have a profound influence on the critical thickness. For water film formed on the titanium surfaces aged at different temperature in a high-temperature furnace, the critical thickness decreases with reducing contact angle, relating the film stability to wettability. Even under the same heat fluxes, the critical thickness of water films on the surfaces made of copper and aluminum is decreasing with operating time due to reduction in their contact angles (aging-induced gain in wettability). The tendency is leveled off after the surface aging is completed (3 h) under experimental conditions. This behavior does not manifest itself with the stainless steel and the aged titanium surfaces, likely because these materials have stable oxidation-resistant properties and thus negligible effect of aging on wettability. The contact angle alone cannot however explain all the effects of material properties and conditions on water film instability. Thermal-physical properties of the heater surfaces also manifest

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Relative Time (s) Fig. 16. Thinning process of a hexane film on heated Ti_200 surface.

15

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Relative Time (s) Fig. 17. Close-up views of Run A and Run B in Fig. 16.

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Time (s) Fig. 18. Thinning process of a hexane film on unheated Ti_200 surface.

themselves through the onset of liquid film instability. For two surfaces with a comparable contact angle, the one (e.g., copper or aluminum) with a high thermal conductivity exhibits a thinner critical film than the one with a low thermal conductivity (e.g., stainless steel or titanium). Such a material-property effect suggests that the significance of conjugate heat transfer in rupture of evaporating film. For the essentially wetting case (contact angle near zero) of hexane film formed on the titanium surface aged at 200 °C in the high-temperature furnace, the hexane film is stable until its thickness gets below 15 lm. The film instability was detected to set in at a thickness of 10 lm for low heat flux, but no instability was observed in tests at higher heat fluxes and hence higher evaporation rates. Such a behavior and the accompanying high-quality measurement data serve a rich benchmark to assess analytical models of film stability and discern the effect of competing forces that govern the film behavior at diminishing thickness and rupture. Acknowledgments This study is made possible by research grant VR-2005-5729 from Vetenskapsrådets (Swedish Research Council). The authors thank Dr. P. Kudinov and Dr. L.X. Li for their constructive suggestions and the staff at the Nuclear Power Safety Laboratory for their technical support in experimental setup. References [1] T.G. Theofanous, J.P. Tu, A.T. Dinh, T.N. Dinh, The boiling crisis phenomenon: part I: nucleation and nucleate boiling heat transfer, Exp. Thermal Fluid Sci. 26 (6-7) (2002) 775–792. [2] T.G. Theofanous, T.N. Dinh, J.P. Tu, A.T. Dinh, The boiling crisis phenomenon, part II: dryout dynamics and burnout, Exp. Therm. Fluid Sci. 26 (6-7) (2002) 793–810. [3] T.N. Dinh, J.P. Tu, The Micro-hydrodynamics that govern critical heat flux in pool boiling, International Conference on Multiphase Flow, ICMF 2007, Leipzig, Germany, July 9–13, 2007. [4] S.G. Bankoff, Minimum thickness of a draining liquid film, Int. J. Heat Mass Transfer 14 (12) (1971) 2143–2146. [5] J. Mikielewicz, J.R. Moszynski, Minimum thickness of a liquid film flowing vertically down a solid surface, Int. J. Heat Mass Transfer 19 (1976) 771–776.

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