Evaporating sessile drops subject to crosswind

International Journal of Thermal Sciences 144 (2019) 1–10

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Evaporating sessile drops subject to crosswind

T

Cosimo Buffone Tianjin Key Lab of Refrigeration Technology, Tianjin University of Commerce, Tianjin City, 300134, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Drop evaporation Infra-red Contact angle Surface tension Whisky

We conducted an experimental investigation on the evaporation of sessile drops subject to an airflow in crosswind arrangement compared with the naturally developing ascending vapor plume and with air speeds up to almost 2 m/s using ethanol, water and a single malt Scotch Whisky as liquids and Teflon as substrate material. We used Infra-Red to map the temperature evolution of the drying drops curved interface and also measured the drop contact angles. We report a significant decrease in temperature of the drop apex as the air speed is increased. The Infra-Red measurements detect also the location of the contact line which remains mainly pinned for drying water and whisky drops, whereas it is greatly affected in the case of drying ethanol drops. The temperature measurements of ethanol drops clearly demonstrate that during the first stage of drop evaporation with pinned contact line, the drop contact line temperature decreases noticeably. In the subsequent stage of contact line de-pinning and constant contact angle, the contact line temperature remains broadly the same. After drop deposition, experimental values of temperature deviate noticeably from the models of Hu and Larson [31] and Semenov et al. [32] and this might be due to the fact that evaporation is not uniform and constant along the drop.

1. Introduction Drops are found in many industrial applications and in everyday life. Inkjet printing, drying of paints, combustion, fertilisers and pesticides for agriculture, rain drops, spray cooling, are among the most widely known applications of drops. During the evaporation process the drop changes volume (i.e., looses mass) with its diameter and/or contact angle changing until the whole drop dries out. The evaporation process can be uniform or not uniform along the drop surface and the heat transfer with the substrate is typically a crucial factor; this leads to a temperature difference between the drop apex and its contact line (where the liquid, solid and gas phases meet). The explanation of the relative difference between the drop apex and contact line temperatures started with two distinct and opposite theories. Steinchen and Sefiane [1] theory says that the contact line temperature is lower than the apex one because most of the evaporation takes place at the contact line. Deegan et al. [2] instead argues that being the apex further away from the substrate than the contact line, it results in lower temperature at the drop apex. These two diametrically opposite conclusions were based on a limited number of cases considered and crude assumptions about the influence of the substrate properties and the air/vapor phase above the drop. More research on the influence of the substrate and the gas phase such as those of Dunn et al. [3], Sefiane and Bennacer [4], and Schofield et al. [5] clearly demonstrate how drop evaporation is strongly

linked to the heat transfer from the substrate below and also very much influenced by the air/vapor above it through the thermophysical properties of these. Recently and numerically Xu et al. [6] and Zhang et al. [7] have postulated that the actual temperature profile along the drop interface strongly depends on the contact angle, the ratio between the substrate and liquid thermal conductivities, and the ratio between substrate thickness and drop contact line radius. Measurements of global evaporation rate of sessile drops in still air showed (as for the work of Birdi et al. [8]) that the evaporation rate is strongly related to the rate of vapor diffusion in the surrounding air and that crucially the evaporation rate is proportional to the diameter of the drop rather than its liquid-vapor surface area. A typical sessile drop evaporation process follows different stages: a Constant Contact Radius stage in which the drop contact angle decreases to account for the loss of mass; a Constant Contact Angle stage in which the drop de-pins and the drop radius decreases to account for loss of mass; and, a typical final combined mechanism of Constant Contact Radius and Constant Contact Angle which is called “Stick-Slip” and it is described in great details in Picknett and Bexon [9], Shanahan [10], Stauber et al. [11], Stauber et al. [12],. Which one of the Constant Contact Radius or Constant Contact Angle mechanism prevails, depends on the affinity of the liquid for the solid surface. Lot of work has been done recently to modify locally the interaction solid-liquid-gas by either depositing special coatings or creating surface patterning (modifying

E-mail address: cosimobuff[email protected]. https://doi.org/10.1016/j.ijthermalsci.2019.05.018 Received 17 December 2018; Received in revised form 24 May 2019; Accepted 25 May 2019 Available online 06 June 2019 1290-0729/ © 2019 Elsevier Masson SAS. All rights reserved.

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FPA detector has a spectral range of 8–9 μm centred in one of the two atmospheric ‘‘windows’’ with a resolution of 320 × 240 pixels and is Stirling cooled to 70 K. We also employed a microscopic IR lens the field of view at minimum focus distance (26 mm) being 10 × 7.5 mm. The IR camera is calibrated annually by FLIR Systems and the error found during the last calibration is within the accuracy stated above. We acquired images at 50 Hz. The image spatial resolution of the present camera is 31.25 μm for a focal distance of 26 mm. Ethanol is a semi-transparent fluid to IR at the camera wavelengths of 8–9 μm. The emissivity of ethanol depends on the liquid thickness as clearly shown also by Brutin et al. [26] for drops in the 3–5 μm spectral range of the IR camera they used. Brutin et al. [26] demonstrated that for ethanol drops of around 1.62 mm thickness, the transmission is around 1%, which means that the temperature measured by IR camera is the drop surface temperature. Water has an emissivity of between 95.0 and 96.3%, therefore using an IR camera what we measure is the drop surface temperature. Being whisky basically a water-ethanol mixture, we can extrapolate and conclude that also for whisky what we read by IR is basically the drop surface temperature. Teflon is completely opaque to IR radiation at the 8–9 μm spectral range of the IR camera and has also high emissivity (over 85% at ambient temperature); therefore, using Teflon as substrate material does not lead to any substantial temperature measurements inaccuracy with the liquid drops used in the present study. On a separate experiment we also used a DSA30 optical drop analyser by Kruss GmbH to monitor automatically the drop two-dimensional shape in the vertical plane along the direction of the airflow. The DSA30 drop analyser has an accuracy in measuring angles of 0.3°. Drops of 3 μL where deposited on the Teflon surface for all liquids. We aligned the optical system of the DSA30 perpendicular to the direction of the horizontally oriented airflow so that we could notice changes by measuring the contact angle of the drop in two-dimensions. The main selected air speeds were of 0.10, 0.50, 1.00, 1.60 and 1.95 m/s, the extreme values being the limitations of the fan assembly used at the given distance between fan assembly and drops (200 mm). Air is blown by a small fan along the horizontal direction in crosswind arrangement with respect to the naturally developing buoyancy ascending vapor plume around the evaporating droplet sitting on a horizontally positioned Teflon block. At the lowest air speed of 0.1 m/s the volumetric air flow rate of the fan is around 2 10−5 m3/s, whereas the amount of water or ethanol vapor produced by evaporation is around 2 10−10 m3/s; therefore, as soon as the fan is turned on, even at the lowest speed, the mass transfer mode is dominated by air forced convection. Abou Al-Sood and Birouk [27] showed clearly that there is an important effect of freestream turbulence intensity on the evaporation of volatile liquids up to turbulence levels of around 20%. In the present case, the estimated freestream turbulence level is between 8 and 12%, which should be reduced. To reach this goal a 30 mm thick honeycomb hexagonal cells with 3 mm diagonal side length was employed to cut the large turbulent structures coming off the fan blades, reduce the turbulence level by dissipating the energy of small structures in the flow, and straighten the flow which is further directed at the drops with the aim of a casing. The liquids were used as received from the manufacturers. The Teflon surface was cleaned with ethanol first, followed by an immersion in ultrasonic bath filled with distilled water and then dried in air between each experimental run. The ambient temperature during the experiments varied between a minimum of 20.4 and a maximum of 21.0 °C and an air-conditioner, located far away from the experimental set-up in the lab, was employed to achieve this temperature stability. The relative humidity measured varied between 34 and 42%. The use of the bulky IR camera/lens did not allow placing the drops and Teflon surface inside a temperature and humidity controlled cell (which the DSA30 can also be equipped with from Kruss GmbH). Therefore, the effect of humidity on evaporation rate for water and whishky drops is not accounted for in these experiments; however, given the use of the

surface roughness) to modify the local interaction between solid and liquid as studied by Misyura [13]. Birdi and Vu [14] report that on a hydrophilic surface the drop evaporates in Constant Contact Radius mode, while on a hydrophobic surface the droplet practically evaporates in Constant Contact Angle mode. Gao et al. [15] conduct an experimental study of droplet evaporation on hydrophilic and hydrophobic surfaces with imposed constant heat flux instead of the usual constant temperature of the solid substrate. Wettability effects are also a key feature of water repellent clothing (Marek and Martinkova [16], Bougourd and McCann [17]). In most of the experimental and numerical works published the drop dries in still air. Whereas in many industrial applications such as combustion, spray cooling, deposition of fertilizers and pesticides, spray coating, rain drops, etc., the drop is subject to an airflow. There have been studies on droplet evaporation subject to an airflow in crosswind arrangement such as those of Navaz et al. [18], Raimundo et a. [19], and Doursat et al. [20] which show the strong effect of air temperature, wind speed, and free stream turbulence level. One previous study of Liu et al. [21] for drops up to 35 μL addresses some of the issues related to methanol drops subject to crosswind configuration, although the imposed maximum air speed is limited to 0.85 m/s. In the present work the air speed is increased up to almost 2 m/s and we also use different liquids: water, ethanol, and a Scotch Whisky which is mainly made of a mixture of water and ethanol. We have chosen a commercially available Scotch Whisky because we wanted to see if there is any effect of liquid diffusion inside the drop due to differential evaporation of the two liquids in the mixture; the second reason is that part of the research was carried out in Scotland where Scotch Whisky is produced. In a previous experiment (Cecere et al. [22]) the important effect of thermo-solutal Marangoni has been shown experimentally and numerically for curved meniscus of ethanol-water mixtures evaporating in still air. Sefiane et al. [23] reported on the evaporation and wetting of water, methanol and three concentrations of their binary mixtures deposited on a PDMS coated silicon wafer and they conclude that methanol evaporates first affecting the wetting stages; after this initial stage of methanol evaporation, the small quantity of methanol remaining inside the drop still influences the wetting of the substrate. We use contact angle and Infra-Red (IR) temperature measurements to quantify the changes of drop physical dimensions (contact angles and drop diameter) and measure the drop interfacial temperature when we impose an airflow in crosswind configuration respect to the case of no airflow. 2. Experimental setup We investigate experimentally the evolution of different droplets on a Teflon (PTFE or Polytetrafluoroethylene) block of 35 × 70 mm with a thickness of 20 mm. Drops were deposited in the middle of the Teflon top surface with their apex at approximately 35 mm from the leading edge facing the freestream. The measured roughness average (Ra) of the Teflon surface near the centre where the drops are deposited is less than 0.4 μm on a 5 × 5 mm2 area. We choose Teflon as substrate because in the IR camera spectral range, Teflon at a thickness of 20 mm is almost completely opaque (Tsai et al. [24]). We used water, ethanol, and a Scotch Whisky, The Balvenie single malt-triple cask whisky aged 12 years which is basically a mixture of ethanol (40% in volume) and water. The experimental apparatus is reproduced in Fig. 1, where the optical and IR systems are used separately on drops of the same liquid. In one experiment, an IR camera is pointed from above the drop along the vertical axis perpendicular to the Teflon surface on which the drop is deposited. The IR camera used in this study is the FLIR ThermaCAM SC3000 that has been already described in a previous study (Buffone and Sefiane [25]). We monitored the evolution of the drop surface temperature as evaporation takes place and the drop dries. The IR camera has a thermal sensitivity of 20 mK at 30 °C, an accuracy of 1% or 1 °C for temperatures up to 150 °C. The GaAs, Quantum Well IR Photon 2

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Fig. 1. Experimental set-up (not to scale) used for Infra-Red temperature and optical measurements of a sessile drop. The directions (N–S and W-E) along which the temperature profiles and the optical measurements have been taken are indicated schematically on the drop contact line. The dashed box shows the typical drop profile evolution obtained with Kruss DSA30 drop analyser. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

dish is nearly linear for all liquids tested for the 5 h duration of the evaporation tests. This means that the liquid diffusion of components is faster than the rate of evaporation for such set-up. What we have also done is repeat the experiment for Whisky only and to extract a sample of liquid from the top of the liquid level in the Petri dish at the following times: 0 s (start of experiment); 60 s; 120 s; 300 s; 600 s; 1200 s; and 1800 s (this last corresponding to the water drop lifetime reported in Fig. 5. On these samples of Whisky we measured surface tension by performed pendant drop (2, 3, 4 μL volume) measurements on the DSA30 machine. Surface tension of Whisky varies in a non-monotonical way; in particular, it decreases for the first 600 s and then increases from there onwards. However, these changes of surface tensions are estimated to be around 4.8% which is just 3 times the stated accuracy of the DSA30 machine by the manufacturer in measuring pendant drop volume for estimating the surface tension of a liquid. We have also performed the same surface tension tests on pendant drops of waterethanol mixture (40% in volume of ethanol) and the results show a more complex behaviour of surface tension; the measured surface tension by DSA30 in this case changed of around 7.6%. Therefore, we are tempted to conclude that there is indeed a small change in surface tension while the Whisky evaporates; however, the estimated surface tension variation over the duration of the typical lifetime of the drop is rather irrelevant.

air conditioning unit with the small variation of humidity aforementioned and the fact that the tests were performed in a rather short period of time, it is reasonably to assume that at least for the same liquid there is little variation of evaporation rate because of the small changes in ambient conditions. We have carried out a preliminary study to ascertain if the IR temperature measurements are time-resolved. We took ethanol (the most volatile of the three liquid considered) and subject the drop at the highest airflow speed of 1.95 m/s. We measured the drop dimensions in time and plotted the drop volume for the entire drop lifetime. We estimated from this plot the evaporation time constant to be around 18 ms whereas the acquisition of the IR camera is 20 ms (50 Hz); so, the temperature measurements are not fully resolved for ethanol and the highest value of the imposed airflow speed. For ethanol and all the other air speeds as well as for water and Whisky, the drop evaporation time constant is higher than the IR acquisition rate and therefore in these cases we can consider the temperature measurements as timeresolved. Analysing the nature of a complex mixture such a Whisky requires complex experimental methods such as Liquid Chromatography and Mass Spectrometry. What we have done is taking a practical and engineering approach to assess what potential effect on surface tension the differential evaporation of water and ethanol at ambient conditions and in unbounded air have. After some preliminary tests using different shape and dimensions of Petri dishes with different volume of liquids inside (distilled water, ethanol, water-ethanol mixture at 40% volume of ethanol, and Whisky), we have monitored the evaporation rate of all these liquids for up to 5 h taking measurements at each minute interval. The Petri dish that better represents our cases is a 60 mm internal diameter and a 10 mm high one filled at the start of the experiment until the rim. We have concluded that the loss of mass from the Petri

3. Results 3.1. Typical transient measurements Fig. 2 shows the IR images of a non-perfectly circular ethanol drop because of a relatively rough Teflon surface (Ra of the order of 0.4 μm) as it dries with 1.6 m/s imposed air speed. The first four frames up to 3

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Fig. 2. Typical temperature pattern of the drying ethanol drop subject to airflow in crosswind arrangement with air speed of 1.6 m/s. The direction of the imposed airflow is shown by the black dashed arrow in the first frame (along N–S direction). The white dashed lines N–S and W-E are the directions along which the temperature profiles have been extracted and reported in subsequent figures.

t = 33 s show some interfacial turbulence which has been ascribed as hydrothermal waves reported by Sefiane et al. [28] and Brutin et al. [26] that generate at the drop curved interface. After around 135 s (last frame of Fig. 2) the ethanol drop has completely dried out and clear concentric cold marks have been left on the Teflon surface; these nearly concentric marks are where the contact line pinned during the drying process. The Teflon surface, cooled by the cold ethanol drop, will require more time to reach ambient temperature after the drop has completely evaporated because of the important evaporative cooling effect due to the phase change at the drop surface. On the first frame of Fig. 2, we report the airflow direction with a dashed arrow and two cuts (N–S and W-E) along which we will extract subsequent temperature profiles of all drops as the drops evaporate and dry out. As ethanol evaporates the higher energy molecules leave the drop at the interface and the molecules which are left are those with lower energy content; it is this the reason of the measured lower drop surface temperature compared to ambient. During the first stage of ethanol drop evaporation, the contact line temperature changes in time more rapidly than the apex one; we believe this is due to the re-supply flow from the drop centre in contact with the Teflon substrate that brings relatively warmer fluid to the contact line, which results in more rapid decrease of interfacial temperature than for the drop apex. Fig. 3 shows the initial temperature profiles along the N–S and W–S for the ethanol drop at 0.5 m/s air speed. The contact line temperature is indicated by the red dots, outside which the temperature is deliberately plotted constant because there the IR measurements are not accurate due to the mismatch between the emissivity of ethanol and Teflon. These profiles reveal several facts. The first is that the profiles are not smooth; in particular, there are high frequency variations inherently connected with the IR camera used and low frequency spatial variations which are a sign of the hydrothermal waves operating on the surface of the ethanol drop. The second aspect is that the drop is not symmetrical and the temperature of the contact line is different around the perimeter of the drop; this is most likely due to both the roughness of the Teflon surface and the hydrothermal waves which for this experiment seems to be randomly oriented. The last fact is that there is a small increase in temperature just inside the contact line before the interfacial temperature starts to decrease monotonically; this is most likely due to edge effects like liquid emissivity change with liquid thickness and/or changes of the view angle.

Fig. 3. Temperature profiles along lines N–S and W-E of first frame in Fig. 2 but for 0.5 m/s air speed, instead. The red dots indicate where the contact line is. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

3.2. Temperature profiles on drop surface In Fig. 4 we report the evolution of the ethanol drop surface temperature subject to an air speed of 1 m/s until it dries out on the Teflon surface. We start with depositing an evaporating drop of ethanol on Teflon and soon after we impose the selected air speed. The temperature profiles of the left frame are along the N–S cut as indicated in Fig. 2 and those on the right frame along the W-E cut. Two important information stand out from these plots. The first is that until 29 s the drop is pinned and the drop temperature, especially at the contact line, decreases noticeably because of both the initial transient of drop evaporation in which the drop looses the most energetic molecules and the imposed airflow which promotes evaporation by diffusing more effectively the vapor generated around the drop. During this stage the drop looses mass by decreasing the contact angle and keeping the drop diameter nearly constant (Constant Contact Radius). During the second 4

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Fig. 4. Temperature profiles of ethanol drop interface as it evaporates completely on Teflon for 1 m/s imposed air speed. Left frame is along the plane in the airflow direction (N–S) and right frame is orthogonal to it (W–E).

Fig. 5. Marangoni number for the ethanol drop (left frame) subject to a 1 m/s airflow speed of Fig. 4 and the water and Whisky drops (right frame) subject to all airflow speeds.

Liu et al. [21]. The present temperature measurements with the FLIR SC3000 camera have much better sensitivity (more than 3 times), double spatial resolution and more than 5 times the temporal resolution (50 Hz compared with 9 Hz) of the Fluke Ti25 camera used in Liu et al. [21]. Lastly, in the present work we show experimental results of two pure liquids and a mixture of these two, whereas Liu et al. [21] present only results of a pure liquid. It is worth noting that for ethanol drops on Teflon the temperature of the contact line is higher than the apex temperature. The temperature decreases monotonically from the contact line to the apex of the ethanol drop, which might follow the explanation brought by Deegan et al. [2] with an apex colder than the contact line because of the thermal conduction through the liquid. In order to shed more light into this point, the relative thickness (ratio between Teflon thickness and drop radius) for ethanol is estimated to be more than 12 at drop deposition and the relative thermal conductivity (ratio between Teflon and liquid thermal conductivities) is around 9. Following the analysis of Zhang et al. [7] it is not possible to assume the present case to be isothermal (i.e., thin substrate); however, being the relative thermal conductivity of the present case rather high (kR ∼ 8.97) and having medium values of contact angle for ethanol at 1 m/s air speed (ranging between 21 and 37° which lead to a relative substrate thickness of hR ∼ 9.5), from Zhang et al. [7] (see their Fig. 3 for kR = 1.5806 and hR = 0.15) we can reasonably assume that the temperature distribution on the drop surface increases monotonically from the drop centre where

stage of evaporation between t = 29 s and t = 70 s, the drop de-pins (Constant Contact Angle) and the contact line temperature remains broadly the same. Right after this the drop enters a phase in which it reduces monotonically the base diameter but at lower rate than during phase two; in this third phase, the drop first decreases and then eventually increases the contact line temperature until it nearly dries out at t = 155 s. This happens because as the drop gets smaller, the evaporative cooling effect is also reduced. At this final stage the Teflon temperature is still considerably lower than ambient because of the evaporative cooling effect due to the phase change in the drop during the drying out process. This finding is in line with general trends reported in the literature but different from the trends shown in Liu et al. [21] where methanol drops deposited on Teflon were also subject to crosswind and the results showed drops that were not pinned at the first stage of evaporation. What Fig. 4 also shows is a qualitative agreement with the surface drop temperature measurements of Liu et al. [21] where the drop temperature first decreases and then eventually increases approaching asymptotically ambient temperature when all liquid has evaporated. However, in the present study we have not detected any increase of the contact angle in the first stage of evaporation after the drop has been deposited on the surface as reported by Liu et al. [21] for methanol drops. The ethanol drops of the present study pin on Teflon from the moment they are deposited, whereas the methanol ones of Liu et al. [21] seem not to pin on Teflon; this difference might be attributed to the Teflon surface finishing which is not characterized in 5

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the conduction path length is largest. The IR measurements of the drop surface are also able to detect the location and motion of the entire contact line around the drop circumference giving an extra dimension compared with a typical twodimensional drop analyser like the one also used in the present work (DSA30). In Supplementary Material SM1 we report the drop interfacial temperature for water and whisky on Teflon at different imposed air speeds. (Worth noticing is the fictitious temperature trough in the middle of the drop; this is due to the high contact angle which results in part of the drop falling out of the IR camera focus, as also reported in an evaporating meniscus inside a capillary tube by Buffone and Sefiane [25]). The other two aspects to point out are the smaller change of contact line temperature for whisky between all imposed air speeds and a steeper variation of interfacial temperature along the drop; while the latter might well be accounted for by the higher evaporative cooling effect of the ethanol present in whisky, the former is more intriguing and warrants a deeper look by analysing different ethanol concentrations in water. Different factors might contribute to this outcome of nearly constant contact line temperature for whisky as the freestream air speed in increased, namely: the ethanol diffusion inside the drop with migration towards the contact line (capillary flow) which might affect the evaporation around the drop contact line; and, coupled geometrical aspects (water, ethanol and whisky drops have very different contact radius and therefore contact angles, for the same initial volume) and evaporation profile considerations as well as thermal conductivity of the liquids might well complicate much further the case of mixtures. ∂σ L ΔT Fig. 5 shows the estimated Marangoni numbers (Ma = − ∂T η α , where σ is surface tension, ΔT is the difference of temperature between drop's contact line and apex, L is the drop characteristic dimension, η is dynamic viscosity, and α is thermal diffusivity) for the ethanol drop (left frame) subject to a 1 m/s airflow speed of Fig. 4 and the water and Whisky drops (right frame) subject to all airflow speeds as in Supplementary Material SM1. The left frame of Fig. 5 shows that the Marangoni number decreases monotonically as the ethanol drop dries out, most likely due to the fact that the evaporative cooling effect on the drop surface is reduced as the drop decreases in size. What stands out of the right frame of Fig. 5 is that at the low air speeds it seems that the Marangoni number for water and whisky drops is either reduced or no much different from that with no imposed airflow; this might be due to the fact that for water and Whisky evaporative cooling has a reduced effect than in the more volatile ethanol.

Fig. 6. Time evolution for average Contact Angle (CA) and base Diameter for water, ethanol and Whisky drops on Teflon with no imposed airflow.

3.3. Contact angle measurements Fig. 7. Change of contact angles (Left and Right) of ethanol drops on Teflon for different imposed air speeds.

We report some of the measurements about contact angles in Figs. 6 and 7 which show the most representative cases. In Supplementary Material SM2 we report the cases of water and whisky contact angle measurements. In Fig. 6 the average contact angle (between LEFT and RIGHT) and the base diameter of the drops are shown for the water, ethanol and whisky in the case of no-airflow imposed. The LEFT contact angle is the one facing the airflow (N in Fig. 1) and the RIGHT is in the opposite direction (S in Fig. 1). From Fig. 6 it can clearly be seen that for water and whisky for the majority of the drop's lifetime, the drop evaporates at constant diameter (Constant Contact Radius); only in the last stage of drop evaporation both the diameter and the contact angle decrease, this is called mixed evaporation mode [9–12]. From Fig. 6 another important fact stands out: as the alcohol content is increased (going from pure water to whisky and eventually to pure ethanol), the initial contact angle decreases and the initial drop diameter increase (for same initial volume of the drop); this is a direct consequence of spreading where liquids with lower surface tension exhibit lower contact angle and larger initial drop diameter. It is noteworthy paying attention to the effect of roughness of the

Teflon surface on the contact angle measurements. There have been studies of practical engineering surfaces (see for instance Kubiak et al. [29]) in which different materials having surfaces with a wide range of roughness ranging from 0.15 to 7.74 μm have been tested for wettability. These types of surfaces are far from been the “molecularly smooth” surfaces with nano-meter size roughness. What Kubiak et al. [29] found is that depending on the contact angle being smaller of larger than 90°, the effect of roughness is an improved or reduced wettability with increasing roughness. The Teflon surface in the present investigation has an average roughness (Ra) of around 0.4 mm and therefore for ethanol and Whisky (having a contact angle below 90°) the non-smooth Teflon surface improves the wettability; in the case of ethanol and Whisky the drops on Teflon surface should follow the Wenzel's theory. Instead for water (having an initial contact angle above 90°), the non-smooth Teflon surface reduces the wettability; in this case the water drops on Teflon should follow the Cassie-Baxter 6

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downward towards the drop surface forming a natural convection descending plume. The last complication is that if air is blown on the drop (as in the present case) the resultant heat and mass transfer is made more complex by the heavenly distorted air and vapor flows around the drop and their consequent influence on evaporation flux distribution on the drop surface. All of these complicated heat and mass transfer mechanisms lead to a very complex analysis that is still not fully resolved. A similar case to the present one was studied by Pan et al. [30] in which a water drop of 2 μL volume evaporates inside still air. Pan et al. [30] develop a numerical model which incorporates evaporative cooling and also natural convection on top of the classical vapor diffusion model. They show that there are three type of regimes depending on the drop contact angle, namely: for surfaces yielding small contact angles (below 60⁰), the vapor diffusion model underestimate the total evaporation rate because the small thermal resistance across the thin drop limits the effect of evaporative cooling; for surfaces yielding intermediate contact angles (between 60⁰ and 90⁰), the vapor diffusion model predicts well the evaporation rate because the effect of evaporative cooling is counterbalanced by the natural convection in the gas phase; and, finally for surfaces exhibiting high contact angles (above 90⁰), the vapor diffusion model overpredicts the evaporation rate because the large evaporative cooling effect suppress evaporation rate noticeably and this results in a reversion of the natural convection in the gas phase.

model. Roughness tends to produce an initial spreading of the drop on the solid surface. The spatial resolution of the IR camera/lens is 31.25 μm and the spatial resolution of the visual CMOS camera of the DSA30 is 8.6 μm. With the DSA30 we have a spatial resolution of nearly 22 times the average measured roughness of the Teflon surface of 0.4 μm. Having not observed any initial spreading of the all drops considered (at a frame rate of 50 Hz), we are tempted to conclude that if there is any initial spreading of such drops, then it must be below the spatial resolution of the equipment used. With ethanol droplets (Fig. 7) there is a substantial change in contact angles as the drop dries and as the air speed is increased. In particular, at 0.1 m/s there are 3 distinct de-pinning of the contact line (marked with A, B and C); at higher air speeds (1 m/s) there is only one de-pinning event (marked with A’) with a higher initial contact angle probably due to the fact (like in the case of water) that the airflow pushed the contact line inwards. The water droplets adhere better to the Teflon surface than the ethanol ones and these latter ones are more prone to de-pinning than the former ones. It is worth noting that for two repeat experiments (that of Fig. 4 and that of Fig. 7) the time at which the contact line de-pins are roughly the same if measured by IR or by DSA30; in particular it happens around 49 s for the IR measurement (forth curve of Fig. 4) and just over than 49 s for the contact angle measurement (third set of curves in Fig. 6). In addition, the initial diameter of the drop estimated with IR measurements (Fig. 4) assuming that the contact line is located at the red dot of Fig. 3 and DSA30 measurements (Fig. 6) for ethanol differs of less than 55 μm (corresponding to less than 2 pixels in the IR measurements and less than 5 pixels in the optical measurement with DSA30); if instead we assume that the contact line position is the local maximum just more inwards of the red dots of Fig. 3, then the error made would be over 195 μm (corresponding to more than 6 pixels in IR and more than 17 pixels for the DSA30). Therefore, we can reasonably assume that it is indeed the red dot of Fig. 3 the most likely location of the contact line. This is an important confirmation that the two measurement techniques can be independently used to study this problem to measure different properties of the evaporating drops and correlate the results obtained. The ethanol drops of the present study do not exhibit the same initial stages of the methanol drops reported in Sefiane et al. [23] where the contact angle increases reaching a maximum before it decreases again. In Sefiane et al. [23] the contact line is basically not pinned whereas in the present case it remains pinned. In addition, in Sefiane et al. [23] the more volatile methanol leads to a significant contraction of the contact line, something we do not see in the less volatile ethanol of the present study.

4.2. Adaptation of existing diffusion limited evaporation model In this section we are going to modify two simplified models to calculate the temperature of the contact line of the ethanol drop for the only case of 1 m/s imposed air speed. The aim of these modified and simplified models is to show how the transient after drop deposition plays a big role in drop evaporation and to confirm that a diffusion limited model to predict drop evaporation is, in most practical cases, inadequate. The drops can be considered as spherical caps because the capillary length for the fluids used ranges between 1.7 and 2.7 mm; because all the drops of this study have a radius smaller than the capillary length values, we can consider the drops in the following relations to be a spherical cap. First, we try to understand in which flow regime we are for the cases considered in the present investigation. To do so, we need to estimate the Grashof (Gr) and Reynolds (Re) numbers. The ratio Gr/Re2 varies between 3 10−2 and 7 10−5, which suggests that forced convection dominates on natural convection for all cases apart from the case of no airflow. As the drop evaporates, it will reduce in size and eventually even de-pins reducing its diameter; the evaporation also reduces overall and the evaporative cooling effect on the drop is less as time progress during the drop drying process. What changes dramatically is the Gr as it depends on the drop diameter at the power of three. Because the freestream Re changes linearly with the drop diameter, as the drop evaporates this results in a consequent linear reduction of the Gr/Re2 ratio and ultimately forced convection dominates even more on the natural convection of the descending air cold plume. It is important to estimate the thickness of the boundary layer at the drop location which develops from the Teflon surface leading edge. We adopt here the Blasius solution for laminar boundary layers, given that the freestream Re on the drop location varies between 232 and 4520. The resultant estimated boundary layer thickness at the drop location that develops from the Teflon leading edge ranges between 11 and 2.6 mm, for freestream speed changing between 0.1 and 1.95 m/s, respectively. Just after drop deposition and with no imposed airflow, water are the tallest drops reaching a height of around 1.15 mm and ethanol are the shortest drops reaching only 0.57 mm. Therefore, we can conclude that mass transport from the drops is affected by forced convection but not controlled by boundary layers at such freestream

4. Simplified analysis 4.1. Background The evaporation of a drop in still air is already a challenging phenomenon to model and predict because of the important interaction between the liquid and the solid surface, the curved liquid-gas interface and especially because of the complex heat and mass transfer mechanism between a drop that changes continuously shape and its surroundings (gas and solid phases). Another very important complication is that when a drop is deposited on a solid surface, depending on the liquid partial pressure in air, the phase change mechanism sets in and there is an important consequent change of drop surface temperature due to the evaporating cooling effect; in addition to the drop surface temperature change there is also a change of the temperature of the solid surface on which the drop sits. For the liquids of the present experimental investigation, the vapor generated by evaporation at the drop surface being lighter than air travels upward into air due to buoyancy. Moreover, given that the surface of the drop is colder than the surrounding air due to evaporative cooling, air is also driven 7

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Fig. 8. Left frame is the normalised Radius, Volume and Contact Angle for an ethanol drop on Teflon and 1 m/s imposed air speed. Right frame shows the contact line temperature as measured by IR and also calculated with various models.

and laminar flow (given that the estimated maximum Rayleigh number is around 102 for the present investigated cases) as follows [33]:

velocities and for the drops deposited at such location from the Teflon leading edge facing the airstream. Hu and Larson [31] proposed an expression for the evaporation rate for a water droplet in still air with contact angle between 0° and 90° which can be used as follows for the ethanol drop evaporating in air of the present work (it is worth noting that in the present study the initial contact angles for water droplets on Teflon are above 90° but those of ethanol are below 40°):

− m˙ = π R D c v (0.27 θ 2 + 1.30)

h=

(1 − cos θ) D M csat (1 − H ) F (θ) sin2 θ ρ

(1)

(Ta − Tw )WithTransient =

m˙ hcap D

= 0.664 Re 0.5 (Re I∞)0.066Sc1/3 ≅ 53

m CP

(6)

4.3. Comparison between modified previous models and experimental results

(2)

During the experiments, we measured the drop diameter and the drop contact angle as evaporation took place and combining Equations (4), (5) we can estimate the corresponding temperature of the drop contact line (Tw) and compare it with the one measured by IR. With Equation (6) we can also estimate the further change of (Tw) considering the drop thermal capacity. Fig. 8 reports on the left plot the volume, the radius and the contact angle of the ethanol drop subject to a 1 m/s air speed (this air speed is chosen as the undisturbed air Reynolds number is well above the value 150 for which the unsteady laminar vortex street behind the drop becomes turbulent and the wake flow structure is three-dimensional and therefore there is less likelihood of large spatio-temporal variations in the temperature readings, characteristic of lower Reynolds numbers), all as normalised values; the right plot reports the temperature profiles as measured by IR and estimated with the use of Equations (4)–(6). In Fig. 8 we should only consider the reported results until after the drop de-pins for the first time (around 49 s) because the models by Hu and Larson [31] and by Semenov et a [32]. were developed for uniform evaporation rate of the drop, which is typical of the pinned phase. As the plot on the right frame of Fig. 8 shows there is a reasonable good agreement between measured and calculated contact line temperatures using Hu and Larson [31] and Semenov et a [32]. models as per Equations (1) and (2) at the

(3)

where hcap is the height of the drop, Iꝏ is the freestream turbulence level, and Sc the Schmidt number that is 1.5 for ethanol in air. In the present work we also assume (for steady state) the latent heat times the evaporation rate is equal the heat transferred from the ambient through the Teflon surface reaching eventually the base of the drop:

π R D c v (0.27 θ 2 + 1.30) ΔHfg = h π R2 (Ta − Tw )

m˙ Δt ΔHfg

where Δt is the time step considered, m is the mass of the drop at the corresponding time step, and Cp is the liquid specific heat at constant pressure.

where, csat is the vapor concentration at saturation, ρ is the liquid density, H is the humidity of ambient air, and F(θ) is a function of the contact angle. For θ > 10 °F(θ) = (0.00008957 + 0.6333 θ + 0.116 θ2 – 0.08878 θ3 + 0.01033 θ4)/sin(θ). Equations (1) and (2) do not consider any effect on m˙ of the removal of vapor by forced air convection. We will assume that the influence of air speed is considered via the Sherwood number in the relation below, which includes also the contribution of the turbulence level:

Sh =

(5)

In the previous formula, k is the air thermal conductivity and Ra is the Rayleigh number. There is another aspect that can be also added to this simplified model. During the transient phase right after deposition the IR measurements and the optical measurements on the drop show that the drop remains pinned, the contact angle decreases and the contact line temperature decreases as well. During this phase the heat lost by the drop because of the evaporation goes also to lower the drop temperature. As a first approximation we can assume that at each time step, Tw in Equation (4) is further lowered because of the thermal capacity of ethanol as follows:

where, m˙ is the evaporation rate, R is the drop base radius, D is the liquid diffusion coefficient, cv is the vapor concentration in air and θ is the contact angle. The drop evaporation model of Hu and Larson [31] applied to water droplets is diffusion limited and they demonstrated that for initial contact angles less than 45°the net evaporation rate from the drop is constant for a pinned drop, despite the evaporation flux tends to peak more and more near the drop contact line as the drop evaporates and the contact angle decreases. Hu and Larson [31] show that their model agrees well, for all initial contact angle between 0° and 90°, with the results of the theoretical analysis presented by Picknett and Bexon [9]. Semenov et a. [32], proposed a different relationship for the evaporation rate from a sessile drop, which is:

− m˙ = 2 π R2

0.54 k Ra1/4 2R

(4)

Where ΔHfg is the ethanol latent heat of evaporation, h is the heat transfer coefficient at the airside, Ta and Tw are the air and drop contact line temperatures. h is evaluated for a cold horizontal plate facing down 8

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balance between evaporative cooling, heat transfer with the substrate and convection in the gas phase takes place. Combining IR and contact angle measurements can help considerably shedding more light on the dynamics of drop evaporation. In practical applications of drop evaporation, the drop does not evaporate in still air; rather it is subject to forced convection. In the present study we have tackled drop evaporation closer to real application using a more pragmatic approach by considering drops of different liquids subject to crosswind of different speeds. The IR temperature measurements of ethanol drops done in the present study clearly show that during the first stage of drop evaporation, when the drop diameter remains constant, the drop contact line temperature decreases noticeably, as in Liu et al. [21]; but crucially the ethanol drop sticks to Teflon at the start of the evaporation and contrary to what Liu et al. [21] reported for a methanol. In the subsequent stage of contact line de-pinning, the contact line temperature remains broadly the same; this phase is not found in the experiments of Liu at al [21]. The simplistic models originally developed by Hu and Larson [31] and Semenov et a [32]. to compare the predicted contact line temperature with that measured by IR of the present experiments, seem to suggest that the drop transient should be accounted for in modelling studies of drop evaporation and that the flow topology and flow regime around the drop seems to be responsible for the large overprediction of the contact line temperature dynamics respect to the measured values. The simplified analysis developed in the present work which accounts for the increase of evaporation rate due to forced convection (through the Sherwood number) and the thermal capacity of the drop (which is operating only during the pinned phase), seem to reproduce rather accurately the drop wedge temperature during the first two stages of drop evaporation. These aspects of initial transient following drop deposition where the drop temperature deepens and nearly constant contact line temperature during drop de-pinning with drops subject to more realistic experimental conditions such as crosswind, if further investigated and understood properly for a wide variety of drops (liquid and volume) evaporating on different surfaces, might lead to a better understanding of the heat and mass transfer of the combined liquid/ solid/gas phases.

very start when the ethanol drop is deposited on the Teflon surface. The measured temperature is almost a couple of degree lower than the predicted one already 30 s after drop deposition on the Teflon surface. This seems to agree with the study of Pan et al. [30]; the larger variations found in the present study might well be due to the enhancement of forced convection. The models of Hu and Larson [31] and Semenov et a [32]. are quite simplistic and from these preliminary measurements it appears that a particular aspect which is worth a closer look from a modelling point of view is the transient phase during which the temperature of the contact line deeps dramatically and it might well be that evaporation on the drop surface is very far from being uniform as the model of Hu and Larson [26] and Semenov et a [32]. assume; in fact, the recently reported transient IR temperature measurements of a curved meniscus interface pinned at a capillary tube mouth (Buffone and Sefiane [34]) shows a very noticeably transient phase. To corroborate this point, if we plot the contact line predicted temperature when also the thermal capacity of the drop is taken into account with Equation (6), we see in Fig. 8 that up to drop depinning (49 s) there is a rather good agreement with the measured temperature by IR; the maximum deviation is 2.3%. We should remember that the IR temperature readings are 1% accurate, as stated by FLIR for the ThermaCAM SC3000 we used; this means that the maximum expected error in the temperature readings is made at drop deposition when the temperature is highest and this amount to ∼0.2 °C. If we continue to use the same modified model including the correction brought by Sherwood number, during the following part of drop evaporation following the first de-pinning of the contact line (point A’ of Fig. 7, in which there is no contribution of the transient change of drop wedge temperature due to the liquid thermal capacity, because the drop wedge temperature remains nearly constant according to the IR measurements reported in Fig. 4), then the agreement between the present simplified model and the experimental temperature readings can be extended until the end of the first de-pinning phase (91 s in Fig. 8); the maximum discrepancy between measured and calculated drop wedge temperature is less than 3%. In the subsequent mixed phase of variable radius and contact angle the simplified model cannot predict the drop wedge temperature. The simplicity of the analytical models developed on drop evaporation to date makes them amenable to treatments in order to explain some important features, whilst they remain far from capturing all possible aspects of a seemingly simple experiment like drop evaporation which is so rich in physics.

Acknowledgements The author would like to thank Dr. Tadhg O'Donovan of HerriotWatt University in Edinburgh for providing the IR camera. Prof. Khellil Sefiane's contribution from The University of Edinburgh is acknowledged for lending the DSA30 drop analyser and initial discussion on the experiments. The author is also indebted to the technicians of the School of Engineering at The University of Edinburgh.

5. Conclusions We analysed the evaporation of drops made with three different liquids (water, ethanol and whiskey) on Teflon surface. We subjected the drops to crosswind with various air speeds (0.10, 0.50, 1.00, 1.60 and 1.95 m/s) and used IR to map the drop interfacial temperature and a contact angle analyser to measure the contact angles of the drop in the direction of the imposed air speed. We showed that IR can detect where the contact line is from the instant the drop is deposited to when the drop is evaporated completely and gives a complete two-dimensional view of the contact line. This is out of reach for contact angle analyser machines; however, IR cannot detect the value of the contact angle. There has been a considerable effort in the literature trying to model analytically the evaporation from sessile drops. These models, while amenable to treatment in order to gain some understanding of the global evaporation from drops, typically fail to capture a wide range of practical cases. The gap between experimental evidence and analytical prediction is still large. The use of numerical simulations corroborated by some experimental evidence such as those of Pan et al. [30], shed some light into this fascinating subject where evaporative cooling, heat transfer at the substrate and convection at the gas phase, all play a different important role. It is established that measuring the interfacial temperature of the evaporating drop is key to understand how the

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