Shedding of Water Drops from a Surface under Icing Conditions

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Shedding of Water Drops from a Surface under Icing Conditions Deepak Kumar Mandal,† Antonio Criscione,‡ C. Tropea,§ and A. Amirfazli*,† †

Department of Mechanical Engineering, York University, Toronto, ON M3J 1P3, Canada New Devices Engineering EMEA, Takata Corporation, D-63743 Aschaffenburg, Germany § Institute for Fluid Mechanics and Aerodynamics, Center of Smart Interfaces, Technische Universität Darmstadt, D-64287 Darmstadt, Germany ‡

Downloaded by RUTGERS UNIV on August 25, 2015 | http://pubs.acs.org Publication Date (Web): August 19, 2015 | doi: 10.1021/acs.langmuir.5b02131

S Supporting Information *

ABSTRACT: A sessile water drop exposed to an air flow will shed if the adhesion is overcome by the external aerodynamic forces on the drop. In this study, shedding of water drops were investigated under icing conditions, on surfaces with different wettabilities, from hydrophilic to superhydrophobic. A wind tunnel was used for experiments in a temperature range between −8 and 24.5 °C. Results indicate that the temperature has a major influence on the incipient motion of drop shedding. The critical air velocity (Uc) at which a drop first starts to shed generally increases under icing conditions, indicating an increase in the adhesion force. The contact angle hysteresis (CAH) and the drop base length (Lb) are found to be the controlling factors for adhesion. A correlation was also developed to deduce the drag coefficient, CD for the drop. It was found that CD can decrease under icing conditions. In general, a lower CD and higher adhesion together lead to a higher critical air velocity. However, there are systems such as water on Teflon for which the critical air velocity remains practically unaffected by temperature because of similar adhesion and CD values, at all temperatures tested.

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INTRODUCTION The shedding of a drop on a substrate has practical relevance, for example, in enhanced oil recovery,1−4 to avoid airfoil icing,5−7 in wind turbines,8,9 for water management in fuel cells,10 for cleaning,11−14 etc. The shedding process has been studied by simulation15−19 or by conducting experiments,20−23 although the shedding of sessile drops under icing conditions has been seldom studied. Experimentally, when a sessile drop is placed on a surface inside a wind tunnel, the air flow induces a drag on the drop, and when the drag force just exceeds the drop surface adhesion, the drop starts to move. This velocity of incipient motion is called the critical air velocity and depends on the shape of the drop, and drop surface adhesion. The higher the adhesion, the higher the drag force required for the drop to shed.20 The adhesion is determined by surface tension,24,25 contact angle (CA), contact angle hysteresis (CAH), and contact line shape and/or size of the drop.26 These parameters are broadly classified as wetting characteristics of the drop on a specific surface. According to Milne and Amirfazli,20 adhesion is higher for a drop on a hydrophilic surface than on a hydrophobic or superhydrophobic surface (SHS) under normal ambient conditions. Thus, the critical air velocity is higher for a drop on a hydrophilic than on a hydrophobic surface, and it is least for a SHS. An example of a superhydrophobic surface is a micro/nanotextured surface where air is trapped in crevices of the surface texture. As such, a © XXXX American Chemical Society

drop sits on top of micro/nanopillars of the surface, as well as on air. The drop contact angle, in this case, will depend on the portion of its contact with air trapped under the drop.27 A higher proportion of air contact will produce a higher macroscopic contact angle. Lowering the temperature to the freezing point of water causes the contact angle of a drop on SHS to reduced considerably, and at the same time, the contact angle hysteresis increases,28 likely because of the condensation of moisture on the surface cavities and/or roughness.29,30 Condensation of moisture causes the drop base length to increase,31 and an increase in drop base length leads to higher adhesion, when all else being equal. A possible hypothesis for the increased adhesion under icing conditions is the formation of a frost layer (near the contact area of the drop) that affects the wettability and, hence, the adhesion. The probability of the formation of a frost layer is higher for a rougher surface (i.e., SHS), because the roughness promotes condensation under icing conditions.32 The condensation may transform the Cassie−Baxter to Wenzel wetting state for a given drop on SHS at lower temperatures,33 as well. Received: June 12, 2015 Revised: August 10, 2015

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DOI: 10.1021/acs.langmuir.5b02131 Langmuir XXXX, XXX, XXX−XXX

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potentiometer). The velocity and temperature of the air flow were measured using an electronic sensor fitted ∼7 cm downstream of the test section (dimensions of the test section cross section, 216 mm × 470 mm). A Phantom v4.3 high-speed camera (Vision Research Inc.), operating at 500 frames/s, was used to capture the side images of the drop through a set of telecentric Navitar lenses (Navitar Inc.) operating at a magnification of 0.56. This magnification resulted in a resolution of 38 μm/pixel. A diffused light source was used for backlighting. The sample surface was placed on top of the Peltier cell before experiments were conducted. Then the surface was allowed to come to the desired temperature from its initial temperature (in the absence of air flow). The maximal time for a surface to achieve the Peltier cell temperature was ∼1.5 min. The temperature of the sample surface was monitored by a digital thermocouple. Immediately after the surface stabilizes to the desired temperature, the drop was placed on top of the sample surface to conduct experiments. The process mentioned above was repeated each time before experiments were conducted (note that each time a fresh surface was used). The surfaces were monitored for any signs of icing, and if any sign was observed, then the data were discarded. The experimental procedure began with placement of a drop of a desired volume on the surface (∼4 cm downstream from the leading edge of the Peltier cell) using a micropipette. The surface and its surroundings were stabilized to the desired temperature before the drop was placed on the surface. Then, both camera and fan were triggered at the same time. The delay between the drop placement and triggering the camera or starting the air flow was typically 3−5 s. The air flow was increased gradually, and the drop shedding process was recorded. After the sequences of images had been recorded, the drop profile and positions of the upstream and downstream contact points were obtained using in-house software (Matlab). Incipient motion was defined as the instant at which the difference between the instantaneous and initial upstream position of the drop was 5 pixels or 190 μm,20 and the corresponding air flow velocity at that time was denoted the critical air velocity for the drop. Details of the postprocessing and determination of the critical air velocity are provided in the Supporting Information. In this work, the shedding of water drops with volumes ranging from 5 to 100 μL (5, 10, 25, 50, and 100 μL) on three surfaces, under icing conditions (surface and air flow temperatures of −1, −5, and −8 °C), were studied (initial water drop temperature of ∼0.6 °C). These surfaces are hydrophilic (PMMA-coated aluminum, denoted PMMA), hydrophobic (Teflon-coated aluminum, denoted Teflon), and superhydrophobic (Teflon-coated etched aluminum, denoted SHS). The methods for preparing these surfaces are explained below. PMMA surfaces were prepared using an aluminum sheet as a substrate, cut to size, and thoroughly cleaned with water and acetone. A solution containing dry toluene and PMMA [1% (w/w) PMMA] was prepared and spread on the aluminum sheet using a spin coater. The surface was placed inside a vacuum chamber for drying (duration of 1 h). A similar method was used to prepare the Teflon-coated surfaces, except the solution containing FC-75 and Teflon [5:1 (v/v) FC-75, 3-M/Teflon AF, Dupont] was used for the coating. For the superhydrophobic surface (SHS), an aluminum surface was cleaned thoroughly with ethanol and acetone and etched for approximately 1.5 min in a 36% solution of hydrochloric acid in deionized (DI) water. The aluminum surface was then removed from the acid, rinsed thoroughly in DI water, and dried in a dry nitrogen stream. The surface was then coated via spin coating with a solution containing FC75 and Teflon [5:1 (v/v) FC-75, 3-M/Teflon AF, Dupont] and placed inside vacuum chamber for drying (duration of 1 h). The percentages of errors for the figures are calculated on the basis of a minimum of three data sets of a given experiment (given drop on a given substrate at any temperature). The percentages of errors are the maxima of the ratios of the standard deviation to the mean of all data sets. The maximal percentages of errors are reported as error bars.

Drop shedding under icing conditions is possibly different, as previous studies show that the contact angle decreases whereas contact angle hysteresis and drop base length increase under these conditions.28,31 Because contact angle, contact angle hysteresis, and drop base length determine the wetting characteristics of a surface, the wettability change can be expected under icing conditions, especially for SHS. Therefore, the question arises how the icing conditions influence the drop shedding on surfaces with different wettabilities, and how consequently the critical air velocity changes? In the present paper, the influence of icing conditions on shedding of a sessile water drop with volumes ranging over 2 orders of magnitude, from surfaces with different wettabilities (from hydrophilic to superhydrophobic), is studied. The results are compared with shedding at a normal temperature (24.5 °C). An analytical model developed by Roisman et al.34 is used to develop a correlation for the measured drag coefficient. It is worth mentioning here that, while our previous paper34 is conceptually related to the study presented here, the following points set this paper apart: the experimental evidence and justification of flattening of a given drop on various substrates under icing conditions, the details about the factors affecting adhesion, and the discussion of the drag coefficient (i.e., procedure to independently calculate the drag coefficient and the insight on the reduction of the drag coefficient under icing conditions).

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EXPERIMENTAL SETUP AND METHODOLOGY

The experimental setup is shown schematically in Figure 1. Different ambient temperatures inside the wind tunnel were obtained using a

Figure 1. Top view schematic of the experimental setup, showing a closed loop icing wind tunnel and accessories such as a high-speed camera, a light source, etc. chiller (HAAKE KT-90, ethanol bath, range of 40 to −90 °C, watercooled). Inside the test section of the wind tunnel, an aluminum surface (surface area of 25 mm × 75 mm, thickness of 0.98 mm, Al 6061-T6) coated with the respective coating was placed on top of a Peltier cell (TE Technology, CP-031, 12 V and 5 A), which was used to control the surface temperature. The sample surface was monitored regularly to make sure that there were no visible signs of frost or ice formation because of the condensation of atmospheric moisture. A fan (maximal air flow of 15 m/s, DPP120-24-1 power supply to deliver 5 A at 24 V) was used to generate the air flow inside the tunnel. The speed of the fan was varied using a regulator (0 to 5 V using a B


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THEORETICAL BACKGROUND To develop a practical theoretical framework for the drop shedding process, experimentally accessible parameters, free air stream velocity (U), contact angles at upstream (θmin) and downstream (θmax) locations, drop base length (Lb), drop height (h), and frontal area of the drop (A), were considered relevant. Upstream and downstream contact angles should be measured at the threshold for the incipient motion of the shedding drop. Notwithstanding the possible variation of the contact angle along the contact line and deviation of the contact line from a circular shape, the adhesion force can be given as35


Fadh = γL b(cos θmin − cos θmax )

RESULTS AND DISCUSSION Figure 2 shows the critical air velocity for drops on all three surfaces at 24.5 and −5 °C. For small drops (volume of 25 μL). Hence, from both panels a and b of Figure 3, it is evident that for a given volume, drops can flatten on surfaces under icing conditions. In general, it can be stated that the flattening is stronger for larger drops, and drops on the Teflon surface are not flattened significantly. For a given volume, a flattened drop implies increased adhesion (see eq 1), because of the larger drop base length. This explains the increase in critical air velocity under icing conditions. Of course, the adhesion can also increase because of higher contact angle hysteresis (eq 1). Figure 4 shows higher contact angle hysteresis at −5 °C than that at 24.5 °C for drops on all three surfaces. Therefore, it can be understood how, for a given drop volume, adhesion can be increased with a decrease in temperature. The higher contact angle hysteresis for a given drop under icing conditions possibly confirms a strong pinning, as well (see Figure 4). Collectively, the factors affecting adhesion are the higher drop base length and higher contact

(2)

where ρ is the density of air and CD is the drag coefficient. At the threshold of shedding (U = Uc, where Uc is the critical air velocity), the drag and adhesion are balanced. As such, by setting eqs 1 and 2 equal to one another, one can write CD =

2γL b(cos θmin − cos θmax ) ρAUc 2

(3)

where A and Uc are given by34 A=

θs 4/3 2 cosθs)2/3

()

(6Vd)2/3 sin (2π + π

θs − sin θs cos θs (1 − cos θs)2

(4)

⎡ νxγL b(cos θmin − cos θmax ) ⎤1/3 Uc = 5.25⎢ ⎥ ⎦ ⎣ 2ρAh2 −5

(5)

where ν is the kinematic viscosity of air (10 m /s) and x is the distance between the leading edge of the surface and the drop (in our case 3.7 cm). The values of h can be found from the equations given below. h=

θs 2/3 2 θs)1/3

2

()

(6Vd)1/3 sin

(2π + π cos

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(6)

If one assumes the critical air velocity in eq 5 as a first-order approximation, then we will represent the drop (which is about to shed) by a truncated sphere with contact angle θs, which is the average of θmin and θmax. Also, eqs 4 and 6 are found by simple geometrical considerations for a truncated sphere with a volume of Vd (equal to the actual drop volume) and a contact angle of θs. Roisman et al.34 showed that eq 5 can successfully predict the critical air velocities found from experiments under ambient and icing conditions for a wide range of water drop sizes. As such, the values of CD found from eq 3 should be at least correct to the first order of magnitude, because the values of θmin and θmax are measured experimentally, and γ (72 mN/m at room temperature) and ρ (1.2 kg/m3 at room temperature) are system constants. C


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Figure 3. (a) Average contact angles and (b) drop base lengths (Lb), at −5 and 24.5 °C, as a function of drop volume. Lines are to guide the eye. For panel a, the errors are 7.2, 6, and 9.8% for PMMA, Teflon, and SHS, respectively. For panel b, the errors are 5.2, 3, and 9.2% for PMMA, Teflon, and SHS, respectively. The legends are the same for both plots.

based on all systems and drop volumes. However, the picture is more complex for a given drop volume on a particular surface. For example, the critical air velocity increases noticeably for drops on SHS and PMMA [for PMMA, a significant increase is observed for larger drop volumes (see Figure 2)], but the increase is negligible for Teflon. The shedding of drops on PMMA, Teflon, and SHS is discussed separately in detail below. Shedding of Drops on PMMA Surfaces. Experimental values of θmin, θmax, contact angle hysteresis, θs, and CD for water drops on PMMA at 24.5, −1, −5, and −8 °C are listed in Table 2. The drag coefficient, CD, is calculated using eq 3. The θmin and θmax values for each drop volume are taken from the experiments (see Table 2). Because of ice formation at −8 °C, the data corresponding to drops of 25, 50, and 100 μL are absent. The shedding of a drop from PMMA is complicated, because a significant increase in critical air velocity is observed for only larger drop volumes (>10 μL) under icing conditions (see Figure 5). The change in critical air velocity is not noticeable for smaller drops. The contact angle hysteresis increases generally as the temperature decreases, especially for highervolume drops (volume of >10 μL) (see Table 2). The drop base length (see Figure 3b) is higher for larger drops under icing conditions, as well. The higher contact angle hysteresis and drop base length (see Figure 3b) together cause the adhesion to increase with a decrease in temperature. For a given drop, the drag coefficient decreases under icing conditions (see Table 2). Taken together, the increase in critical air velocity, especially for larger drops, can be understood. The values of drag coefficient for larger drops (50 and 100 μL) at 24.5 °C show an abrupt increase (see Table 2). For smaller drops, a significant increase in critical air velocity is not observed under icing conditions, although the drag coefficient decreases (see Table 2). It was found that the drag coefficient values are sensitive to θmin and θmax. The drag coefficient for a given drop is calculated for all θmin and θmax values obtained while repeatability experiments are conducted at a given temperature. The maximum of the ratio of standard deviation to mean of all drag coefficients calculated is reported as the uncertainty for a given case (see Table 2 for drops on PMMA). The variation in CD was found to be high, especially for smaller drops, practically making the drag coefficient almost the same under both room-temperature and icing conditions. With regard to adhesion, the drop base length (see Figure 3b) is almost the same for smaller drops. Hence, the adhesion remains unaffected under icing conditions for smaller drops. Unexplained, nonmonotonous values of θmin, θmax, and contact angle

Figure 4. Variation of contact angle hysteresis with drop volume at −5 and 24.5 °C. Lines are to guide the eye.

angle hysteresis, but critical air velocity may also increase, if the drag coefficient decreases; this will be considered below. The drag coefficient is calculated from eq 3 using equations 3 and 4, knowing the θs. The θmin and θmax for each drop volume are taken from the experiments, while the other parameters (Lb, Rd, h, and A) are calculated from the geometry of a truncated sphere knowing θs and volume. Table 1 shows CD values for drops on different surfaces at 24.5 and −5 °C. The drag coefficient for a given drop decreases under icing conditions on all three surfaces. A lower drag coefficient and higher adhesion for a given drop volume together provide an explanation for why a higher critical air velocity was observed to shed a drop under icing conditions. The discussions this far were overall observations Table 1. Calculated CD Values from eq 3 at 24.5 and −5 °C for Drops on All Three Surfaces surface

volume (μL)

PMMA

5 10 25 50 100 5 10 25 50 100 5 10 25 50 100

Teflon

SHS

CD at 24.5 °C 1.3 0.9 0.8 1.1 1.0 0.9 1.2 0.7 0.7 0.7 4.1 3.4 2.9 9.6 8.2

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.59 0.40 0.17 0.30 0.34 0.46 0.49 0.30 0.29 0.29 2.3 1.7 1.4 3.3 3.3

CD at −5 °C 0.3 0.2 0.2 0.2 0.1 0.2 0.2 0.1 0.1 0.1 1.5 0.6 0.5 0.2 0.9

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.15 0.07 0.07 0.07 0.04 0.09 0.07 0.04 0.05 0.05 0.72 0.31 0.22 0.08 0.37 D


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Table 2. θmin, θmax, Contact Angle Hysteresis, and θs under Air Flow Conditions at Different Temperatures for Drops on a PMMA Surfacea temp (°C)

Vd (μL)

θmin (deg)

SD

θmax (deg)

SD

CAH

SD

θs (deg)

24.5

5 10 25 50 100 5 10 25 50 100 5 10 25 50 100 5 10

68 67 67 72 73 75 69 67 66 67 64 62 61 62 58 68 73

1.9 2.1 3.6 1.9 0.8 1.0 2.1 2.3 4.0 2.6 3.4 7.6 6.4 4.0 3.0 3.6 7.1

90 89 91 92 94 90 90 88 89 88 90 87 86 90 88 89 88

0.6 1.6 1.8 0.0 0.0 0.0 0.0 3.9 2.5 3.6 0.0 4.6 3.5 0.0 2.3 1.6 2.8

19 20 18 15 18 15 21 21 23 21 26 25 25 28 30 21 16

2.3 0.6 4.7 1.9 0.8 1.0 2.1 3.6 4.3 0.9 3.4 9.4 5.7 4.0 0.7 5.2 4.5

79 78 79 82 83 82 79 77 77 77 77 74 73 76 73 78 80

−1


−5

−8

CD 1.3 0.9 0.8 1.1 1.0 0.2 0.2 0.2 0.2 0.1 0.3 0.2 0.2 0.2 0.1 0.2 0.2

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.59 0.40 0.17 0.30 0.34 0.08 0.08 0.09 0.08 0.06 0.15 0.07 0.07 0.07 0.04 0.07 0.08

At −8 °C, icing was observed for drops with volumes of 25, 50, and 100 μL, so the corresponding values are absent. SD denotes standard deviation. The calculated CD values are also given.

a

validated), except for −5 °C for a Vd of 25 μL. For smaller drops (volume of ≤25 μL), nonmonotonous changes in contact angle hysteresis are observed at −5 and −8 °C. However, the drop base length (see Figure 3b for drops on Teflon) remains almost the same (as that at 24.5 °C) for different drops under icing conditions. Therefore, overall it can be said that the adhesion remains the same. For smaller drops, contact angle hysteresis at −5 and −8 °C does not seem to affect the adhesion, because the adhesion remains the same, although the contact angle hysteresis values are nonmonotonous. The values of the drag coefficient for all drops are listed in Table 3. The drag coefficient for a given drop decreases under icing conditions. However, the sensitivity in calculating CD was found to be high (see Table 3). Therefore, it can be said that the CD for a given drop remains practically the same at all temperatures. The drag coefficient values at −1, −5, and −8 °C are similar (see Table 3). Taken together, critical air velocity does not increase significantly (see Figure 6a). The water− Teflon system is not substantially affected under icing conditions. In the case of drops on Teflon, the drop base length seems to be the primary factor that affects adhesion, because an almost constant drop base length for a given drop makes the adhesion

Figure 5. Critical air velocity as a function of drop volume at 24.5, −1, −5, and −8 °C for the drops on PMMA. Lines are to guide the eye.

hysteresis are also observed at different temperatures in Table 2. Therefore, the drop base length for smaller drops and the drop base length and contact angle hysteresis for larger drops seem to be the primary factors influencing adhesion. Shedding of Drops from Teflon Surfaces. The critical air velocity decreases with drop volume, as seen in Figure 6a, similar to the case in the water−PMMA system. In Figure 6a, the critical air velocities at all temperatures are in the same range (statistically validated). The temperature effect is much smaller than that of drops on PMMA (especially for larger drop volumes on PMMA). The contact angle hysteresis values of the water−Teflon system are given in Figure 6b, where at any given temperature, it remains constant with drop volume (statistically

Figure 6. (a) Critical air velocity and (b) contact angle hysteresis with drop volume for water drops on Teflon at 24.5, −1, −5, and −8 °C. The legends are the same for both plots. Lines are to guide the eye. E


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Langmuir Table 3. Calculated Drag Coefficients at Different Temperatures for Drops on Teflon and SHS Surfaces surface

Vd (μL)

Teflon

5 10 25 50 100 5 10 25 50 100


SHS

CD at 24.5 °C 0.9 1.2 0.7 0.7 0.7 4.1 3.4 2.9 9.6 8.2

± ± ± ± ± ± ± ± ± ±

CD at −1 °C

0.46 0.49 0.30 0.29 0.29 2.3 1.7 1.4 3.3 3.3

0.6 0.2 0.2 0.1 0.1 1.5 0.5 0.2 0.1 0.2

± ± ± ± ± ± ± ± ± ±

0.30 0.06 0.06 0.04 0.04 0.8 0.3 0.07 0.06 0.07

CD at −5 °C 0.2 0.2 0.1 0.1 0.1 1.5 0.6 0.5 0.2 0.9

± ± ± ± ± ± ± ± ± ±

0.09 0.07 0.04 0.05 0.05 0.72 0.31 0.22 0.08 0.37

CD at −8 °C 0.2 0.2 0.1 0.1 − 1.5 0.2 0.2 0.2 −

± ± ± ±

0.04 0.04 0.04 0.04

± ± ± ±

0.6 0.03 0.03 0.03

Figure 7. (a) Critical air velocity and (b) CAH vs drop volume for drops on SHS at 24.5, −1, −5, and −8 °C. The legends are the same for both plots. Lines are to guide the eye.

constant under icing conditions, although θs and contact angle hysteresis show changes similar to those seen for the water− PMMA or water−SHS system. The drag coefficient for a given drop also remains the same at all temperatures [taking sensitivity into account (see Table 3)]. Therefore, the drop base length and drag coefficient together become the determining factors when drop shedding on Teflon is concerned. The Teflon surface showed less pinning for a given drop under icing conditions. In general, lower contact angle hysteresis means less pinning. The variation of the contact angle hysteresis with volume for water drops on Teflon at different temperatures in Figure 6b shows that the contact angle hysteresis does not increase considerably between room temperature and icing conditions at −1 C. The pinning is also associated with the shape of the drop; i.e., the shape of a given drop can change once the drop is brought to icing conditions from room temperature, because of pinning. For the case presented here, the shape of the drop on Teflon remains almost the same under icing conditions at incipient motion (Figure 3b); hence, the drop surface adhesion remains constant. The drag coefficients in Table 3 and the high uncertainty in calculating the drag coefficients show that the drag coefficient remains the same under icing conditions and confirms the unchanged shape of a given drop on Teflon. The constant contact angle hysteresis, drop base length, and drag coefficient justify that the level of pinning of a given drop on Teflon is low under icing conditions. Shedding of Drops from SHS. The critical air velocities as a function of drop volumes are shown in Figure 7a. It can be observed that at normal temperature, the critical air velocity decreases from its value for drops with volumes of 5−10 μL, and it remains practically constant for the rest of the drop volumes. Figure 7a shows that critical air velocity increases under icing conditions (−1, −5, and −8 °C) compared to its

room-temperature value. The critical air velocity practically remains constant with volume under icing conditions. The maximal limit of the y-axis (in Figure 7a) is kept as 8 m/s to allow the reader to compare results from all three surfaces. The contact angle hysteresis as a function of drop volume is shown in Figure 7b. The contact angle hysteresis remains constant at normal temperature for all drop volumes, but for icing conditions, there are sharp increases initially followed by a plateau. For a given temperature, the contact angle hysteresis increases with volume, similar to the case for the water−PMMA system. θs decreases, and drop base length increases (see Figure 3a,b for drops on SHS), as well. Hence, adhesion increases, similar to the case for the water−PMMA system. The calculated drag coefficients for all drops at different temperatures are listed in Table 3. The drag coefficient for a given drop decreases under icing conditions [even considering the sensitivity (see Table 3)]. However, the values of CD at 24.5 °C are very large (see Table 3) for larger drops (50 and 100 μL). Sudden increases in CD are also observed for all drop volumes (except a 5 μL drop) at −5 °C in Table 3, compared to the respective data at 24.5 and −1 °C. A reduced drag coefficient (Table 3) and a higher adhesion together result in a higher critical air velocity (Figure 7a) under icing conditions. The difference in critical air velocity is negligible among all icing condition data as the change in drag coefficient and contact angle hysteresis together with drop base length is similar in each case.

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OVERALL IMPACT OF THESE FINDINGS The wettability of a surface changes under icing conditions because of changes in contact angle and contact angle hysteresis, especially for SHS. As a result, the adhesion for a given drop can increase because of an increase in contact angle hysteresis and drop base length. Therefore, the drop shedding F


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process is hindered under icing conditions on surfaces. However, one has to keep in mind that drops on Teflon are less affected because of icing conditions. This study shows icing for larger drop volumes (>10 μL) on all three surfaces when the temperature is equal to or lower than −8 °C. The critical air velocity is almost the same on both hydrophobic and superhydrophobic surfaces for larger drops [volume of >25 μL (see Figure 2)] under icing conditions. Fabrication of hydrophobic surfaces is easier than that of SHS, as well. Therefore, the hydrophobic surfaces could be an option for drop shedding under icing conditions where is the no heating provided5 to the surfaces.


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CONCLUSIONS The experiments show that the drop base length and contact angle hysteresis of a given drop increase and θs decreases under icing conditions compared to their values at room temperature. A larger drop base length, a lower θs, and higher contact angle hysteresis together signify that the adhesion increases for a given drop volume. The drop is flattened on the surface. The drag coefficient can decrease under icing conditions. In general, a lower drag coefficient and higher adhesion together lead to a higher critical air velocity for a given drop volume under icing conditions. However, the increase in critical air velocity is different for drops on surfaces with different wettabilities. The drops on SHS and on PMMA (in this case, larger drop volumes) show that critical air velocity increases significantly under icing conditions, whereas for Teflon, the critical air velocity remains practically unaffected under icing conditions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b02131. Postprocessing and analysis and comparison between theoretical and experimental drop base lengths (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research was supported by NSERC, CRIAQ, PWC, and Bombardier Canada. The research work of A.C. was supported by the German Scientific Foundation (DFG) in the framework of the SFB-TRR 75 collaborative research center. We thank Mr. Thomas Bauer for the icing wind tunnel design.

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REFERENCES

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Shedding of Water Drops from a Surface under Icing Conditions

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