Analysis of Wetting Characteristics on Microstructured Hydrophobic Surfaces for the Passive Containment Cooling System

As the heat transfer surface in the passive containment cooling system, the anticorrosion coating (AC) of steel containment vessel (CV)mustmeet the requirements on heat transfer performance. One of thewall surface ACswith simple structure, highmechanical strength, and well hydrophobic characteristics, which is conductive to form dropwise condensation, is significant for the heat removal of the CV. In this paper, the grooved structures on silicon wafers by lithographic methods are systematically prepared to investigate the effects of microstructures on the hydrophobic property of the surfaces. The results show that the hydrophobicity is dramatically improved in comparison with the conventional Wenzel and Cassie-Baxter model. In addition, the experimental results are successfully explained by the interface state effect. As a consequence, it is indicated that favorable hydrophobicity can be obtained even if the surface is with lower roughness and without any chemical modifications, which provides feasible solutions for improving the heat transfer performance of CV.


Introduction
The advanced pressurized water reactor [1] adopts a passive containment cooling system [2,3] (PCCS) relying on heat removal by condensation to maintain the steel containment vessel (CV) within the design limits of pressure and temperature, which effectively prevents the leakage of radioactive materials under accident situations.As the condensation surface in PCCS, the safety-related anticorrosion coating (AC) of CV must meet the requirements of heat removal capacity.The thermal conductivity of current applicative coating on CV is about 1.0 Wm −1 K −1 ; besides the thickness of the coating is in the range of 50-150 m, which results in high thermal resistance.Meanwhile, the contact angle of the coating is lower than 30 ∘ ; such high wettability results in filmwise condensation [4].Compared with filmwise condensation, heat transfer coefficients for dropwise condensation of steam are greater with one to two orders of magnitude [5][6][7][8][9], which can effectively enhance the ability of heat transfer on CV, while dropwise condensation takes place on a hydrophobic surface where the contact angle is usually larger than 90 degrees, whose heat transfer rate increased with the increase in the contact angle [10].Therefore, for further improving the running safety of the existing or future highpower nuclear power plant, the lower thermal resistance, simple structure, excellent physical and chemical stability, and optimized hydrophobic surface are highly in demand for the safety margin of CV.
Si is one of the particularly promising coating materials because of low cost [11], higher thermal conductivity [12], favorable chemical stability [13], and mature processing technologies.Therefore, as the coating material, Si has great advantages in the heat transfer requirements of CV.In the present work, the grooved structures in different sizes on silicon wafers by lithographic methods are systematically prepared to investigate the effects of microstructures on the hydrophobic property of the surfaces.The results demonstrate that outstanding hydrophobic performance can be

Materials and Methods
2.1.Fabrication.Si wafers (1 × 1 cm 2 ) were grooved to form a groove pattern structure of width "" and spacing "." Substrates with different combinations ( and ) were used in the present study.Hereinafter, these patterns were referred to as "width/spacing." Patterns were etched into silicon wafers using standard photolithography techniques.The samples were spin coated with a positive photoresist (Shipley S1813) at 4000 r/min for 60 s (1.5 m thick coating).After a preexposure bake at 115 ∘ C for 3 min, the wafers were exposed in the ultraviolet (Karl Suss) for 18 s with the desired pattern.After a postexposure bake at 110 ∘ C for 10 min, the samples were developed in Microposit 351 for 30 s and rinsed with deionized water.The silicon was then dry-etched using ICP (Oxford Plasmalab System100 ICP180) with O 2 and SF 6 at an etch rate of 110 m/h.Meanwhile, the etching heights were controlled by managing the etching time.

Characterization Methods.
The microstructure was observed and evaluated on a scanning electron microscope (SEM, FEI nova 430) and a profilometer (Bruker DektakXT).The surface contact angles (CAs) on the fabricated substrates were determined using a CA measurement system (Kruss DSA 100).Using a deionized water droplet of about 5 L at room temperature, an average of static CAs measured at three different locations were used for presentation.

Results and Discussion
Figure 1 shows the SEM images of the grooved surface prepared using a photomask (width/spacing ratio = 1 : 1 and with approximate heights of 5 m).It is obvious that the surface is uniform and the structural integrity is not violated.The measurement results show that the dimensions of width/spacing are 40/40, 60/60, 90/90, 120/120, and 150/150 m, respectively.
The wetting behavior of solid surfaces by a liquid is usually expressed by the CA [14].The CA concept is of fundamental importance in all solid-liquid-fluid interfacial phenomena [15,16].In this work, when the width/space is 40/40 m, the CA is 132 ∘ , and the CAs decrease as the dimension of width/spacing increases.When the dimension of width/spacing reaches 150/150 m, the CA decreases to 122 ∘ , and the values of CAs are summarized in Table 1.
At present, two wetting models are successively proposed to describe the relationship between surface roughness and the apparent contact angle of a solid surface: Wenzel [17,18] and Cassie-Baxter [19] models.The basic assumption in the Wenzel model (a noncomposite state) is that liquids completely fill the grooves of rough surfaces.And the Wenzel model can be expressed by the following equation [17]: where   is the apparent contact angle in the Wenzel state,   is Young's contact angle [20], and  is the surface roughness factor, the ratio between the actual surface area and the apparent surface area of a rough surface.The Wenzel equation predicts that surface roughness enhances both hydrophilicity and hydrophobicity, which is dependent on the nature of the corresponding surface.If the surface roughness factor is larger than 1, a hydrophilic surface becomes more hydrophilicity with the increase in surface roughness [21].
Conversely, a hydrophobic surface will present increased hydrophobicity.
Cassie-Baxter model [19] is proposed to clarify the relationship between chemical heterogeneities and the contact angle.The basic assumption in the Cassie-Baxter model (a composite state) is that liquids only contact the top of solid asperities, and air pockets are presumed to be trapped underneath the liquid.The Cassie-Baxter model can be expressed by the following equation [19]: where   is the fraction of the liquid base in contact with the solid surface,   < 1, and (1 −   ) is the fraction of the liquid base in contact with air pockets.  is apparent contact angles in the Cassie-Baxter model.In this case,   and  V are Young's contact angles corresponding to the two components, that is, solid and air.Air is not able to be wetted by water; therefore the water/air CA equals 180 ∘ ; what is more the cosine of the CA is −1.The Cassie-Baxter equation can be derived as In our case, the surface roughness factor and the fraction are defined as  = ( +  + ℎ)/( + ) and   = /( + ), respectively, due to the parallel grooved surface.In addition,   is 69.5 ∘ achieved by the measurement of intrinsic Si without grooved surface; then the apparent contact angles   in the Wenzel model and   in the Cassie-Baxter model can be obtained from (1) and (3); the calculated results are summarized in Table 1.
As can be seen from Table 1, according to the Wenzel model, the apparent CAs   (calculated value) are lower than those of   .On the other hand, the apparent CAs   , calculated by Cassie-Baxter model, are larger than those of   .In addition, based on the Cassie-Baxter model, even if  and  are increased from 40 m to 150 m,   is constant of 0.5 due to the constant width/spacing ratio, and its corresponding Herein, considering that the noncomposite contact tends to form hydrophilic surface, whereas composite contact tends to arrive at hydrophobic surface, it is reasonable to assume that the wetting behavior of grooved surface belongs to composite state.In order to verify and validate the above analysis, two series of grooved surface with etching height ℎ of 15 m and 50 m are prepared on Si wafers by controlling the etching time.As can be seen from Table 2, the measurement results show that both the CAs of  /ℎ15 and  /ℎ50 decrease from ∼134 ∘ to ∼120 ∘ as the dimension of width/spacing increases from 40 m to 150 m, which is consistent with the measurement results of  /ℎ5 .It is indicated that the CAs are independent of the groove height and the droplet tends to sit on the grooved surfaces, whose behavior is consistent with that described in the Cassie-Baxter model.
Based on the above experimental results, it is demonstrated that the system is attributed to the composite state; that is, the water droplet rests on the surface without penetration.However, it is important to note that, when compared  with   calculated from Cassie-Baxter equation (dashed line in Figure 2), the measurement value   still exhibits significantly distinct features; that is, conventional Cassie-Baxter model underestimates the CAs 15-25 ∘ .It is suggested that the composite state is different from the conventional Cassie-Baxter model.By further analysis, such obvious distinction is originated from the formation of interface states effect in grooved surface, which will be discussed below.As shown in Figure 3(a), at the interface of liquid and solid, an air bubble is found besides the conventional air pocket.Furthermore, different etching height ℎ of the sample also has the extra air bubble, which implies that such phenomenon is repeatable.As a result, a semiquantitative reinforced Cassie-Baxter model via the formation of air bubbles is proposed to explain the dramatically improved hydrophobic properties.As shown in Figures 3(b) and 3(c), on the basis of Cassie-Baxter model, extra air bubbles are trapped beneath the liquid.In such a case the liquid contact with the solid surface is greatly reduced.Therefore, the corresponding apparent CAs are considerably enhanced.In addition, the contact area reduced by air bubble can be calculated from (3).For instance, for the microstructure of 120/120 m, substituting the measured   and Young's contact angle of Si   into (3), it is easy to calculate that the fraction   equals 0.3, which is lower than the theoretical value 0.5.It is intensely demonstrated that the existence of bubble reduces the contact area between liquid and solid by 40 percent on the basis of conventional Cassie-Baxter model.It is also indicated that excellent hydrophobicity properties can be achieved, even if the surface is without chemical modifications, which provides a feasible solution for improving the heat transfer performance of CV in PCCS.In order to obtain deeper insight into interface states, more work will be carried out by experimental and theoretical study in the future.

Conclusions
The grooved structures on silicon wafers by lithographic methods are systematically fabricated to investigate the effects of microstructures on the hydrophobic property of the surfaces, and the hydrophobic performance of Si surface is optimized by microstructure manufacturing.A strong correlation between the microstructure and hydrophobic characteristics of grooved surface is obtained.The mechanism of hydrophobic enhancement is successfully explained and discussed by the interface state effect.Based on the results of this study, the following conclusions can be made: (1) The hydrophobicity is dramatically enhanced in comparison with the conventional Wenzel or Cassie-Baxter models; specifically the measurement results

Figure 2 :
Figure 2: Effect of groove size ( and ) for constant width/spacing ratio.Dashed line denotes the CAs calculated from Cassie-Baxter model.

Table 1 :
The characteristics of prepared grooved surface: width , spacing , roughness factor , apparent CAs in the Wenzel model   , fraction   , apparent CAs in the Cassie-Baxter model   , and the measurement results of CAs  /ℎ5 (ℎ = 5 m).

Table 2 :
The characteristics of prepared grooved surface: width , spacing , the measurement results of CA with 15 m height  /ℎ15 and 50 m height  /ℎ50 .