pubs.acs.org/Langmuir © 2010 American Chemical Society
Infrared Thermography Investigation of an Evaporating Sessile Water Droplet on Heated Substrates Fabien Girard,† Micka€el Antoni,*,† and Khellil Sefiane‡ † ‡
Universit e Paul Cezanne, UMR CNRS 6263 ISM2, 13397 Marseille Cedex 20, France, and School of Engineering, University of Edinburgh, Kings Buildings, Edinburgh EH9 3JL, U.K. Received December 24, 2009. Revised Manuscript Received February 8, 2010
The present study is an experimental investigation of the thermal evolution of millimeter-sized sessile water droplets deposited on heated substrates. Infrared thermography is used to record temperature profiles on the droplet interface in time as evaporation takes place. The local measurements of the interface temperature allowed us to deduce the local evaporation rate and its evolution in time. To our knowledge, this is the first time that such measurements have been performed. The deduced evaporation rate using thermography data has been validated with optical measurements. Temperature evolution is used to reveal the contact line location and transient temperature fields. Temperature differences between the apex of the droplet and the contact line are shown to decrease in time. The rate of local temperature increase at the interface is found to behave linearly with time. The slope of this linear increase turns out to be more pronounced as the substrate temperature is increased. A generalized linear trend, using dimensionless properties for the interface temperature rise, is deduced from the measurements.
Introduction The evaporation of liquid droplets and their interaction with solid substrates has been subject to increasing interest in the scientific community.1-5 This interest has been driven by an increase in the range of applications underpinned by this phenomenon.2 The interaction of droplets with heated substrates impinges on a wide range of applications such as spray cooling, nuclear applications and coating technologies. A full understanding of the nature of these interactions and the processes involved is essential. When depositing a droplet on a heated substrate, many scenarios are possible depending on the relative temperatures of the droplet and the substrate. If the droplet is cooler than the substrate, there will be a transient regime whereby the droplet temperature will tend to that of the hot substrate. This first transient stage is followed by a quasi-isothermal phase where the liquid droplet evaporates. Most previous studies on droplets evaporation in the literature are dedicated to isothermal quasi-steady cases.1,4 Transient regimes due to temperature differences have not yet been fully explored. Indeed, many questions remain unanswered regarding the dynamics of the droplets and the kinetic mechanisms controlling the first transient stage. In studying droplet evaporation, researchers resort in most cases to the use of optical techniques. These techniques have many limitations, especially in cases where the thermal properties of the investigated systems are important and must be monitored. For the deposition and evaporation of droplets on heated substrates, (1) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827. (2) Bigioni, T. P.; , Lin, X.; , Nguyen, T. T.; , Corwin, E.I.; , Witten, T. A.; Jaeger, H. M. Kinetically driven self assembly of highly ordered nanoparticle monolayers. Nat. Mater. 2006, 5, 265-270. (3) Bourges-Monnier, C.; Shanahan, M. E. R. Influence of evaporation on contact angle. Langmuir 1995, 11, 2820-2829. (4) Hu, H.; Larson, R. G. Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir 2005, 21, 3972-3980. (5) Dunn, G.; Wilson, S. K.; Duffy, B.; David, S.; Sefiane, K. A mathematical model of the evaporation of a thin sessile liquid droplet: comparison between experiment and theory. Colloids Surf., A 2008, 323, 50-55.
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thermal fields determine the dynamics and evolution of the droplets. This information clearly cannot be obtained using conventional optical techniques. In addition to this, at small contact angles toward the end of the droplet lifetime, the resolution of optical techniques cannot detect the presence of the then very thin liquid film left from the initial droplet. Nonetheless, this stage of evaporation of the droplet must be investigated because it seems to be determinant in the contact line dynamics in the latter stages of the droplet lifetime. The precise characterization of thin liquid film evaporation is still an open problem although it is probably key to achieving an accurate determination of the exact lifetime of the droplet. The infra-red (IR) technique is a noncontact, nondestructive test measurement method. It is based on the fact that all objects, above absolute zero, emit infrared radiant heat at a rate that is directly related to the temperature of the object. When droplet deposition and evaporation are investigated on heated substrates, the infrared thermography technique offers many advantages such as local temperature measurements, a new approach to characterizing contact line evolution (and its location), and the possibility to estimate local heat flux. This technique has been successfully used to investigate interfacial phenomena.6 Other techniques have been used to reveal the heat transfer near the contact line of an evaporating meniscus and droplets.7 H€ohmann and Stephan8 have demonstrated that unsealed thermochromic liquid crystals can be successfully used for microscale temperature measurements of an evaporating meniscus with submicrometer resolution. Optical techniques give access to droplet’s geometrical properties such as the volume, angle, radius, and height, but the measurement of the overall evaporation time is limited by the (6) Schwabe, D.; Zebib, A.; Sim, B. C. Oscillatory thermocapillary convection in open cylindrical annuli. Part 1. Experiments under microgravity. J. Fluid Mech. 2003, 491, 239-258. (7) McGaughey, A. J. H.; Ward, C. A. Temperature discontinuity at the surface of an evaporating droplet. J. Appl. Phys. 2002, 91, 6406-6415. (8) H€ohmann, C.; Stephan, P. Microscale temperature measurement at an evaporating liquid meniscus. Exp. Thermal Fluid Sci. 2002, 26, 157-162.
Published on Web 03/03/2010
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optical resolution. IR thermography, however, gives access to temperatures that allow monitoring of the evaporation of the droplet at the very end of its lifetime, which is not accessible by conventional optical techniques. Despite the huge interest and large number of investigations of evaporating droplets and contact line problems the evaporative flux distribution along the surface, to the best of our knowledge, remains to be experimentally characterized.9,10 The objective of this study is to investigate droplet deposition and evaporation on heated substrates experimentally. The investigation focuses on studying transient regimes and reveals the temperature field evolution on the liquid-vapor surface of the droplet.
Experimental Approach and Results The experimental procedure involves the deposition of water droplets of a given initial volume (1.4 μL) at a controlled temperature (20 C) on heated copper substrates and recording the droplet surface temperature in time until it completely evaporates. This procedure is repeated for droplets and substrates at different temperatures (Ts = 30, 40, 50, and 60 C). The reproducibility of the experimental data is verified by repeating each experiment more than five times. The (ambient) far-field temperature (T¥) and pressure as well as relative humidity (H) are controlled and monitored in time. The initial water temperature (Twater) is also controlled. The IR camera used in this study is an FLIR ThermaCAM SC3000; it has a thermal sensitivity of 20 mK for the temperature range considered in this letter. The GaAs quantum well infrared photon FPA detector has a spectral range of 8 to 9 mm with a resolution of 320 pixels 240 pixels. The field of view at the minimum focus distance (25 mm) is 10 mm 7.5 mm. A continuous electronic zoom (one to four times) is used. The system can acquire images in real time or at high speed with a reduction of the picture size so that each frame contains only one droplet. The images acquired are transferred to a dedicated PC with special built-in software. The emissivity of water is used to read the temperature on the droplet interface. In the contact line region, the accuracy of the measurements is limited by the exact location of the three-phase contact line. The IR map shows a dip in temperature as we move to the copper region (dry substrate). The exact location of the contact line is thus taken as the maximum in temperature along the radial coordinate. Beyond this position, the temperature readings are meaningless because of the selected emissivity. It is worth mentioning that in most investigated cases droplets are spherical caps and hence maintain an axisymetrical geometry. In addition to IR thermography experiments, optical measurements using a goniometer were undertaken. Similar droplets under the same conditions as investigated with thermography are studied. Data on droplets profile (volume, base, and height) and evaporation rates were obtained and have been used to validate the measurements and conclusions obtained using the IR technique.
Results When a droplet is deposited on a substrate, it spreads rapidly to reach the maximum contact radius. This spreading process is very fast and occurs over a time scale of a fraction of a second. In our experiments, this spreading process is not captured; instead, we start studying the droplet once it has reached the maximum spreading radius. This very first spreading stage is thermally and mechanically transitory and is beyond the scope (9) Wayner, P. C. Intermolecular forces in phase-change heat transfer: 1998 Kern award review. AIChE J. 1999 45, 2055-2068. (10) Shanahan, M. E. R. Condensation transport in dynamic wetting. Langmuir 2001, 17, 3997-4002.Shanahan, M. E. R. Spreading of water: condensation effects Langmuir 2001, 17, 8229-8235.
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Figure 1. (a) Thermographic picture of a droplet with a contact radius of 1 mm and a substrate temperature of Ts = 60 C (T¥= 20 C, Twater = 20 C, and H = 25%). The color scale gives the corresponding temperatures. (b) Droplet interface temperature profile during evaporation at different times as a function of radial coordinate r. (c) Contact line and apex temperature difference as a function of time; the solid line is a quadratic fitting of the ensembleaveraged data (filled circles).
of this investigation. Although the initial droplets are taken at the same temperature of 20 C, the initial recorded temperature profiles indicate different values for different substrate temperatures. This is due to rapid heating during the spreading process. Following the deposition of the droplets on the substrate, the IR images reveal temperature differences along the water-air interface, with the apex of the droplets being colder than the contact line as illustrated in Figure 1a for the case of a substrate DOI: 10.1021/la9048659
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Figure 2. (a) Three-dimensional plot of the droplet interface temperature as a function of r and time when Ts = 60 C (T¥ = 20 C, Twater= 20 C, and H = 25%). The solid black line is the droplet contact line location. (b) Contact line radius evolution of the droplet for Ts = 40, 50, and 60 C. Lines are obtained from nonlinear fittings.
temperature of 60 C. This profile evolves with time and is found to exhibit the same trend for all investigated substrate temperatures. Dedicated image software treatment is used to extract the radial temperature profiles illustrated in Figure 1b for successive time steps during the lifetime of the droplet. We estimate the overall interface temperature difference between the apex and the contact line of the droplets. The sharp temperatures decrease right after the maximum temperature is reached, due to the emissivity difference between water and copper. The IR camera is indeed initially calibrated on pure water emissivity. This means that it can accurately provide only water-temperature measurements. When the temperature difference is plotted in time, we observe a decreasing trend as displayed in Figure 1c. Ensemble averages are also plotted in this figure as well as the quadratic fitting of the latter. A very slight increase in the temperature difference is observed in the first stage over a transient period of approximately 15 s. A very clear decline is then noticed for the remainder of the droplet lifetime. This can be explained by the fact that as time passes, the droplet heats up, tending toward an isothermal situation. The IR data allowed us to study the time evolution of the contact line position. Figure 2a shows a 3D plot of the temperature evolution in time along the radial coordinate. The contact line location is also identified and plotted. This latter is 4578 DOI: 10.1021/la9048659
determined from the maximum in the temperature profile of Figure 1b. Figure 2a indicates the global heating of the droplet (from about 48 up to 59 C) as evaporation takes places because of the heat transfer from the substrate. A detailed inspection of this figure shows mainly two regimes: a pinned contact line regime for t < 50 s and a receding contact line regime when t > 50 s, with the latter accelerating before complete evaporation of the droplet. In this very last period of the droplet lifetime, the temperature in the vicinity of the contact line remains close to a constant value (approximately 59 C). The contact radius evolution is shown in Figure 2b for several substrate temperatures. This figure indicates that the droplets remain pinned (constant contact line radius) for most of their lifetime. This can be explained by the fact that the substrate that is used is rather rough. This result is in good quantitative and qualitative agreement with the measurements performed using the optical technique. The optical measurements also show the same order of magnitude of the droplet base radius as estimated using the IR technique. It is worth noting here that the use of IR thermography in this specific case allows us to monitor and detect the existence of liquid even when the droplet is reduced to a very thin film that is no longer accessible to optical techniques. The local temperature at a radial coordinate of r=0.5 mm in time is shown for discussion. Figure 3a displays the time evolution Langmuir 2010, 26(7), 4576–4580
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to 1. Despite the variability in the experimental data, the obtained correlation is rather satisfactory. This is an interesting result because it indicates that there is a common behavior for the temperature evolution. We believe that a universal law could be extracted from this observation and used as a prediction tool. It is worth emphasizing that the slope of this dimensionless correlation depends on the nature of the liquid. In what follows, we attempt to deduce the local evaporative flux using interfacial temperature measurements. We assume that all energy required for evaporation at the interface is conducted through the droplet from the heated substrate and we neglect any convection within the droplet.11 Under these conditions, the conductive heat transfer within the liquid is driven by the temperature gradients between the substrate and the interface. For a given time, it can be written as qcond ðrÞ ¼
kðTs - TðrÞÞ hðrÞ
ð1Þ
where r is the radial coordinate, h(r) is the liquid thickness at location r, and k is the thermal conductivity of the liquid that is assumed to be constant everywhere in the droplet. The evaporative flux across the interface can be written as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi ∂h qev ðrÞ ¼ ΔHvap JðrÞ 1 þ ∂r
ð2Þ
where J(r) is the local evaporative mass flux and ΔHvap is the latent heat of vaporization. The energy balance at the interface implies that qev(r) = qcond(r). Making use of eqs 1 and 2 gives, as shown in ref 12, Figure 3. (a) Droplet interface temperature evolution at radial coordinate r = 0.50 mm with time for several substrate temperatures Ts (T¥ =20 C, Twater =20 C, and H = 25%). (b) Normalized time evolution of droplet temperatures at radial coordinate r=0.50 mm.
of this local interface temperature for various substrate temperatures. The curves show a linearly rising trend with a slope that increases with substrate temperature. On Figure 3a, multiple experimental data are represented to illustrate the reproducibility of these measurements. Solid lines are obtained from a linear fitting. The sharp decline in these curves at the end of the droplets lifetime indicates their complete evaporation and reveals the bare copper surface. Similar measurements performed at different radial positions showed the same trends. These measurements suggest that the rate of the interface temperature rise in time is independent of the radial coordinate and hence of the considered position on the droplet liquid/air interface. As a result, it depends only on the substrate temperature. The data corresponding to each substrate temperature plotted in Figure 3a are further averaged, and the obtained average curves are normalized and plotted in Figure 3b. In the latter, time is normalized by the evaporation time (droplet lifetime, tf, where t~=t/tf), and temperature is normalized by the initial temperature (T~ = T/Tt=0) at r = 0.5 mm (temperatures are expressed in Celsius). The droplet lifetime, tf, is determined from a quadratic extrapolation to zero of the contact angle evolution. When this normalization is performed, all of the curves of Figure 3a collapse, showing that the interface temperature evolution follows the same trend at any substrate temperature. The normalized data in Figure 3b are further averaged and fitted in the linear range by ~ 0.15 t~þ 1 with a correlation coefficient close the linear law T= Langmuir 2010, 26(7), 4576–4580
JðrÞ ¼
kðTs - TðrÞÞ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi ∂h hðrÞΔHvap 1 þ ∂r
ð3Þ
As droplets have spherical cap geometry and the temperature profile is known from thermographic measurements, one can deduce from the above equation the profile of the evaporative mass flux along the interface. In eq 1, the substrate temperature is supposed to remain constant although it probably changes initially because of the cooler droplet, but no significant cooling has been initially detected in the temperature measurements. This can be explained by the accuracy of the temperature-regulating system that is used and by the large thermal conductivity of the copper substrate. Both tend to maintain the substrate at a fixed temperature. Still, one cannot exclude short-time temperature fluctuations at the substrate solid/liquid interface, but we believe the latter not to be larger than few fractions of a degree. The data for the evaporative flux are represented in a 3D plot in Figure 4a to illustrate the evolution of this parameter in time. As time proceeds, the evaporation rate increases. This is due to the thinning of the droplet and the reduction in thermal resistance. As already observed in Figure 2, the contact line location remains steady for t < 50 s (when the droplet is pinned) whereas for later times fast depinning occurs. Increasing mass flux is evidenced in Figure 4a, in particular, in the vicinity of the contact line (11) Girard, F.; Antoni, M.; Sefiane, K. On the effect of Marangoni flow on evaporation rates of heated water drops. Langmuir 2008, 24, 9207-9210. (12) Xu, X.; Luo, J. Marangoni flow in an evaporating water droplet. Appl. Phys. Lett. 2007, 91, 124102.1-124102.3.
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(about 3.0 10-2 kg 3 m-2 3 s-1) at the contact line location. This last result suggests that, at the very end of the evaporation process of the droplets, incoming heat flow from the substrate does not generate any more increase in evaporative mass flow because of the rapidly receding contact angle. The evaporative flux along the radial coordinate is presented in Figure 4b for different times. This figure shows, for a given time, an increase in the evaporation rate when approaching the contact line that is in agreement with the theories proposed for the evaporation of menisci.9 This figure also shows that the evaporative flux at the apex of the droplet is not strongly time-dependent whereas in the vicinity of the contact line (for r > 0.8 mm) the local evaporative flux increases as evaporation proceeds. It is worth noting that this profile is obtained on the basis of experimental temperature profile measurements on the interface of the droplet. It is the first time, to our knowledge, that the local evaporation flux is deduced from experimental measurements. This shows that the thermography technique could be a powerful tool for accessing local properties of evaporating systems.
Conclusions
Figure 4. (a) Three-dimensional plot of the local mass flow as a function of the radial coordinate and time for the same droplet than in Figure 2a. A clear increase is shown in the contact line region, highlighted here as a solid line. (b) Evaporative flux as a function of radial coordinates at different times.
that shows, in the pinned droplet regime, an increase from 9.5 10-3 up to 2.5 10-2 kg 3 m-2 3 s-1. A detailed investigation of this Figure also indicates that the mass flow in the vicinity of the contact line continues to increasing up to time t ≈ 60 s where it reaches a value close to 3.0 10-2 kg 3 m-2 3 s-1. Beyond this time, in the last evaporation regime, the droplet contact line rapidly shrinks, with an almost constant mass flow
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In this study, an infrared thermography technique has been used to investigate the time evolution of the interface temperature of water droplets deposited on heated substrates. Temperature differences on the interface decrease in time. The global heating of the droplets due to substrate heating is investigated, as is the contact line dynamics. In the pinned evaporative regime of the droplets, a general correlation for interfacial temperature evolution is demonstrated. The use of local energy conservation laws associated with the local measurements of the interface temperature allowed us to deduce the time evolution of the local evaporative mass flux. This parameter exhibits a constant magnitude on the apex of the droplet whereas a clear increase is shown in the vicinity of the contact line. To our knowledge, this is the first time that local evaporative fluxes in systems undergoing phase change have been experimentally measured. A description of the very last stage of the droplets’ evaporation is also proposed and suggests that both the temperature and mass flux remain constant near the receding contact line.
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