Dropwise condensation rate of water breath figures on polymer surfaces having similar surface free energies

Applied Surface Science 259 (2012) 515–523

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Dropwise condensation rate of water breath figures on polymer surfaces having similar surface free energies Ikrime O. Ucar, H. Yildirim Erbil ∗ Gebze Institute of Technology, Department of Chemical Engineering, Cayirova, Gebze 41400, Kocaeli, Turkey

a r t i c l e

i n f o

Article history: Received 15 March 2012 Received in revised form 14 July 2012 Accepted 16 July 2012 Available online 23 July 2012 Keywords: Dropwise condensation Contact angle hysteresis Surface coverage Roughness Polyolefin

a b s t r a c t This study investigates the effect of surface roughness, wettability, water contact angle hysteresis (CAH) and wetting hysteresis (WH) of polymeric substrates to the water drop condensation rate. We used five polyolefin coatings whose surface free energies were in a close range of 30–37 mJ/m2 but having different surface roughness and CAH. The formation of water breath figures was monitored at a temperature just below the dew point. The initial number of the condensed droplets per unit area (N0 ) and droplet surface coverage were determined during the early stage of drop condensation where the droplet coalescence was negligible. It was found that the mean drop diameter of condensed droplets on these polymer surfaces grow according to a power law with exponent 1/3 of time, similar to the previous reports given in the literature. It was determined that surface roughness and corresponding CAH and WH properties of polymers have important effects on the number of nucleation sites and growth rate of the condensed water droplets. N0 values and the surface coverage increased with the increase in surface roughness, CAH and WH of the polymer surfaces. The total condensed water drop volume also increased with the increase in surface roughness in accordance with the increase of the number of nucleated droplets. © 2012 Elsevier B.V. All rights reserved.

1. Introduction If a condensate does not completely wet a surface, dropwise condensation occurs and many droplets whose diameters ranging from a few nanometers to micrometers occupy the condensing area. Dropwise condensation is desired in most of the heat transfer applications because thermal conductivity greatly increases due to the absence of a continuous film on the condensing surface [1–4]. When we breathe on a hydrophobic surface, a fog of tiny droplets named as “breath figures” forms [5–16]. The number of condensed droplets per unit area and mean droplet sizes vary according to the properties of the solid surface. This indicates the important role of substrate surface free energy, wettability and contact angle hysteresis on the behavior of condensed water droplets [8–11,16–22]. Most of the condenser surfaces are generally made of metals in heat exchangers, and metals usually exhibit filmwise condensation rather than dropwise because of their high surface free energies and require surface modification to shift into dropwise condensation [23–25]. Polymeric or organic coatings were used on metals as “promoters” to reduce their surface free energy and to obtain dropwise condensation in industry [23,26–28].

∗ Corresponding author. Tel.: +90 262 605 2141; fax: +90 262 653 8490. E-mail address: [email protected] (H.Y. Erbil). 0169-4332/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2012.07.076

In general, dropwise condensation consists of a combination of several processes: numerous minute droplets are formed after the vapor impinges on a surface cooled to a temperature below the saturation temperature, releasing the latent heat of condensation and these droplets grow very rapidly due to the continuing direct condensation of vapor onto them. Some of the droplets touch each other and coalesce to form larger drops and droplets shift their positions a little at each coalescence, leaving open areas on the surface where initial droplets can be nucleated again. It is almost impossible and does not make sense to attempt to treat the nucleation and coalescence steps separately [6–13,16]. In most of the published drop condensation studies, flowing water vapor at a specific humidity was directed onto cool surfaces causing rapid condensation [6–10,12,14–16,29,30]. Nevertheless, non flowing vapor experiments, i.e. condensation of water vapor from ambient air was also studied [11,13,21,22]. The early stage of condensation where the droplet coalescence is negligible was the less frequently studied stage of droplet growth [8,9]. The “surface coverage” parameter was used in most of the droplet condensation studies and defined as the ratio of surface area covered by the droplets over the total substrate area in order to quantify the droplet growth by optical microscopy photographs. This quantity varies while drop perimeter grows and other droplets nucleate by time depending on the growth, coalescence and re-nucleation steps [6–16,31]. Surface coverage change by dropwise condensation was investigated on silanized glass [6,7,16],

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various polymer [8,9,11,22], and patterned superhydrophobic model surfaces [12,13,29,30,32–37]. It was reported that the magnitude of surface coverage and the extent of dropwise condensation are dependent on the surface properties of the substrate such as surface tension [19,20,26–28,31], initial contact angle [10,11,16,22], and contact angle hysteresis (CAH) [10,16,17]. Contact angle is the angle formed by a liquid drop at the intersection point of three-phase boundary and it is included between the tangent plane to the surface of the liquid and the tangent plane to the surface of the solid. Equilibrium contact angle,  e , is a quantitative measure of the wetting of a solid by a liquid and it is a manifestation of the thermodynamic equilibrium of the three-phase system [38]. Low values of contact angles indicate a strong liquid–solid interaction and the liquid tends to spread on the solid surface. The increase in surface coverage with the decrease in contact angle and corresponding heat transfer efficiency was reported in some of the articles for a broad range of contact angles [10,11,16,28]. If an ideal surface (chemically homogeneous, rigid, and atomically flat) is present, there would be a unique equilibrium contact angle  e . However, as a consequence of the non-ideal nature of any real surface, the presence of surface roughness, chemical heterogeneity and surface restructuring can cause to measure different contact angle values on a surface. When a liquid drop is formed on a substrate surface by injecting the liquid from a needle connected to a syringe, it is allowed to advance on the fresh solid surface and the measured angle is called as “advancing contact angle”,  a . The other contact angle type is the “receding contact angle”,  r and it can be measured when a previously formed sessile drop on the substrate surface is contracted by applying a suction of the drop liquid through a needle. Contact angle hysteresis, CAH on a surface is the difference between advancing,  a and receding,  r contact angles (CAH =  a −  r ) and is a measure of the surface roughness and chemical heterogeneity of the surface [38–40]. The wetting hysteresis (WH) is defined as the adhesion energy to cause contact angle hysteresis [WH =  LV (cos  r − cos  a )]. CAH was regarded as an important factor to determine the efficiency of the drop condensation process [2,6,10,16,17,19,20,29]. In these reports, authors generally investigated CAH effect on the droplet coalescence [2,6,10,29] and on heat transfer efficiency of a surface and found that a decrease of CAH results in high heat transfer at the last stage of condensation because large droplets easily flows on surfaces having low CAH [16,17,19,20]. CAH effect on the growth of the condensation pattern was reported by Zhao and Beysens and it was found that the contact-line-pinning on the chemically heterogeneous surface prevented the full coalescence of droplets, and the saturated surface coverage is significantly increased depending on the hysteresis strength [10]. Beysens and coworkers showed that ellipsoidal and not hemispherical droplets form after coalescence by the CAH effect and the surface left free by coalescence may not be large enough to compensate for the growth and preserve scaling and thus surface coverage increases continuously; interconnected droplet structures form, leading to pseudo-wetting films [2,6,29]. Neumann and coworkers presented detailed experimental results on CAH effects on drop condensation and concluded that heat transfer strongly depends on CAH during the dropwise condensation and increases with decreasing CAH [17]. The decrease on the mobility of the condensed droplets and the efficiency on the condensation heat transfer with the increase in CAH were reported by Ma and coworkers [19,20]. However, none of these articles investigated CAH effect on the formation of breath figures in the early stage of drop condensation. On the other hand, the variation of CAH on patterned model surfaces depends on the size and separation distance between the pillars [32–37,41,42]. Wier and McCarty showed that water droplets nucleated and grew both on top of and between the pillars on ultrahydrophobic surfaces

and when condensation progressed, water between the pillars was forced upward to the surface. Cooling this sample below the dew point resulted in a decrease in  r down to 0◦ and an increase in CAH. Condensed droplets pinned at the contact lines and water drop mobility reduced on the patterned surfaces [32]. In this study, we monitored the formation of the water breath figures for the early stage of drop condensation where the droplet coalescence is negligible in ambient conditions on horizontal polyolefin surfaces whose surface temperatures were just below the dew point. Our aim is to investigate the effect of surface roughness and corresponding CAH and WH on the surface coverage and the rate of slow dropwise condensation of water vapor from ambient air when surface free energies of the surfaces are in a close range. We especially preferred to study the drop condensation in this stage in order to achieve better discrimination of the surface roughness effects. We used five different polyolefin surfaces having similar surface free energies in a range of 30–37 mJ/m2 having different surface roughness. Initially, it was found that the mean drop diameter of condensed droplets on these polymer surfaces grow according a power law with exponent 1/3 of time as reported previously in the literature where the droplet coalescence is negligible. It was also determined that surface roughness, initial contact angle, CAH and WH effects are important on both the nucleation and drop condensation rates. The results are discussed throughout the text. 2. Experimental 2.1. Materials Commercial polypropylene (PP) was purchased from PETKIM, Turkey (PETKIM MH 418); ethylene–vinyl acetate copolymer containing 12% vinyl acetate content by weight (EVA) was provided by Dupont (ELVAX 660); high density polyethylene (HDPE) was provided from Basell Inc. (HOSTALEN-GM8255), polypropylene–polyethylene copolymer elastomer containing 12% polyethylene content by weight (PPPE) was purchased from Dow Chemical Co. (VERSIFY 2300) and low density polyethylene (LDPE) was supplied from PETKIM, Turkey (F5-21T). These polymers were used as received to prepare polymer solutions in technical grade xylene solvent (TEKKIM, Turkey). 76 mm × 26 mm standard glass slides (ISOLAB, Turkey) were coated with the above polymers by dip coating technique [43]. Two-component adhesive polyepoxide layer (404 Chemicals, Turkey) was applied as the primer coating onto glass slides to compensate weak adherence of polyolefins. Spectroscopic grade water, methylene iodide, ␣-bromo naphthalene, ethylene glycol and formamide liquids (all purchased from Merck) were used to form droplets where contact angles were measured to calculate solid surface free energy. 2.2. Sample preparation 76 mm × 26 mm standard glass slides were initially cleaned in chromic acid, rinsed with distilled and Milli-Q® water, and dried in a vacuum oven. PP, HDPE, PPPE, LDPE and EVA polymers were dissolved in xylene between 60 and 130 ◦ C to obtain solutions from 20 to 40 mg/ml (w/v). Polyepoxide coated glass slides were prepared from its chloroform solution and were dip-coated in these polymer solutions at specific temperatures and dipping rates by using a mechanical dipper. Specific dipping solution temperatures were 102, 115, 100, 130 and 105 ◦ C for PP, HDPE, PPPE, LDPE and EVA samples. Specific glass slide dipping rates were 77, 57, 360, 320 and 612 mm/min for PP, HDPE, PPPE, LDPE and EVA samples. Chemically heterogeneous surfaces having varying surface roughness were formed from copolymers by phase segregation during this controlled dip coating and solvent evaporation process [43–46].

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Polymer-coated glass slides were dried in a vacuum oven overnight and kept in a desiccator until further experimentation. The thicknesses of PP and EVA coatings were 0.5–1.0 ␮m; it was around 1.5–2.0 ␮m for PPPE; 3.0 ␮m for HDPE and 2.0 ␮m for LDPE. We measured the same surface temperatures on the surfaces during the drop condensation experiments, so we assumed that thickness variations of 0.5–3.0 ␮m did not make a significant change in the drop growth rates. 2.3. 2D images by optical microscopy and 3D images by surface profilometer 2D surface topography of all the coated samples was investigated by using a NIKON ECLIPSE LV 100D Optical Microscope with 500× magnification. 3D images of the samples were taken by using a surface profilometer attached on the same optical microscope with a Clemex Camera, using Clemex Professional Edition, Image Analyzing System with 3D Modeling Module and Motorized Stage with 500× magnification. Root mean square roughness (Rrms ) values were determined by using the data of surface profilometer. 2.4. Static contact angle measurements Contact angle measurements were carried out with a KSV CAM 200 model goniometer (KSV, Finland) equipped with a digital camera connected to a PC. 5 ␮l ultra pure grade water droplets were formed on the samples using a motorized dispenser and equilibrium contact angles ( e ) were determined immediately by using video frame grabbing method in order to prevent the drop evaporation errors [47]. Advancing contact angles ( a ) were measured when the droplet volume was increased on the fresh surface by adding 5 ␮l water on a preformed 3 ␮l droplet. Receding contact angles ( r ) were measured by slowly sucking 4–5 ␮l water from the preformed 8 ␮l droplet. Drop evaporation experiments were also applied to obtain  r and compare it with the results of drop suction method through a needle in order to obtain reliable  r values [38,40,48]. Measurements were taken from at least 3 different locations on each sample and the reported values were the averages of at least 6 measurements. All the average contact angle results were within ±1◦ to standard error. 2.5. Surface free energy calculation van Oss–Good–Chaudhury method (acid–base approach) [39,49] was used to determine surface free energy values of the polymeric surfaces. Equilibrium contact angles of water, ethylene glycol, formamide, methylene iodide and ␣-bromo naphthalene droplets were measured on all polyolefin surfaces for this purpose. This method comprises dispersive, polar and non-asymmetric hydrogen-bonding interactions.



L (1 + cos e ) = 2(

SLW LLW +



S+ L− +



S− L+ )

(1)

Methylene iodide and ␣-bromo naphthalene contact angle results,  e were used to calculate SLW , and water–ethylene glycol; water-formamide pairs were used to calculate S+ , S− values [39,49]. 2.6. Water drop condensation experiments Substrates rapidly cooled from the room temperature down to 292 K which is just below the dew point temperature of the medium. Dew point temperature was calculated by using thermodynamical tables depending on the relative humidity of the

517

Table 1 Root mean square roughness (Rrms ),  a ,  e ,  r , contact angle hysteresis (CAH) and wetting hysteresis (WH) results of polyolefin surfaces. Polymer

Rrms

a

e

r

CAH

WH

PP HDPE PPPE LDPE EVA

0.54 0.40 0.38 0.31 0.29

123 112 107 105 95

116 107 105 101 93

78 77 83 89 84

45 35 24 16 11

54.8 43.6 30.2 20.1 14

medium (RH) and room temperature [50]. Clean glass slides dipcoated with PP, HDPE, PPPE, LDPE and EVA polymers located horizontally on a pure electrolytic copper cell having a wall thickness of 1 mm. Cooling water was circulated in the cooling cell at 290 K by using a LAUDA RE 200 model constant-temperature bath. Room temperature was 299.5 K and RH = 63% and surface temperature on the polymer was measured as 292 K by a K type thermocouple placed onto the polymeric substrate during all the experiments. 292 K was approximately just below the dew point temperature at these conditions. Condensation of water vapor from ambient air on the polymer samples was conducted under identical experimental conditions. Images of condensation patterns on polymeric surfaces were taken by using an optical microscope (NIKON ECLIPSE LV 150L) at 200× magnification and a Clemex model camera attached to this optical microscope as seen in Fig. S1 in the Supplementary Data showing the indicative photograph of the laboratory set-up. Periodically taken images of growth of condensed water droplets were then analyzed by using an UTHSCSA Image analysis program and two parameter spherical cap geometry equations for the surface area and volume analysis, Eqs. (5)–(7) [51]. 3. Results and discussion 3.1. Roughness, CAH and surface free energy of polyolefin surfaces Optical microscopy images of polyolefin surfaces at 500× magnification and surface roughness profiles at 500× magnification are given in Fig. 1. Root mean square roughness (Rrms ) values as formulated in Eq. (2) determined by surface profilometer are given in Table 1 and were found to be in the order of PP > HDPE > PPPE > LDPE > EVA.

  n 1 Rrms =  y2 n

i

(2)

i=1

The roughness profile contains (n) ordered, equally spaced points along the trace, and (yi ) is the vertical distance (␮m) from the mean line. As seen from Fig. 1 and Table 1, LDPE and EVA surfaces were flatter than PP and HDPE and the population of the peaks per unit area (␮m2 ) was largest on the PP surface. Semi-crystalline HDPE and LDPE surfaces have a spherulitic texture having borders with average diameters of 30–60 ␮m for HDPE and 50–80 ␮m for LDPE.  e ,  a ,  r , CAH and WH results of water drops on polymeric coatings are also given in Table 1. As seen in this table, the order of Rrms ,  e , CAH and WH results were parallel.  e results of methylene iodide, ␣-bromo naphthalene, formamide and ethylene glycol droplets were given in Table 2. SLW , S+ , S− and Stot values of the polymer samples were calculated by using van Oss–Good method [39,49] using Eq. (1) and also given in Table 2. Surface free energy values of all the polyolefin substrates were found to be in a narrow range of 30–37 mJ/m2 whereas, CAH varied considerably from 11◦ up to 45◦ . In general, the magnitude of CAH and WH depends on two factors: the variation in surface roughness and chemical

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Fig. 1. Optical microscope images and surface roughness profiles at 500× magnification for PP, HDPE, PPPE, LDPE and EVA surfaces. The scales are in ␮m in the right images.

heterogeneity [38]. If we exclude the EVA surface which has a partially polar character due to the acetate group, then the surface free energy of all the other polyolefin samples varied in a very narrow range of 30–34 mJ/m2 showing that the chemical heterogeneity

effect was low for the selected polyolefin surfaces. On the other hand, CAH varied nearly four-fold because of the increase of surface roughness due to the phase separation which occurred during dipcoating of these polymers onto glass slides [43–46]. This result is

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519

Fig. 2. Optical microscope images of condensed water droplets on PP, HDPE, PPPE, LDPE and EVA surfaces at 200× magnification.

4.0

consistent with our main objective of testing the independent effect of roughness and CAH on dropwise condensation when surface free energies are close to each other.

3.5 3.0

3.2. Growth of the droplets in the early stage of condensation

Ln D

In this part of the study, we examined the growth of the condensed water droplets on polyolefin surfaces in the early stage of condensation where drop coalescence is negligible. Black and white plan view images of condensed water droplets on these surfaces for 1, 2, 4, 6, 8 and 12 min were given in Fig. 2. We calculated plan radius (R) of the condensed droplets from these images by using UTHSCSA Image analysis program [51]. As seen from Fig. 2, the growth behavior of the condensed droplets was different depending on the substrate surface properties. Briscoe and Galvin [8,9] reported that droplets can grow according to two fundamentally different growth laws: at the beginning of the condensation, droplets behave as isolated droplets and coalescence has a negligible influence on the average rate of droplet growth and growth of the droplets was limited by the rate at which latent heat could be dissipated. On the other hand, in the second regime, coalescence has its maximum influence on the droplet growth and latent heat was easily dissipated among the droplets and the system evolved according to a constant flux of condensing

2.5 2.0 1.5

HDPE

1.0

PPPE

0.5

LDPE

0.0 3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

Ln t Fig. 3. Ln D (mean droplet diameter) – Ln t (time) plot for HDPE, PPPE and LDPE surfaces.

vapor. They showed that the mean diameter of the droplets scaled as [D ∝ time1/3 ] during the first regime and scaled as [D ∝ time] for the second regime. We plotted log–log plots of our droplet mean diameter data with time for HDPE, PPPE and LDPE surfaces in Fig. 3.

Table 2 Equilibrium contact angle results of test liquid drops and the calculated surface free energy component values according to van Oss–Good method. Polymer

MeI2 

Br-Naph 

Form 

EG 

sLW

s+

PP HDPE PPPE LDPE EVA

59 54 56 49 48

45 41 52 27 30

76 83 88 82 73

74 68 77 74 67

31.1 33.5 30.2 31.3 37.4

0.03 0.06 0 0 0

s− 0 0 0.07 0.44 1.38

 tot 31.1 33.5 30.2 31.3 37.4

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6000

PP

PP

R² = 0.87815

40

HDPE PPPE

Surface Coverage %

No (mm-2)

5000 4000 PPPE

3000 2000

HDPE

EVA

1000

LDPE

0 0.2

0.3

0.4

0.5

0.6

Rrms Fig. 4. Change of number of the initial nucleation per unit area, N0 (mm change in Rrms roughness on polymer surfaces.

−2

LDPE

30

EVA

20

10

0

0

200

400

600

800

Time (sec.)

) with the

Fig. 5. Change of surface coverage % with the increase of time on polymer surfaces.

The slope of the lines were 0.29 for HDPE, 0.34 for PPPE, 0.31 for LDPE (and also 0.38 for EVA) indicating that all the droplet growth on the surfaces took place in the first regime where drop coalescence is not important. These findings are also in accordance with the previous reports [2,6,7,29]. 3.3. Relation of number of the condensed droplets and surface coverage with the substrate surface properties N is the number of the condensed droplets per unit area (mm−2 ) at any time; and N0 is the initial number of the condensed droplets per unit area as determined from the optical black and white images obtained at the first minute in our experimental conditions. Surface coverage (%) was calculated by using UTHSCSA Image analysis program [51] to give the ratio of black area to the total area. Values of N0 , N and surface coverage on each polymer surface are given in Table S1 in the Supplementary Data. We plotted N0 values against Rrms roughness values of the polyolefin surfaces in Fig. 4 and found that N0 values increased linearly with the increase in Rrms roughness of the polyolefin surfaces with a regression coefficient of 0.88. This shows that rough surfaces create more nucleation sites during drop condensation similar to another report given in the literature [23]. The nucleation rate of condensed droplets was also dependent on CAH values: As seen in Fig. 2, the highest value of N was found on the roughest PP surface having the largest CAH value, however only a few large drops and tiny droplets can form on flat EVA and LDPE surfaces having smaller CAH values under the same experimental conditions. This behavior is attributed to the high number of nucleation sites that arises from the highest surface roughness on the PP surface and few nucleation sites on the smoother LDPE and EVA surfaces. In addition, the coalescence tendency of the droplets on the PP surface with the neighboring droplets was low because they could not overcome the energy barriers on the PP surface having high peak population per unit area resulting in a strong pinning effect. Dmean , is the diameter of liquid/solid interface and when Dmean , was plotted versus time, the pinning of the drop diameter was seen especially on the rough surfaces such as PP. Condensed droplets moves with a slip-stick motion on the PP surface. This kind of motion is indicative of the presence of an energy barrier at the drop perimeter. Slip-stick motion was partially seen on HDPE and PPPE polymers. On the other hand, surface coverage results of HDPE and PPPE were close to each other although the size of the droplets on HDPE was larger than that of on PPPE. The value of N on PPPE surface was larger than that of on HDPE and this effect counterbalance the surface coverage % (Table S1). Since Rrms roughness values of HDPE and PPPE were very close to each other (Table 1), it is possible that PPPE

substrate having both PP and PE groups on the surface has slightly higher chemical heterogeneity and produces more nucleation sites for dropwise condensation. It was concluded that the presence of CH3 group on both PP and PPPE cause the decrease in the condensed droplet size and increase in the value of N. Rrms roughness values were found to be intermediate for HDPE and PPPE surfaces, and few drop coalescing was seen on these surfaces. On the contrary, LDPE and EVA had amorphous surfaces giving low CAH due to their low Rrms roughness values and behavior of dropwise condensation on these surfaces was different than on PP, HDPE and PPPE surfaces. The value of N was very low on LDPE and EVA surfaces due to their smooth surface and causing droplet growth to large sizes without coalescence. The increase of surface coverage % with time is given in Fig. 5. As seen in this figure, the surface coverage values were between 0.08 and 0.38 at 12 min, which was far less than the equilibrium coverage value of 0.50–0.55 reported in the literature [7–10]. In general, it was found that the surface coverage increased with the increase of time for all the samples, however the growth behavior and rates of drop condensation were different as seen in Figs. 2 and 5. The monitoring of the droplet growth in this early condensation region resulted in better discrimination of the surface roughness effects onto the drop nucleation and condensation rates. It was determined that the surface coverage was maximum on the roughest PP coating and minimum on the smoother LDPE and EVA surfaces as seen in Fig. 5. The order of the magnitude of surface coverage was PP > HDPE > PPPE > LDPE > EVA for most of the drop condensation steps, which was parallel to the order of Rrms ,  e , CAH and WH values as given in Table 1. Briscoe and Galvin reported dropwise condensation of water on a flat polyethylene (PE) surface having a CAH of 17◦ [9]. Their results were in good agreement with the semi-empirical equation given below which was proposed by Vincent [52] and derived by Briscoe and Galvin [8] which describes the evolution dependence of the fraction of droplet coverage over number of droplets per unit of substrate area which is independent of the nature of the intrinsic growth. ˛e − ˛ N = ˛e − ˛o N0

(3)

In this equation, ˛ is surface coverage at any given time, ˛o is the initial coverage, ˛e is the equilibrium coverage, N is number of the droplets per unit area (mm−2 ) and N0 is the initial number of the droplets per unit area (mm−2 ). We plotted the left-hand side of Eq. (3) as a function of the right-hand side (N/N0 ) in Fig. 6 by using the experimental values of ˛, N and N0 of HDPE, PPPE and EVA polymers from Fig. 2 and taking as ˛e = 0.53 similar to Ref. [9], since

I.O. Ucar, H.Y. Erbil / Applied Surface Science 259 (2012) 515–523

(a) Surface Coverage % (720 sec.)

1.0 HDPE PPPE EVA

(α α e -α)/(αe-αο)

0.8

LDPE

0.6

0.4

40

521

R² = 0.92050

PP

30

PPPE HDPE

20 EVA

LDPE

10 0

90

95

100

105

115

120

θe

0.2

0.2

0.4

0.6

0.8

1.0

(N/No) Fig. 6. (˛e − ˛)/(˛e − ˛o ) versus (N/N0 ) plot for HDPE, PPPE, LDPE and EVA surfaces.

˛e was generally obtained between 0.50 and 0.55 for growth of water breath figures on horizontal surfaces [7–10]. In this plot, Eq. (3) is represented by the diagonal straight line. (We did not plot the data of PP in Fig. 6 because of the very high initial nucleation on its rough surface and not very consistent N figures obtained.) As seen in Fig. 6, only HDPE results fit Eq. (3) well. This finding is interesting because, Eq. (3) was derived only for surfaces having no CAH, however PE substrate having a CAH value of 17◦ which was used in Briscoe and Gavin paper [9] also showed very good fit with Eq. (3) indicating that semi-empirical Eq. (3) is not dependent on CAH. On the other hand, PPPE results also showed the same linear trend as HDPE but were parallel to the theoretical diagonal line with a shift in N/N0 value of 0.2 to the left. Both N0 and N values were approximately twice as on PPPE than on HDPE, but the rate of decrease of N/N0 was more rapid on PPPE than that of on HDPE due to higher drop coalescence on PPPE surface. It seems that drop condensation can be successfully described by Eq. (3) when N0 was around 1000–2000 mm−2 . Meanwhile, EVA and LDPE surfaces had very low N0 values which were around 230–250 mm−2 , and N/N0 ratio decreased very slowly and their data points were located near N/N0 ∼ = 1 in Fig. 6. In summary, the results in Fig. 6 indicate that Eq. (3) can be applied to surfaces having moderate roughness when their surface temperature is just below the dew point and drop condensation takes place in atmospherical conditions, when the initial nucleation was around 1000–2000 mm−2 . On the other hand, it was also determined that, N values did not change generally by time except on the PPPE surface (Table S1) and this effect is attributed to the slightly higher drop coalescing behavior on the PPPE surface. We plotted the surface coverage results of 12 mins with the change of  e in Fig. 7(a) and a linear relationship was obtained with good regression coefficient. We also found that surface coverage increases linearly with the increase of CAH as seen in Fig. 7(b) with a good regression coefficient. This result is consistent with the results previously reported [10]. The highest surface coverage value was found on the roughest PP surface having the largest CAH value. A similar trend was obtained between surface coverage and WH which was given in Fig. S2 in the Supplementary Data. Fig. 7(c) shows the plot between surface coverage and the change of root mean square (Rrms ) roughness values of the polyolefin surfaces with a good regression coefficient. We also determined that this good

40

R² = 0.92459

PP

30

PPPE HDPE

20 EVA

10

LDPE

0

0

10

20

30

40

50

CAH

(c) Surface Coverage % (720 sec.)

0.0

Surface Coverage % (720 sec.)

(b) 0.0

110

40

R² = 0.97071

PP

30

HDPE PPPE

20

10

LDPE EVA

0 0.2

0.3

0.4

0.5

0.6

Rrms Fig. 7. Dependence of surface coverage % obtained at 720 s. to the change in (a) water contact angle, (b) CAH and (c) Rrms roughness on polymer surfaces.

linearity between surface coverage ratio and Rrms roughness values of the polyolefin surfaces in Fig. 7(c), not only exists at 720 s but also present at all of the stages of the condensation process which were analyzed with one minute intervals and the regression coefficients change between 0.93 and 0.99. However, when we plot the change of surface coverage with the change of surface free energy values of all the polymers, only a slight inverse dependence was found as given in Fig. S3 in the Supplementary Data indicating that surface free energy effect is not important on drop condensation rate. It is clear that surface roughness on polyolefin surfaces is an important surface parameter to affect the drop nucleation and growth. Since CAH and WH are mainly dependent on the increase in surface roughness for the chemically

I.O. Ucar, H.Y. Erbil / Applied Surface Science 259 (2012) 515–523

homogeneous or slightly heterogeneous surfaces, a good linear relationship was also obtained for these parameters. There are some reports on CAH effects on dropwise condensation in the literature where the authors investigated the effect of drop behavior generally in the drop coalescence stage [2,6,10,29] and also in the last stages of condensation [16,17,19,20]. They mostly determined that heat transfer increases with the decrease of CAH because large droplets easily flows on surfaces having low CAH [16,17,19,20]. Our drop condensation conditions were different than the conditions reported in these articles because we did not investigate the drop coalescence and last stage of condensation where the droplets fall of from the inclined surfaces but we only searched the surface roughness and corresponding CAH effect on the formation of breath figures in the early stage of drop condensation on horizontal surfaces without aiming the heat transfer efficiencies. 3.4. Total surface area and total volume increase of droplets

(4)

For the present study, rb values were calculated from Eq. (4) using  e values taken from Table 1 (we assumed that  e was constant throughout the drop condensation). Surface area of the liquid–solid interface, ALS , and surface area of the liquid–air interface, ALV , for a sessile drop are given by using the two parameter spherical cap geometry, as, ALS = rb2 ALV =

(5)

2rb2

1 + cos 

(6)

The volume of the drop is given as, V=

rb3 (2 − 3 cos  + cos3 ) 3 sin3 

PP HDPE

4.0 E-13

PPPE LDPE EVA

3.0 E-13 2.0 E-13 1.0 E-13 0.0 E+00

0

200

400

600

800

Time (sec.) Fig. 8. Change of total volume (m3 ) of all the condensing droplets on sample surfaces with time during droplet growth.

Since surface coverage % gives only the plan area ratio of the liquid/solid interface, we also attempted to test the dependence of the total liquid/air interfacial area and volume of the condensing droplets to the solid surface properties. For this purpose, we calculated the contact area of liquid/solid interface (ALS ) and liquid/air interfaces (ALV ) and volume (V) of every individual droplet by using two-parameter spherical cap geometry equations used in drop evaporation studies [53,54]. A spherical cap geometry of a drop shape can be characterized by using four different parameters which are the drop height (h), the contact radius (rb = Dmean /2), the radius of the sphere forming the spherical cap (R), and the contact angle (). The relationships between the two different radii and the contact angle are given as, rb = R sin 

5.0 E-13

V(m 3)

522

(7)

UTHSCSA Image analysis program gives the drop areas in square pixel dimensions and we then converted these pixel results into real dimensions in meter units by applying dimensional calibration. Total surface area and total volume of the droplets were obtained by summing the area and volume respectively of each of the droplets present in the image taken at any given time. Since we did not have any geometric description of the surface roughness, we could not take into account of the roughness influence for the calculation of surface area of liquid–solid interface and droplet volume. The increase of total V (m3 ) by time is plotted in Fig. 8. Similar to surface coverage results, the same order of PP > HDPE > PPPE > LDPE > EVA was obtained for the total volume condensation rates. The increase of ALS and ALV areas (m2 ) with time are plotted and given in Figs. S4 and S5 in the Supplementary Data, respectively. However, no good linear relationship was obtained between ALS and ALV and drop condensation and both of these plots were similar to the volume increase which is given in Fig. 8. According to

these results, we can conclude that the rate of total condensed drop volume increased with the increase in surface roughness because of the rough surfaces creates more nucleation sites [23] in drop condensation. 4. Conclusions It was determined that in the early stage of condensation, the surface roughness and contact angle hysteresis have an important effect on nucleation and condensation rate of water droplets on polyolefin surfaces at a temperature just below the dew point when the drop condensation takes place in atmospheric conditions where the droplet coalescence is negligible. Initially, it was found that mean drop diameter of condensed droplets on these polymer surfaces grow according a power law with exponent 1/3 of time as previously given in the literature. Secondly, it was determined that the surface coverage increased with the increase in surface roughness and corresponding CAH, WH and initial  e values of the substrates. The rate of increase of surface coverage was maximum for the roughest PP and minimum for smoothest EVA surfaces. The number of the initially nucleated droplets per unit area and the total volume of the condensed water increased with the increase of surface roughness in this early region due to the creation of more nucleation sites for the condensed droplets on the rough surfaces. Besides, Vincent equation was found to be successfully applicable to surfaces having moderate roughness when their surface temperature is just below the dew point. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. apsusc.2012.07.076. References [1] P. Meakin, Reports on Progress in Physics 55 (1992) 157–240. [2] D. Beysens, Atmospheric Research 39 (1995) 215–237. [3] X. Ma, J.W. Rose, D. Xu, J. Lin, B. Wang, Chemical Engineering Journal 78 (2000) 87–93. [4] J.W. Rose, Proceedings of the Instituation of Mechanical Engineers Journal of Power and Energy 216 (2002) 115–128. [5] H. Tanaka, Journal of Heat Transfer-Transactions of the ASME, Series C 97 (1975) 341–346. [6] D. Beysens, C.M. Knobler, Physical Review Letters 57 (1986) 1433–1436. [7] D. Fritter, C.M. Knobler, D.A. Beysens, Physical Review A 43 (1991) 2858–2869. [8] B.J. Briscoe, K.P. Galvin, Physical Review A 43 (1991) 1906–1917. [9] B.J. Briscoe, K.P. Galvin, Colloids and Surfaces 56 (1991) 263–278.

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