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Evaporation of water droplets on soft patterned surfaces Yu-Chen Chuang, Che-Kang Chu, Shih-Yao Lin and Li-Jen Chen* The evaporation process of a sessile drop of water on soft patterned polydimethylsiloxane (PDMS) substrates is investigated in this study. Different softness of a regular pillar-like patterned PDMS substrate can be achieved by controlling the mixing ratio of a PDMS's prepolymer base and a curing agent at 10 : 1, 20 : 1 and 30 : 1. The receding contact angle is smaller for softer pillar-like patterned substrates. Consequently, the evaporation rate is faster on softer pillar-like substrates. A sessile drop on the regular pillar-like PDMS substrates, prepared at the mixing ratio of a base to a curing agent of 10 : 1 and 20 : 1, is observed to start evaporating in the constant contact radius (CCR) mode then switching to the constant contact angle (CCA) mode via stepwise jumping of the contact line, and finally shifting to the mixed mode sequentially. During the evaporation, a wetting transition from the Cassie to the Wenzel state occurs earlier for the softer substrate because softer pillars relatively cannot stand the increasingly high Laplace pressure. For the softest regular pillar-like PDMS substrate prepared at the mixing ratio of the base to the curing agent of 30 : 1 (abbreviated by PDMS-30 : 1 substrate), the pillars collapse irreversibly after the sessile drop exhibits the wetting transition into the Wenzel state. Furthermore, it is interesting to
Received 24th October 2013 Accepted 4th February 2014
find out that the initial stage of evaporation of a sessile drop on the PDMS-30 : 1 substrate in the Cassie state is in the CCR mode followed by the CCA mode with stepwise retreatment of the contact line.
DOI: 10.1039/c3sm52719k
Further evaporation would induce the wetting transition from the Cassie to the Wenzel state (due to the
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collapse of pillars) and resume the CCR mode followed by the CCA mode again sequentially.
1. Introduction Evaporation is a common phenomenon we can see in our daily life. The evaporation of sessile drops plays an important role in various applications, such as microuidics, lab-on-a-chip application, combustion, ink-jet printing, pesticide spraying and so on. In 1977, Picknett and Bexon investigated the evaporation of sessile drops and distinguished three modes of evaporation, that is, constant contact angle mode, constant contact area mode and mixed mode.1 Usually, at the early stage of the drop evaporation process, the contact angle decreases and the contact area remains constant, which is called a constant contact area or constant contact radius (CCR) mode. When the contact angle keeps decreasing down to its receding contact angle, the contact line starts to recede and the constant contact angle (CCA) mode takes over. In other words, the contact radius decreases and the contact angle remains constant. Toward the end of evaporation, both contact radius and contact angle may decrease simultaneously and that is termed the mixed mode. They also worked on the evaporation rate by a mass prole and the theoretical analysis can obtain a reasonable prediction.1
Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan. E-mail: [email protected]
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Bourg` es-Monnier and Shanahan studied the evaporation of water and n-decane on various substrates.2 They classied the evaporation process into four stages, and proposed a model to determine the diffusion coefficient of the vapor in air. The rst stage of evaporation corresponds to a saturated atmosphere and the other three stages correspond to the CCR, CCA and mixed modes.2 McHale and coworkers3–6 have studied the evaporation of sessile drops on different surfaces, including at surfaces with the initial contact angle greater than 90 and less than 90 and also working on patterned surfaces. They found that, for at surfaces, when the initial contact angle is less than 90 , the CCR mode dominates and when the initial contact angle is larger than 90 , the CCA mode dominates. They also suggested that the CCA mode is due to the local saturated vapor created near the contact line.6 In addition, McHale et al. worked on the SU-8 textured superhydrophobic surface.3 They found that the evaporation initially proceeded in the CCR mode and then followed by stepwise retreatment associated with the lattice structure of the substrate. They studied not only the evolution of contact angle and contact radius but also the evaporation rate considering the diffusion model and the spherical geometry for the CCR and CCA modes. It has been pointed out by Kulinich and Farzaneh that the contact angle hysteresis is the main factor affecting drop evaporation.7 The evaporation process of a sessile drop on a high-hysteresis surface follows the CCR mode and in
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contrast, that of a low-hysteresis surface follows the CCA mode. It is also observed that water evaporates faster on the highhysteresis surface.7 Evaporation of sessile drops on rough surfaces can also trigger the wetting transition from the Cassie state to the Wenzel state. McHale3 had observed a few cases that the wetting transition happened abruptly with a sharp step-like decrease in contact angle and a step-like increase in contact radius. Reyssat et al. deposited a water droplet on the hydrophobic surfaces decorated with regular micropillars.8 During evaporation, the drop transferred from the Cassie state to the Wenzel state. They suggested that the reason is due to the deformation of the interface below the drop. When evaporating, the drop curvature decreases and the Laplace pressure increases. The increasing pressure would enforce the deformation of the liquid–vapor interface below the drop and while the liquid–vapor interface touches the ground surface, the wetting transition happens. By this hypothesis, they proposed a simple criterion to determine when the transition would happen. Tsai et al. also studied the evaporation-triggered wetting transition on hydrophobic surfaces and it is observed how the Cassie state transferred into the Wenzel state from the observation of the bottom view.9 They used the surface energy minimization to predict the critical size at wetting transition and got a nice consistency with the experimental results. It is interesting to note that a sessile droplet can deform an elastic surface due to the surface tension and capillary pressure.10–13 As a consequence, the elasticity of the substrate would have a strong effect on contact angle hysteresis, wetting behavior, and evaporation.14–19 It was found that the contact angle hysteresis is larger for the soer surfaces. That is, the advancing and receding contact angles become larger and smaller, respectively, for the soer surfaces. Recently, the evaporation of sessile water drops on so at polydimethylsiloxane (PDMS) surfaces has been examined and found that the total evaporation time is shorter for the soer surfaces.15,16 The biocompatible elastomer PDMS has been widely used in biomedical applications, such as microuidic devices, mock arteries, etc.20–26 In addition, we have demonstrated that the wetting transition from the Cassie state to the Wenzel state occurs on the so pillar-like patterned PDMS surfaces due to the collapse of pillars.14 Consequently, the pillars may collapse during the evaporation, that certainly induces the change of evaporation mode. In this study, the water evaporation on the so pillar-like patterned PDMS surfaces is carefully examined to investigate how the soness of pillars would inuence the evaporation mechanism and the wetting behavior.
2.
Experimental procedure
2.1
Preparation of the patterned substrates
The patterned silicon master was prepared by photolithography and further modied by a self-assembled octadecyltrichlorosilane (Aldrich) monolayer to further minimize its surface energy.27–30 The mixture of polydimethylsiloxane (PDMS, Sylgard 184, Dow corning, USA), a prepolymer base and a curing agent (10 : 1, 20 : 1 or 30 : 1 by mass) was poured onto the patterned
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silicon masters. Aer thermal curing at 70 C for 18 hours, a regular pillar-like PDMS substrate was obtained by peeling off the PDMS mold from the patterned silicon master.14 The microstructure of the regular pillar-like PDMS substrate is illustrated in Fig. 1 with a mm a mm square pillars separated by a distance d mm and the pillar height h mm. The surface topology of this patterned PDMS substrate was examined by using a scanning electronic microscope (SEM, JOEL JSM-5600) and a ¼ 9.9 mm, d ¼ 19.2 mm and h ¼ 16.1 mm. A tensile strength instrument (model LRX, LLOYD Instruments, USA) was used to measure the Young's moduli of the at PDMS substrates prepared at three different mixing ratios of the base to the curing agent (10 : 1, 20 : 1, and 30 : 1 by mass). The Young's moduli for these three substrates range from 3.87 to 0.17 MPa, as listed in Table 1. In addition, the advancing and receding contact angles of water on these at PDMS substrates are determined by the embedded needle method21–23 and reported in Table 1. The PDMS substrate becomes soer by increasing the mixing ratio and the advancing and receding contact angles get larger and smaller, respectively.14,15 For simplicity, the PDMS-10 : 1, PDMS-20 : 1 and PDMS30 : 1 substrates are used hereaer to stand for the regular pillar-like patterned PDMS substrates prepared at the mixing ratio of the base to the curing agent 10 : 1, 20 : 1 and 30 : 1, respectively. When a water drop is deposited on the PDMS-30 : 1 substrate, all the pillars underneath the drop would collapse aer the evaporation. Therefore, the PDMS-30 : 1 substrate was covered by water and aer the evaporation all the pillars would collapse. This patterned substrate of collapsed pillars is abbreviated as the PDMS-collapsed-pillars substrate hereaer.
2.2
Evaporation
We used pipette to place a 6 mL water droplet on the PDMS substrate at an ambient environment and observed the evaporation process of the sessile drop from top view and side view. Water was puried by double distillation and then followed by a PURELAB Maxima Series (ELGA, LabWater) purication system with the resistivity always better than 18.2 MU cm. For all the
Fig. 1 SEM image of the surface structure with a mm a mm square pillars separated by a distance d mm and the pillar height h mm. a ¼ 9.9, d ¼ 19.2 and h ¼ 16.1.
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Table 1 Young's moduli, advancing (qa) and receding (qr) contact angles of water on the flat PDMS substrates prepared at different mixing ratios of the prepolymer base to the curing agent (10 : 1, 20 : 1, and 30 : 1)
Substrate
Young's modulus (MPa)
qa ( )
qr ( )
PDMS 10 : 1 PDMS 20 : 1 PDMS 30 : 1
3.87 0.17 0.56 0.06 0.17 0.02
108 2 112 2 116 1
81 4 56 2 49 8
evaporation experiments, the temperature and relative humidity were in the range of 25 2 C and 53% 2%, respectively. A homemade enhanced video-microscopy system incorporated with a digital image analysis was used to observe the side view of a sessile drop during the evaporation process. The frame rate of a solid state charge coupled device camera (Point Grey, Canada) was set at 1 frame per second to record the evaporation process. The images of side view (i.e., drop prole) were used to extract the information of contact angles and contact radii by the digital image analysis. An optical microscope (Olympus, BXFM) was applied to observe the evolution of water drop evaporation from top view. Each condition was repeated at least three times to ensure the reproducibility. 2.3 Advancing/receding contact angle measurement by using an embedded needle method The homemade enhanced video-microscopy system incorporated with a digital image analysis was also used to perform the advancing and receding contact angle measurements. Initially, we placed the prepared PDMS substrate in the environmental chamber (Rame-hart instrument co.) and a needle was positioned inside the chamber. Then a syringe pump (Orion, Sage, model M362) was turned on to generate a water droplet on the substrate. Aer this drop-forming step, water was again continuously and slowly pumped into (or sucked from) the droplet and simultaneously the evolution of the water droplet was recorded to further measure the advancing (or receding) contact angle via the enhanced video-microscopy system. The experimental details can be found in our previous studies.28–30 The rate of water pumping and suction through the needle to perform the advancing and receding contact angle measurement, respectively, was always kept lower than 0.03 mL min1.
3.
Results and discussion
PDMS substrates with the same patterned structure but different ratios of the base to the curing agent were used to examine the inuences of soness on the evaporation mechanism. In this study, the experiments of evaporation of water sessile drops were performed on four different substrates: PDMS-10 : 1, PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsedpillars. The viewing angle along the side of the square array is dened to be 0 , and the viewing angle along the diagonal of the square array is dened to be 45 , as illustrated in Fig. 2(a). The center of the contact diameter in the very rst frame of an
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evaporation process is dened as the reference point and the contact diameter is separated into two radii: contact radius on the le hand side (rl) and on the right hand side (rr), as illustrated in Fig. 2(b). The coordinates of the reference point is xed throughout the evaporation process that enable us to observe the asymmetric evaporation process. In addition, the contact angles on the le hand side (ql) and on the right hand side (qr) of a drop are also dened in Fig. 2(b). Fig. 3 shows the evolution of contact angle and contact radius during the evaporation process on four different substrates along two viewing angles 0 and 45 . Initially, the drop stands on the top of the pillars, that is, in the Cassie state, and the initial contact angle is around 145 , except the PDMScollapsed-pillars substrate. The evaporation starts with the constant contact radius (CCR) mode: the contact angle decreases, the contact line is pinned and the contact radius remains almost constant. For example, one may see evolution of contact angle and contact radius as a function of time for the PDMS-20 : 1 substrate in the region of CCR mode specied by green long dashed line shown in Fig. 3(a) and (b). Once the receding contact angle is attained, the constant contact angle (CCA) mode takes over. That is, the contact line starts to recede, the contact radius decreases and the contact angle remains almost constant, as one can see the region of CCA mode observed on the PDMS-20 : 1 substrate specied in-between two vertical green long dashed lines shown in Fig. 3(a) and (b). Finally, in the third mode observed on the PDMS-10 : 1, PDMS20 : 1 and PDMS-collapsed-pillars substrates, both contact radius and contact angle decrease, as shown in Fig. 3(a) and (b) again, that is, the mixed mode. We will come back to discuss the evaporation mechanism aer the CCA mode observed on the PDMS-30 : 1 substrate later on. Table 2 lists the advancing/receding contact angle at different viewing angles 0 and 45 obtained from embedded needle measurement and from evaporation. According to the results of embedded needle measurements, the advancing contact angles (qa) for the substrates of three different sonesses are essentially the same around 155 and the receding contact angle (qr) becomes smaller when the substrate is soer. On the other hand, the advancing and receding contact angles for the PDMS substrate with collapsed pillars are as low as 144 and 5 , respectively. The advancing/receding contact angles from the viewing angle 0 are slightly larger than that from the viewing angle 45 due to the asymmetry of the drop shape. It is interesting to compare the receding contact angle determined from embedded needle measurement to that determined from the
Fig. 2 The definition of (a) viewing angle, (b) contact radii, contact angles and reference point.
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The evolution of (a and c) contact angle and of (b and d) contact radius during evaporation from (a and b) the viewing angle of 0 and from (c and d) the viewing angle of 45 . The red (1), green (2), blue (3) and orange (4) lines represent the, respectively, PDMS-10 : 1, PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrates. Two vertical green long dashed lines, shown in (a) and (b), are used to separate the regions of CCR, CCA and mixed modes for the evaporation process of a water droplet on the PDMS-20 : 1 substrate. Note that the reference point (defined by Fig. 2(b)) is determined in the very first frame (i.e. the very beginning) of an evaporation process and fixed throughout the evaporation process. For certain droplets, the contact line is pinned at one side and only the other side shrinks and moves inwards. That is, the relative contact radius may decrease even become negative, as curve 2 (PDMS-20 : 1) shown in (d). Fig. 3
Table 2
Advancing and receding contact angles of water on the patterned PDMS substrates By embedded needle measurement qr
qa
By evaporation qr,evap
qr,evap,maxi
qr,evap,mini
Viewing angle 0 PDMS-10 : 1 PDMS-20 : 1 PDMS-30 : 1 PDMS-collapsed-pillars
153.7 155.4 154.9 144.1
3.8 4.0 1.6 6.7
135.2 124.0 120.4 5.1
2.2 2.8 1.8 2.5
132.4 5.4 123.2 3.4 120.2 3.5
136.8 2.2 125.6 2.8 122.2 2.1
128.0 3.3 120.8 1.8 118.2 3.7
Viewing angle 45 PDMS-10 : 1 PDMS-20 : 1 PDMS-30 : 1 PDMS-collapsed-pillars
153.0 151.3 151.2 142.3
6.2 6.3 4.5 4.6
132.8 122.1 118.8 10.6
1.9 4.9 1.6 4.8
129.1 7.3 124.9 6.1 120.4 3.5
135.0 4.6 130.0 4.1 124.3 2.4
123.3 3.6 119.8 1.5 117.7 1.8
evaporation process in the CCA mode. Note that the contact angle on the patterned surfaces in the CCA mode does not maintain constant but varies periodically. The contact angle decreases down to its receding contact angle (a minimum contact angle reached right before the contact line jumping inwards), then the contact angle suddenly jumps to a higher value and the contact radius reduces stepwise, as shown in Fig. 4–6. Then the contact angle decreases again to another receding contact angle and the relative contact radius maintains to be almost constant before another jump. Strictly speaking, the evaporation mechanism switches back to the CCR mode. However, the contact angle increases around 5 or less for each jump, as shown in Fig. 4–6. In spite of this short term CCR mode for each jumping period, the time window ranging
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from dashed line A to dashed line B shown in Fig. 4–6 is identied as the CCA mode. For each jumping period, the minimum contact angle, as pointed out by a black arrow shown in Fig. 4, is considered as the receding contact angle. Consequently, there exist many receding contact angles, as the minimum contact angles for each jumping cycle identied by black arrows shown in Fig. 4, in the CCA mode for each evaporation process. These receding contact angles are not constant. Table 2 lists the maximum (qr,evap,maxi), minimum (qr,evap,mini) and average (qr,evap) receding contact angles determined from the evaporation process in the CCA mode. Overall, the average receding contact angle (qr,evap) determined from evaporation has a good agreement with the receding contact angle (qr) determined by embedded needle measurement, as shown in Table 2. It should
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Evolution of (a) contact angle and (b) contact radius of a water drop deposited on the PDMS-20 : 1 substrate during the evaporation process from the viewing angle of 0 . Blue (1) and green (2) lines stand for the contact radius and contact angle on the right and left hand sides of the drop, respectively. It is obviously observed that the contact line on the right hand side is pinned most of the time while that of the left hand side recedes. Black dashed line A points out the occurrence of transition from the CCR mode to the CCA mode. Red dashed line B indicates the occurrence of wetting transition from the Cassie state to the Wenzel state. Fig. 5
Evolution of (a) contact angle and (b) contact radius of a water drop deposited on the PDMS-10 : 1 substrate during the evaporation process from the viewing angle of 0 . Blue (1) and green (2) lines stand for the contact radius and contact angle on the right and left hand sides of the drop, respectively. It is obviously observed that the contact line on the right hand side is pinned while that of the left hand side recedes in the early stage of the CCA mode. Black dashed line A points out the occurrence of transition from the CCR mode to the CCA mode. Red dashed line B indicates the occurrence of wetting transition from the Cassie state to the Wenzel state. Fig. 4
be pointed out that the receding contact angle is the key factor to determine the occurrence of the transition between the CCR and CCA modes. Furthermore, the soer the substrate is, the smaller the receding contact angle is. Thus the soer substrate would stay in the CCR mode for a longer time to reduce the contact angle down to its receding contact angle. Now we take a close look at the CCA mode, as shown in Fig. 4–6, observed on PDMS-10 : 1, PDMS-20 : 1 and PDMS30 : 1 substrates, respectively. In the CCA mode, the contact angle reaches the receding contact angle, the contact radius suddenly decreases and the contact angle jumps simultaneously. Both the contact angle and the contact radius then slowly decrease until that the contact angle reaches another receding contact angle. This step-by-step retreatment is periodically repeated and somehow related to the patterned square pillar-like substrate. It should be noted that the water droplet is standing on top of the pillars to begin with. That is, the water droplet falls into the Cassie state during the evaporation process in the CCR and CCA modes. When the three-phase
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contact line recedes, it jumps inwards from one pillar to the next nearby pillar. Therefore the contact radius does not smoothly decrease but decreases stepwise. This is also known as the slip-jump-stick behavior. Table 3 lists the average distance retreated per jumping step during the evaporation process from different viewing angles. The average retreated distance per jumping step along the viewing angle 0 (L0) is about 29 mm which is consistent with the unit length of the patterned structure (a + d). In the direction of the viewing angle 45 , the average retreated distance per jumping step (L45) is 21 mm, aþd pffiffiffi . This consistent with half of the diagonal unit length 2 observation implies that stepwise reduction in contact radius is directly related to a row-to-row jumping of contact line retreatment, as schematically illustrated in Fig. 7. From the viewing angle of 0 , the contact line stands parallel to the square array and recedes from one row to the next, as schematically shown in Fig. 7(a). From the viewing angle of 45 , the contact line also stands on the row but along the diagonal direction of the square array, thus it jumps half of the diagonal unit length every retreatment, as shown in Fig. 7(b).
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Fig. 7 The schematic deduction of the contact line movement from (a) the viewing angle of 0 and from (b) the viewing angle of 45 during the evaporation process.
Fig. 6 Evolution of (a) contact angle and (b) contact radius of a water drop deposited on the PDMS-30 : 1 substrate during the evaporation process from the viewing angle of 0 . Blue (1) and green (2) lines stand for the contact radius and contact angle on the right and left hand sides of the drop, respectively. It is obviously observed that the contact line on the left hand side is pinned while that of the right hand side recedes. Black dashed line A points out the occurrence of transition from the CCR mode to the CCA mode. Red dashed lines B and C indicate the occurrence of wetting transition from the Cassie state to the Wenzel state on the right and left hand sides of the drop, respectively.
Table 3
Average distance retreated per jumping step in the CCA
mode
Substrate
L0 (mm) (viewing angle 0 )
L45 (mm) (viewing angle 45 )
PDMS-10 : 1 PDMS-20 : 1 PDMS-30 : 1
28.8 0.3 29.1 0.4 28.4 0.7
21.5 1.2 21.2 0.4 19.7 1.5
It should be pointed out that the contact line retreatment is not necessarily a symmetric movement due to the pinning of the contact line on some defects. We deliberately analyzed the contact radius of the drop in terms of a relative distance from the starting center of the drop, the reference point dened in Fig. 1(b). It is interesting to nd out that usually one side is more favorable to slide than the other side, as shown in Fig. 4–6. For example, at the same time period from 2500 to 3150 s, as shown in Fig. 6, the contact line on the right hand side (blue
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curve) jumps 6 times but that on the le hand side (green curve) jumps only once on the PDMS-30 : 1 substrate. This indicates that the contact line on the right hand side is more favorable to move and the contact lines on both sides do not have to recede simultaneously. Sometimes the contact line is pinned at one side and only the other side exhibits the slip-jump-stick behavior. This phenomenon is probably related to the surface which is not perfectly homogeneous, for example, there are some defects on the surface or the different roughnesses on the top of the micropillars. At the end of the CCA mode, a wetting transition from the Cassie state to the Wenzel state occurs consistently on the PDMS-10 : 1, PDMS-20 : 1 and PDMS-30 : 1 substrates, as the red dashed line B marked in Figs. 4–6, respectively. It is interesting to note that when the wetting transition occurs, there is a slight increase in the contact radius and a sudden decrease in the contact angle. Aer this wetting transition, the contact radius seems to be pinned again and gradually decreases. For the hardest PDMS-10 : 1 substrate, the wetting transition happens at the very end of the evaporation process, as shown in Fig. 3 and 4. As the substrate becomes soer, the wetting transition happens earlier. It is believed that the early transition is due to the so texture, in which the pillars are not strong enough to bear the increasing Laplace pressure during evaporation. The most obvious evidence is that for the soest PDMS30 : 1 substrate the micropillars collapse aer the evaporation process. Through the optical microscope observation from the top view, we can see that before the wetting transition, the micropillars stand upright well. During evaporation in the CCR and CCA modes, the micropillars remain intact. The micropillars collapse when the wetting transition from the Cassie to the Wenzel state happens, as shown in Fig. 8(a). The wetting transition oen occurs at somewhere close to the contact line or defects and then water impales from the top of pillars into the bottom of the substrate and ows from one side to the other. At this moment, the micropillars are also pushed down by the water ow leaking from the Cassie droplet and nally the whole droplet transits into the Wenzel state.14 This observation can be further conrmed by the experimental data of evolution of contact angle and contact radius of a water drop on the PDMS30 : 1 substrate during the evaporation process from the side view observation, as shown in Fig. 6. That is, a slight increase in
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Fig. 8 (a) The optical microscope images of the PDMS-30 : 1 substrate during the wetting transition from the Cassie state to the Wenzel state. Initially, the pillars stood upright well and the water drop was in the Cassie state. At a moment the pillars were pushed down by the water flow leaking from the Cassie droplet, and finally the droplet transited into the Wenzel state and all the pillars under the droplet collapsed. The whole process, from the start of collapse of the first pillar to the end of collapse of all the pillars in the image, took about 45 seconds. (The image size is about 0.58 mm 0.58 mm.) (b) Variation of contact diameter of the sessile drop on the PDMS-30 : 1 substrate as a function of time during evaporation. (c) Optical microscope image of a circular “stain” (collapsed pillars) left on the PDMS-30 : 1 substrate after the evaporation process. The diameter of the circular stain (red solid line shown in (c)) is consistent with the wetting transition point illustrated in the evolution of contact diameter, as the red dashed line shown in (b).
contact radius and a sudden decrease in contact angle are rst observed at 3285 s on the right hand side (blue curves) of the water drop, as the red dashed line B marked in Fig. 6. And then 65 s later, another increase in contact radius and sudden decrease in contact angle are observed at 3350 s on the le hand side (green curves) of the water drop, as the red dashed line C marked in Fig. 6. Consequently, aer the evaporation process, there is a circular “stain” le on the PDMS-30 : 1 substrate due to those collapsed pillars, as shown in Fig. 8(c). The pattern of the collapsed pillars is related to the water ow, in which the direction of collapse of pillars is the same as the direction of the water ow.14 See the movie in the ESI of ref. 14 for the detail of the impregnating process of the water ow penetrating inbetween the pillars and the direction of collapse of pillars.14 It is noticed that, during wetting transition, the penetration of water is not limited to one spot (defect) only. Usually there are two spots (defects) or more simultaneously impaled by water, and it probably depends on the number and the location of the defects. Thus the pattern of the collapsed pillars might be variable, but the pillars at the outer ring, which is at the boundary between the collapsed pillars and the intact pillars, always collapse towards inside due to the shrinkage and surface tension of the drop. Because of some defects on the surface, the dimension of the circular stain is not uniform and therefore we
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cannot specically determine the relationship between the soness and the wetting transition. However, the dimension of the circular stain of collapsed pillars is consistent with the contact diameter of the wetting transition point, as shown in Fig. 8(b) and (c). Consequently, the circular stain of collapsed pillars is the ngerprint of the wetting transition from the Cassie state to the Wenzel state. We also performed the experiments of evaporation of a sessile drop on the PDMS-collapsed-pillars substrate. It was found that the evaporation on this PDMS-collapsed-pillars substrate is quite different from that of the other patterned substrates. Fig. 9(a) shows the evolution of contact angle and contact radius in the evaporation process of a sessile drop on the PDMS-collapsed-pillars substrate. It is obvious that the contact radius increases and the contact angle decreases at the beginning stage of the evaporation process. An optical microscope was applied to delineate the origin of this phenomenon from the top view observation. A series of top view images are shown in Fig. 9(b). There are lots of air bubbles trapped among the collapsed pillars initially when a water drop is gently deposited onto the PDMS-collapsed-pillars substrate. The size of bubbles decreases along with time and eventually all the trapped bubbles disappear. The water drop completely wets the PDMS-collapsed-pillars substrate and becomes a Wenzel drop. Therefore the initial increase and decrease in the contact radius and contact angle, respectively, are simply due to the relaxation of the wetting process to eliminate air bubbles trapped inside the deposited water drop on the substrate. Aer the trapped air bubbles are removed, as one can observe in Fig. 9(a), the evaporation process of the water droplet on the PDMScollapsed-pillars substrate follows the CCR mode, then the CCA mode, and nally the mixed mode sequentially.
(a) The overall process of the evaporation on PDMS-collapsed pillars. Blue line is referred to contact angle and green line represents relative contact radius. (b) A series of top view images through the water droplet sitting on PDMS-collapsed pillars. In the beginning, there was air trapped inside. As time passed by, the bubbles gradually decreased. At 500 seconds, all the bubbles almost disappeared.
Fig. 9
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It is hard to determine the receding contact angle for the PDMS-collapsed-pillars substrate either by embedded needle measurement or by evaporation. For example, in Fig. 3(a), it seems to have a receding contact angle at 30 along the viewing angle of 0 . On the other hand, there is no obvious CCA mode observed along the viewing angle of 45 , as shown in Fig. 3(c). The receding contact angles determined by embedded needle measurement are as low as 5.1 and 10.6 along the viewing angle of 0 and 45 , respectively, smaller than that observed from the evaporation process (Fig. 3(a)). The evaporation process of a sessile drop on the PDMScollapsed-pillars substrate is similar to the evaporation process aer the CCA mode on the soest PDMS-30 : 1 substrate, as shown in Fig. 3(a) and (b). It is reasonable for them to have the similar tendency, because both substrates are fabricated with exactly the same mixing ratio of the prepolymer base to the curing agent and at last the water drops are in the Wenzel state with collapsed pillars. Whenever the contact area is completely wetted, the contact line seems to be pinned again and the contact angle gradually reduces, as the feature of the CCR mode. However, it is hard to recognize whether there are another receding contact angles in the Wenzel state due to the gradually diminishing and attening drop as well as the limit of resolution. It is even harder for the PDMS-10 : 1 and PDMS-20 : 1 substrates to be recognized that there is another CCR mode and receding contact angle in the Wenzel state, since the initial size of the droplet in the Wenzel state is already too small to analyze. According to the theory of drop evaporation,1,15,31 the evaporation rate can be described by the diffusion model with the f(q) factor:
1 dV 4pD 3V 3 ¼ ðcs cN Þf ðqÞ dt rL pb b ¼ 2 3 cos q + cos3 q
(1)
(2)
t V ¼ V0 1 CCR ; t
where Vo is the initial drop volume and tCCR is the total evaporation time in the CCR mode.1,15,32 Our experimental data of drop volume (V) as a function of time (t) are tted to eqn (4) and (5) to determine tCCA and tCCR, as well as to determine the transition point between the CCA and CCR modes. The experimental data of drop volumes were obtained from the side view images by integration of the drop prole and assuming that the drop was composed of symmetric discs. Fig. 10 shows the experimental results and theoretical calculations of volume change during the evaporation process. The curves for the PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrates have been displaced vertically for the ease of visualization. That is, the initial drop volume of the system for the PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrates were shied downward by, respectively, one, two and three units in the log scale, as shown in Fig. 10. The solid line stands for our experimental results. The dotted line and dashed line are the theoretical calculations for the CCR and CCA modes, respectively. Generally, eqn (4) and (5) can well describe our experimental data. As the substrate becomes soer, the time duration of the CCR mode becomes longer. Eqn (4) ts well in the CCA mode, although in our observation the contact angle does not really maintain constant. Note that at the later stage of evaporation the Wenzel state dominates, since the size of the droplet in the Wenzel state is too small to analyze the results of PDMS-10 : 1 and PDMS-20 : 1 substrates; the result of the PDMS-30 : 1 substrate is chosen for further discussion. Fig. 11 shows the variation of the volume and contact diameter of sessile drops on the PDMS-30 : 1 substrate as a function of time. Aer the wetting transition from the Cassie state to the Wenzel state occurs, the dynamic behavior of the evaporation process closely follows the CCR mode. Thus the experimental data of drop volume from the beginning of the Wenzel state can be well described by eqn
f ðqÞ ¼ 0:00008957 þ 0:6333q þ 0:1160q2 0:08878q3 þ 0:01033q4 for 0:175 # q # p ¼ 0:6366q þ 0:09591q2 0:06144q3 for 0 # q\0:175 radians where V is the drop volume, t is time (s), D is the diffusivity (m2 s1), cs is the concentration of vapor at the liquid–vapor interface (kg m3), and cN is the concentration of vapor at innite distance (kg m3). In the CCA mode, because of the constant value of contact angle, f(q) is also constant. Eqn (1) could be integrated by time and found that the V2/3 is proportional to t. 3 t 2 V ¼ V0 1 CCA ; t
(4)
where Vo is the initial drop volume and tCCA is the total evaporation time in the CCA mode.1,15,31 However, in the CCR mode, only numerical solution can be found and it has been observed that the volume decreases linearly with time in the CCR mode.1,15,32
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(5)
(3)
(5), as blue dashed-and-dotted line shown in Fig. 11. It is obvious that this second CCR mode only lasts for relatively a short period of time, from 3303 to 4373 s, compared to the rst CCR mode (yellow dashed-and-dotted line), from 0 to 2587 s. Right aer the second CCR mode, another CCA mode takes over, as blue dashed line shown in Fig. 11, consistent with the results of the evaporation process of a sessile drop on the PDMS-collapsed-pillars substrate. Finally, it is interesting to nd out that the evaporation process of a sessile drop on the soest PDMS-30 : 1 substrate is identied to exhibit four stages sequentially: CCR / CCA / CCR / CCA. When the evaporation process of the sessile drop falls in the rst CCR and CCA modes, the sessile drop is in the Cassie state. Aer the sessile drop transitions into the Wenzel state, the second sequence of the CCR and CCA modes is observed in the evaporation mechanism.
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Fig. 11 Variation of drop volume (black solid line) and contact diameter (green solid line) as a function of time during the evaporation process of a water drop on the PDMS-30 : 1 substrate along the viewing angle of 0 . Dashed-and-dotted and dashed lines represent the theoretical calculation results of the evaporation process, respectively, in the CCR mode and in the CCA mode. Yellow and blue colors stand for the theoretical calculation results of the drop in the Cassie state and in the Wenzel state, respectively. Red solid line A points out the occurrence of transition from the CCR mode to the CCA mode in the Cassie state. Red solid line B indicates the occurrence of wetting transition from the Cassie state to the Wenzel state and the transition from the CCA mode to the CCR mode. Red solid line C points out the occurrence of transition from the CCR mode to the CCA mode in the Wenzel state.
Fig. 10 The experiment and theoretical calculations of volume change with time (a) from the viewing angle of 0 (b) from the viewing angle of 45 . Solid line stands for the experimental results, dashedand-dotted line is the theoretical calculation of the CCR mode and the dashed line is the theoretical calculation of the CCA mode. The red, green, blue and orange lines represent the PDMS-10 : 1, PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrates, respectively. The curves for the PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrates have been displaced vertically for ease of visualization.
Finally, Fig. 10 also demonstrates that the total evaporation time for four different substrates is in the order of PDMS-10 : 1 > PDMS-20 : 1 > PDMS-30 : 1 > PDMS-collapsed-pillars. In other words, a water droplet on the so patterned substrate evaporates faster than that of the hard patterned substrate, consistent with the nding for at PDMS substrates.15 Furthermore, we also performed the evaporation experiments of 6 mL water droplets on the at PDMS (30 : 1) substrate to examine the effect of the surface pattern on the evaporation process. It is interesting to nd out that the total evaporation time for three different substrates of same elasticity (at a xed mixing ratio 30 : 1) is in the order of PDMS-30 : 1 > at PDMS (30 : 1) > PDMS-collapsedpillars. That is, the water droplet on the at PDMS (30 : 1) substrate evaporates faster than that of the PDMS-30 : 1 substrate, consistent with a recent study on hard surfaces,33 but slower than that of the PDMS-collapsed-pillars substrate. As pointed out by Lopes and Bonaccurso,15 a water droplet completely evaporates in CCR mode much faster than that in CCA mode with a same initial condition. Therefore, as the substrate becomes soer, the receding contact angle becomes smaller, the time duration in CCR mode becomes longer, and
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the evaporation becomes faster. The receding contact angles of these three substrates of same elasticity are in the order of PDMS-30 : 1 > at PDMS (30 : 1) > PDMS-collapsed-pillars, as given in Tables 1 and 2. That is, the smaller the receding contact angle is, the faster the evaporation is.
4. Conclusions In this study, the evaporation of sessile drops on four different substrates: PDMS-10 : 1, PDMS-20 : 1, PDMS-30 : 1 and PDMScollapsed-pillars are carefully examined. Three modes (CCR, CCA and mixed mode) can be distinguished during evaporation of sessile drops on the PDMS-10 : 1, PDMS-20 : 1, and PDMScollapsed-pillars substrates. The CCR mode comes at rst, and when the receding contact angle is attained, the CCA mode takes over. Finally, both contact radius and contact angle decrease and the mixed mode appears till the end of evaporation. The soness of the patterned substrate has a great effect on the receding contact angle: the soer the substrate is, the smaller the receding contact angle is. Therefore, with the same initial condition, a sessile drop on the soest PDMS-30 : 1 substrate will stay in the CCR mode for the longest time due to the smallest receding contact angle. The contact angle of the sessile drop does maintain to be almost constant in the CCA mode during the evaporation and the three-phase-contact-line of the sessile drop exhibits the slip-jump-stick behavior periodically accompanied by the stepwise decrease of contact radius. The average slip-jump-stick distance is directly related to the patterned structure: from the viewing angle of 0 , the average distance per slip-jump-stick is just a unit length of the patterned structure (a + d); from the viewing angle of 45 , the average distance per slip-jump-stick is about half of the unit
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aþd pffiffiffi . The CCA mode ends when the wetting 2 transition from the Cassie state to the Wenzel state occurs. While the substrate is soer, the wetting transition happens earlier because the soer pillars relatively cannot stand the increasingly high Laplace pressure. Especially for the soest PDMS-30 : 1 substrate, the micropillars collapsed to induce the early wetting transition and ended up remaining a rounded mark. Right aer the wetting transition, the sessile drop is in the Wenzel state and further evaporation resumes the CCR mode followed by the CCA mode sequentially. Consider the evaporation rate, a water droplet on the at substrate evaporates faster than that of the patterned substrate and the water droplet on the soer patterned surface evaporates faster.
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of diagonal
Nomenclature a cs cN d D f(q) h rl rr t tCCA tCCR V Vo ql qr q
The dimension of pillar [mm], dened in Fig. 1 The concentration of vapor at the liquid–vapor interface [kg m3] The concentration of vapor at innite distance [kg m3] The distance between two pillars [mm], dened in Fig. 1 The diffusivity [m2 s1] A function of contact angle q, dened by eqn (3) The pillar height [mm], dened in Fig. 1 Relative contact radius on the le hand side of a drop, dened in Fig. 2(b) Relative contact radius on the right hand side of a drop, dened in Fig. 2(b) Time [s] The total evaporation time in CCA mode [s] The total evaporation time in CCR mode [s] The drop volume The initial drop volume Contact angle on the le hand side of the drop, dened in Fig. 2(b) Contact angle on the right hand side of the drop, dened in Fig. 2(b) Contact angle [radians].
Acknowledgements This work was supported by the National Science Council of Taiwan.
References 1 R. G. Picknett and R. Bexon, J. Colloid Interface Sci., 1977, 61, 336–350. 2 C. Bourg` es-Monnier and M. E. R. Shanahan, Langmuir, 1995, 11, 2820–2829. 3 G. McHale, S. Aqil, N. J. Shirtcliffe, M. I. Newton and H. Y. Erbil, Langmuir, 2005, 21, 11053–11060.
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4 S. M. Rowan, M. I. Newton and G. McHale, J. Phys. Chem., 1995, 99, 13268–13271. 5 S. M. Rowan, G. McHale, M. I. Newton and M. Toorneman, J. Phys. Chem. B, 1997, 101, 1265–1267. 6 G. McHale, S. M. Rowan, M. I. Newton and M. K. Banerjee, J. Phys. Chem. B, 1998, 102, 1964–1967. 7 S. A. Kulinich and M. Farzaneh, Appl. Surf. Sci., 2009, 255, 4056–4060. 8 M. Reyssat, J. M. Yeomans and D. Quere, Europhys. Lett., 2008, 81, 26006. 9 P. C. Tsai, R. G. H. Lammertink, M. Wessling and D. Lohse, Phys. Rev. Lett., 2010, 104, 116102. 10 R. Pericet-Camara, G. K. Auernhammer, K. Koynov, S. Lorenzoni, R. Raiteric and E. Bonaccurso, So Matter, 2009, 5, 3611–3617. 11 R. Pericet-Camara, A. Best, H. J. Butt and E. Bonaccurso, Langmuir, 2008, 24, 10565–10568. 12 G. Pu and S. J. Severtson, J. Phys. Chem. C, 2011, 115, 18729– 18735. 13 E. R. Jerison, Y. Xu, L. A. Wilen and E. R. Dufresne, Phys. Rev. Lett., 2011, 106, 186103. 14 Y. H. Yeh, K. H. Cho and L. J. Chen, So Matter, 2012, 8, 1079–1086. 15 M. C. Lopes and E. Bonaccurso, So Matter, 2012, 8, 7875–7881. 16 G. Pu and S. J. Severtson, Langmuir, 2012, 28, 10007–10014. 17 C. W. Extrand and Y. Yumagai, Contact angles and hysteresis on so surfaces, J. Colloid Interface Sci., 1996, 184, 191–200. 18 M. E. R. Shanahan and A. Carre, Viscoelastic dissipation in wetting and adhesion phenomena, Langmuir, 1995, 11(4), 1396–1402. 19 A. Carre, J. C. Gastel and M. E. R. Shanahan, Viscoelastic effects in the spreading of liquids, Nature, 1996, 379, 432–434. 20 J. C. McDonald and G. M. Whitesides, Acc. Chem. Res., 2002, 35, 7. 21 G. M. Whitesides, Nature, 2006, 442, 27. 22 A. Colombo, H. Zahedmanesh, D. M. Toner, P. A. Cahill and C. Lally, J. Mech. Behav. Biomed. Mater., 2010, 3, 470–477. 23 M. L. Poll, F. Zhou, M. Ramstedt, L. Hu and W. T. S. Huck, Angew. Chem., Int. Ed. Engl., 2007, 46, 6634–6637. 24 J. Frienda and L. Yeo, Biomicrouidics, 2010, 4, 026502. 25 J. H. Yeon and J. K. Park, BioChip J., 2007, 1(1), 17–27. 26 I. Meyvantsson and D. J. Beebe, Annu. Rev. Anal. Chem., 2008, 1, 423–449. 27 K. Y. Yeh, L. J. Chen and J. Y. Chang, Langmuir, 2008, 24, 245–251. 28 K. H. Cho and L. J. Chen, Nanotechnology, 2011, 22, 445706. 29 K. Y. Yeh, K. H. Cho and L. J. Chen, Langmuir, 2009, 25, 14187–14194. 30 W. F. Kuan and L. J. Chen, Nanotechnology, 2009, 20, 035605. 31 H. Y. Erbil, Adv. Colloid Interface Sci., 2012, 170, 67–86. 32 F. Schoenfeld, K. Graf, S. Hardt and H.-J. Butt, Int. J. Heat Mass Transfer, 2008, 51, 3696–3699. 33 W. Xu, R. Leeladhar, Y. T. Kang and C. H. Choi, Langmuir, 2013, 29, 6032–6041.
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Evaporation of water droplets on soft patterned surfaces Yu-Chen Chuang, Che-Kang Chu, Shih-Yao Lin and Li-Jen Chen* The evaporation process of a sessile drop of water on soft patterned polydimethylsiloxane (PDMS) substrates is investigated in this study. Different softness of a regular pillar-like patterned PDMS substrate can be achieved by controlling the mixing ratio of a PDMS's prepolymer base and a curing agent at 10 : 1, 20 : 1 and 30 : 1. The receding contact angle is smaller for softer pillar-like patterned substrates. Consequently, the evaporation rate is faster on softer pillar-like substrates. A sessile drop on the regular pillar-like PDMS substrates, prepared at the mixing ratio of a base to a curing agent of 10 : 1 and 20 : 1, is observed to start evaporating in the constant contact radius (CCR) mode then switching to the constant contact angle (CCA) mode via stepwise jumping of the contact line, and finally shifting to the mixed mode sequentially. During the evaporation, a wetting transition from the Cassie to the Wenzel state occurs earlier for the softer substrate because softer pillars relatively cannot stand the increasingly high Laplace pressure. For the softest regular pillar-like PDMS substrate prepared at the mixing ratio of the base to the curing agent of 30 : 1 (abbreviated by PDMS-30 : 1 substrate), the pillars collapse irreversibly after the sessile drop exhibits the wetting transition into the Wenzel state. Furthermore, it is interesting to
Received 24th October 2013 Accepted 4th February 2014
find out that the initial stage of evaporation of a sessile drop on the PDMS-30 : 1 substrate in the Cassie state is in the CCR mode followed by the CCA mode with stepwise retreatment of the contact line.
DOI: 10.1039/c3sm52719k
Further evaporation would induce the wetting transition from the Cassie to the Wenzel state (due to the
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collapse of pillars) and resume the CCR mode followed by the CCA mode again sequentially.
1. Introduction Evaporation is a common phenomenon we can see in our daily life. The evaporation of sessile drops plays an important role in various applications, such as microuidics, lab-on-a-chip application, combustion, ink-jet printing, pesticide spraying and so on. In 1977, Picknett and Bexon investigated the evaporation of sessile drops and distinguished three modes of evaporation, that is, constant contact angle mode, constant contact area mode and mixed mode.1 Usually, at the early stage of the drop evaporation process, the contact angle decreases and the contact area remains constant, which is called a constant contact area or constant contact radius (CCR) mode. When the contact angle keeps decreasing down to its receding contact angle, the contact line starts to recede and the constant contact angle (CCA) mode takes over. In other words, the contact radius decreases and the contact angle remains constant. Toward the end of evaporation, both contact radius and contact angle may decrease simultaneously and that is termed the mixed mode. They also worked on the evaporation rate by a mass prole and the theoretical analysis can obtain a reasonable prediction.1
Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan. E-mail: [email protected]
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Bourg` es-Monnier and Shanahan studied the evaporation of water and n-decane on various substrates.2 They classied the evaporation process into four stages, and proposed a model to determine the diffusion coefficient of the vapor in air. The rst stage of evaporation corresponds to a saturated atmosphere and the other three stages correspond to the CCR, CCA and mixed modes.2 McHale and coworkers3–6 have studied the evaporation of sessile drops on different surfaces, including at surfaces with the initial contact angle greater than 90 and less than 90 and also working on patterned surfaces. They found that, for at surfaces, when the initial contact angle is less than 90 , the CCR mode dominates and when the initial contact angle is larger than 90 , the CCA mode dominates. They also suggested that the CCA mode is due to the local saturated vapor created near the contact line.6 In addition, McHale et al. worked on the SU-8 textured superhydrophobic surface.3 They found that the evaporation initially proceeded in the CCR mode and then followed by stepwise retreatment associated with the lattice structure of the substrate. They studied not only the evolution of contact angle and contact radius but also the evaporation rate considering the diffusion model and the spherical geometry for the CCR and CCA modes. It has been pointed out by Kulinich and Farzaneh that the contact angle hysteresis is the main factor affecting drop evaporation.7 The evaporation process of a sessile drop on a high-hysteresis surface follows the CCR mode and in
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contrast, that of a low-hysteresis surface follows the CCA mode. It is also observed that water evaporates faster on the highhysteresis surface.7 Evaporation of sessile drops on rough surfaces can also trigger the wetting transition from the Cassie state to the Wenzel state. McHale3 had observed a few cases that the wetting transition happened abruptly with a sharp step-like decrease in contact angle and a step-like increase in contact radius. Reyssat et al. deposited a water droplet on the hydrophobic surfaces decorated with regular micropillars.8 During evaporation, the drop transferred from the Cassie state to the Wenzel state. They suggested that the reason is due to the deformation of the interface below the drop. When evaporating, the drop curvature decreases and the Laplace pressure increases. The increasing pressure would enforce the deformation of the liquid–vapor interface below the drop and while the liquid–vapor interface touches the ground surface, the wetting transition happens. By this hypothesis, they proposed a simple criterion to determine when the transition would happen. Tsai et al. also studied the evaporation-triggered wetting transition on hydrophobic surfaces and it is observed how the Cassie state transferred into the Wenzel state from the observation of the bottom view.9 They used the surface energy minimization to predict the critical size at wetting transition and got a nice consistency with the experimental results. It is interesting to note that a sessile droplet can deform an elastic surface due to the surface tension and capillary pressure.10–13 As a consequence, the elasticity of the substrate would have a strong effect on contact angle hysteresis, wetting behavior, and evaporation.14–19 It was found that the contact angle hysteresis is larger for the soer surfaces. That is, the advancing and receding contact angles become larger and smaller, respectively, for the soer surfaces. Recently, the evaporation of sessile water drops on so at polydimethylsiloxane (PDMS) surfaces has been examined and found that the total evaporation time is shorter for the soer surfaces.15,16 The biocompatible elastomer PDMS has been widely used in biomedical applications, such as microuidic devices, mock arteries, etc.20–26 In addition, we have demonstrated that the wetting transition from the Cassie state to the Wenzel state occurs on the so pillar-like patterned PDMS surfaces due to the collapse of pillars.14 Consequently, the pillars may collapse during the evaporation, that certainly induces the change of evaporation mode. In this study, the water evaporation on the so pillar-like patterned PDMS surfaces is carefully examined to investigate how the soness of pillars would inuence the evaporation mechanism and the wetting behavior.
2.
Experimental procedure
2.1
Preparation of the patterned substrates
The patterned silicon master was prepared by photolithography and further modied by a self-assembled octadecyltrichlorosilane (Aldrich) monolayer to further minimize its surface energy.27–30 The mixture of polydimethylsiloxane (PDMS, Sylgard 184, Dow corning, USA), a prepolymer base and a curing agent (10 : 1, 20 : 1 or 30 : 1 by mass) was poured onto the patterned
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silicon masters. Aer thermal curing at 70 C for 18 hours, a regular pillar-like PDMS substrate was obtained by peeling off the PDMS mold from the patterned silicon master.14 The microstructure of the regular pillar-like PDMS substrate is illustrated in Fig. 1 with a mm a mm square pillars separated by a distance d mm and the pillar height h mm. The surface topology of this patterned PDMS substrate was examined by using a scanning electronic microscope (SEM, JOEL JSM-5600) and a ¼ 9.9 mm, d ¼ 19.2 mm and h ¼ 16.1 mm. A tensile strength instrument (model LRX, LLOYD Instruments, USA) was used to measure the Young's moduli of the at PDMS substrates prepared at three different mixing ratios of the base to the curing agent (10 : 1, 20 : 1, and 30 : 1 by mass). The Young's moduli for these three substrates range from 3.87 to 0.17 MPa, as listed in Table 1. In addition, the advancing and receding contact angles of water on these at PDMS substrates are determined by the embedded needle method21–23 and reported in Table 1. The PDMS substrate becomes soer by increasing the mixing ratio and the advancing and receding contact angles get larger and smaller, respectively.14,15 For simplicity, the PDMS-10 : 1, PDMS-20 : 1 and PDMS30 : 1 substrates are used hereaer to stand for the regular pillar-like patterned PDMS substrates prepared at the mixing ratio of the base to the curing agent 10 : 1, 20 : 1 and 30 : 1, respectively. When a water drop is deposited on the PDMS-30 : 1 substrate, all the pillars underneath the drop would collapse aer the evaporation. Therefore, the PDMS-30 : 1 substrate was covered by water and aer the evaporation all the pillars would collapse. This patterned substrate of collapsed pillars is abbreviated as the PDMS-collapsed-pillars substrate hereaer.
2.2
Evaporation
We used pipette to place a 6 mL water droplet on the PDMS substrate at an ambient environment and observed the evaporation process of the sessile drop from top view and side view. Water was puried by double distillation and then followed by a PURELAB Maxima Series (ELGA, LabWater) purication system with the resistivity always better than 18.2 MU cm. For all the
Fig. 1 SEM image of the surface structure with a mm a mm square pillars separated by a distance d mm and the pillar height h mm. a ¼ 9.9, d ¼ 19.2 and h ¼ 16.1.
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Table 1 Young's moduli, advancing (qa) and receding (qr) contact angles of water on the flat PDMS substrates prepared at different mixing ratios of the prepolymer base to the curing agent (10 : 1, 20 : 1, and 30 : 1)
Substrate
Young's modulus (MPa)
qa ( )
qr ( )
PDMS 10 : 1 PDMS 20 : 1 PDMS 30 : 1
3.87 0.17 0.56 0.06 0.17 0.02
108 2 112 2 116 1
81 4 56 2 49 8
evaporation experiments, the temperature and relative humidity were in the range of 25 2 C and 53% 2%, respectively. A homemade enhanced video-microscopy system incorporated with a digital image analysis was used to observe the side view of a sessile drop during the evaporation process. The frame rate of a solid state charge coupled device camera (Point Grey, Canada) was set at 1 frame per second to record the evaporation process. The images of side view (i.e., drop prole) were used to extract the information of contact angles and contact radii by the digital image analysis. An optical microscope (Olympus, BXFM) was applied to observe the evolution of water drop evaporation from top view. Each condition was repeated at least three times to ensure the reproducibility. 2.3 Advancing/receding contact angle measurement by using an embedded needle method The homemade enhanced video-microscopy system incorporated with a digital image analysis was also used to perform the advancing and receding contact angle measurements. Initially, we placed the prepared PDMS substrate in the environmental chamber (Rame-hart instrument co.) and a needle was positioned inside the chamber. Then a syringe pump (Orion, Sage, model M362) was turned on to generate a water droplet on the substrate. Aer this drop-forming step, water was again continuously and slowly pumped into (or sucked from) the droplet and simultaneously the evolution of the water droplet was recorded to further measure the advancing (or receding) contact angle via the enhanced video-microscopy system. The experimental details can be found in our previous studies.28–30 The rate of water pumping and suction through the needle to perform the advancing and receding contact angle measurement, respectively, was always kept lower than 0.03 mL min1.
3.
Results and discussion
PDMS substrates with the same patterned structure but different ratios of the base to the curing agent were used to examine the inuences of soness on the evaporation mechanism. In this study, the experiments of evaporation of water sessile drops were performed on four different substrates: PDMS-10 : 1, PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsedpillars. The viewing angle along the side of the square array is dened to be 0 , and the viewing angle along the diagonal of the square array is dened to be 45 , as illustrated in Fig. 2(a). The center of the contact diameter in the very rst frame of an
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evaporation process is dened as the reference point and the contact diameter is separated into two radii: contact radius on the le hand side (rl) and on the right hand side (rr), as illustrated in Fig. 2(b). The coordinates of the reference point is xed throughout the evaporation process that enable us to observe the asymmetric evaporation process. In addition, the contact angles on the le hand side (ql) and on the right hand side (qr) of a drop are also dened in Fig. 2(b). Fig. 3 shows the evolution of contact angle and contact radius during the evaporation process on four different substrates along two viewing angles 0 and 45 . Initially, the drop stands on the top of the pillars, that is, in the Cassie state, and the initial contact angle is around 145 , except the PDMScollapsed-pillars substrate. The evaporation starts with the constant contact radius (CCR) mode: the contact angle decreases, the contact line is pinned and the contact radius remains almost constant. For example, one may see evolution of contact angle and contact radius as a function of time for the PDMS-20 : 1 substrate in the region of CCR mode specied by green long dashed line shown in Fig. 3(a) and (b). Once the receding contact angle is attained, the constant contact angle (CCA) mode takes over. That is, the contact line starts to recede, the contact radius decreases and the contact angle remains almost constant, as one can see the region of CCA mode observed on the PDMS-20 : 1 substrate specied in-between two vertical green long dashed lines shown in Fig. 3(a) and (b). Finally, in the third mode observed on the PDMS-10 : 1, PDMS20 : 1 and PDMS-collapsed-pillars substrates, both contact radius and contact angle decrease, as shown in Fig. 3(a) and (b) again, that is, the mixed mode. We will come back to discuss the evaporation mechanism aer the CCA mode observed on the PDMS-30 : 1 substrate later on. Table 2 lists the advancing/receding contact angle at different viewing angles 0 and 45 obtained from embedded needle measurement and from evaporation. According to the results of embedded needle measurements, the advancing contact angles (qa) for the substrates of three different sonesses are essentially the same around 155 and the receding contact angle (qr) becomes smaller when the substrate is soer. On the other hand, the advancing and receding contact angles for the PDMS substrate with collapsed pillars are as low as 144 and 5 , respectively. The advancing/receding contact angles from the viewing angle 0 are slightly larger than that from the viewing angle 45 due to the asymmetry of the drop shape. It is interesting to compare the receding contact angle determined from embedded needle measurement to that determined from the
Fig. 2 The definition of (a) viewing angle, (b) contact radii, contact angles and reference point.
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The evolution of (a and c) contact angle and of (b and d) contact radius during evaporation from (a and b) the viewing angle of 0 and from (c and d) the viewing angle of 45 . The red (1), green (2), blue (3) and orange (4) lines represent the, respectively, PDMS-10 : 1, PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrates. Two vertical green long dashed lines, shown in (a) and (b), are used to separate the regions of CCR, CCA and mixed modes for the evaporation process of a water droplet on the PDMS-20 : 1 substrate. Note that the reference point (defined by Fig. 2(b)) is determined in the very first frame (i.e. the very beginning) of an evaporation process and fixed throughout the evaporation process. For certain droplets, the contact line is pinned at one side and only the other side shrinks and moves inwards. That is, the relative contact radius may decrease even become negative, as curve 2 (PDMS-20 : 1) shown in (d). Fig. 3
Table 2
Advancing and receding contact angles of water on the patterned PDMS substrates By embedded needle measurement qr
qa
By evaporation qr,evap
qr,evap,maxi
qr,evap,mini
Viewing angle 0 PDMS-10 : 1 PDMS-20 : 1 PDMS-30 : 1 PDMS-collapsed-pillars
153.7 155.4 154.9 144.1
3.8 4.0 1.6 6.7
135.2 124.0 120.4 5.1
2.2 2.8 1.8 2.5
132.4 5.4 123.2 3.4 120.2 3.5
136.8 2.2 125.6 2.8 122.2 2.1
128.0 3.3 120.8 1.8 118.2 3.7
Viewing angle 45 PDMS-10 : 1 PDMS-20 : 1 PDMS-30 : 1 PDMS-collapsed-pillars
153.0 151.3 151.2 142.3
6.2 6.3 4.5 4.6
132.8 122.1 118.8 10.6
1.9 4.9 1.6 4.8
129.1 7.3 124.9 6.1 120.4 3.5
135.0 4.6 130.0 4.1 124.3 2.4
123.3 3.6 119.8 1.5 117.7 1.8
evaporation process in the CCA mode. Note that the contact angle on the patterned surfaces in the CCA mode does not maintain constant but varies periodically. The contact angle decreases down to its receding contact angle (a minimum contact angle reached right before the contact line jumping inwards), then the contact angle suddenly jumps to a higher value and the contact radius reduces stepwise, as shown in Fig. 4–6. Then the contact angle decreases again to another receding contact angle and the relative contact radius maintains to be almost constant before another jump. Strictly speaking, the evaporation mechanism switches back to the CCR mode. However, the contact angle increases around 5 or less for each jump, as shown in Fig. 4–6. In spite of this short term CCR mode for each jumping period, the time window ranging
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from dashed line A to dashed line B shown in Fig. 4–6 is identied as the CCA mode. For each jumping period, the minimum contact angle, as pointed out by a black arrow shown in Fig. 4, is considered as the receding contact angle. Consequently, there exist many receding contact angles, as the minimum contact angles for each jumping cycle identied by black arrows shown in Fig. 4, in the CCA mode for each evaporation process. These receding contact angles are not constant. Table 2 lists the maximum (qr,evap,maxi), minimum (qr,evap,mini) and average (qr,evap) receding contact angles determined from the evaporation process in the CCA mode. Overall, the average receding contact angle (qr,evap) determined from evaporation has a good agreement with the receding contact angle (qr) determined by embedded needle measurement, as shown in Table 2. It should
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Evolution of (a) contact angle and (b) contact radius of a water drop deposited on the PDMS-20 : 1 substrate during the evaporation process from the viewing angle of 0 . Blue (1) and green (2) lines stand for the contact radius and contact angle on the right and left hand sides of the drop, respectively. It is obviously observed that the contact line on the right hand side is pinned most of the time while that of the left hand side recedes. Black dashed line A points out the occurrence of transition from the CCR mode to the CCA mode. Red dashed line B indicates the occurrence of wetting transition from the Cassie state to the Wenzel state. Fig. 5
Evolution of (a) contact angle and (b) contact radius of a water drop deposited on the PDMS-10 : 1 substrate during the evaporation process from the viewing angle of 0 . Blue (1) and green (2) lines stand for the contact radius and contact angle on the right and left hand sides of the drop, respectively. It is obviously observed that the contact line on the right hand side is pinned while that of the left hand side recedes in the early stage of the CCA mode. Black dashed line A points out the occurrence of transition from the CCR mode to the CCA mode. Red dashed line B indicates the occurrence of wetting transition from the Cassie state to the Wenzel state. Fig. 4
be pointed out that the receding contact angle is the key factor to determine the occurrence of the transition between the CCR and CCA modes. Furthermore, the soer the substrate is, the smaller the receding contact angle is. Thus the soer substrate would stay in the CCR mode for a longer time to reduce the contact angle down to its receding contact angle. Now we take a close look at the CCA mode, as shown in Fig. 4–6, observed on PDMS-10 : 1, PDMS-20 : 1 and PDMS30 : 1 substrates, respectively. In the CCA mode, the contact angle reaches the receding contact angle, the contact radius suddenly decreases and the contact angle jumps simultaneously. Both the contact angle and the contact radius then slowly decrease until that the contact angle reaches another receding contact angle. This step-by-step retreatment is periodically repeated and somehow related to the patterned square pillar-like substrate. It should be noted that the water droplet is standing on top of the pillars to begin with. That is, the water droplet falls into the Cassie state during the evaporation process in the CCR and CCA modes. When the three-phase
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contact line recedes, it jumps inwards from one pillar to the next nearby pillar. Therefore the contact radius does not smoothly decrease but decreases stepwise. This is also known as the slip-jump-stick behavior. Table 3 lists the average distance retreated per jumping step during the evaporation process from different viewing angles. The average retreated distance per jumping step along the viewing angle 0 (L0) is about 29 mm which is consistent with the unit length of the patterned structure (a + d). In the direction of the viewing angle 45 , the average retreated distance per jumping step (L45) is 21 mm, aþd pffiffiffi . This consistent with half of the diagonal unit length 2 observation implies that stepwise reduction in contact radius is directly related to a row-to-row jumping of contact line retreatment, as schematically illustrated in Fig. 7. From the viewing angle of 0 , the contact line stands parallel to the square array and recedes from one row to the next, as schematically shown in Fig. 7(a). From the viewing angle of 45 , the contact line also stands on the row but along the diagonal direction of the square array, thus it jumps half of the diagonal unit length every retreatment, as shown in Fig. 7(b).
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Fig. 7 The schematic deduction of the contact line movement from (a) the viewing angle of 0 and from (b) the viewing angle of 45 during the evaporation process.
Fig. 6 Evolution of (a) contact angle and (b) contact radius of a water drop deposited on the PDMS-30 : 1 substrate during the evaporation process from the viewing angle of 0 . Blue (1) and green (2) lines stand for the contact radius and contact angle on the right and left hand sides of the drop, respectively. It is obviously observed that the contact line on the left hand side is pinned while that of the right hand side recedes. Black dashed line A points out the occurrence of transition from the CCR mode to the CCA mode. Red dashed lines B and C indicate the occurrence of wetting transition from the Cassie state to the Wenzel state on the right and left hand sides of the drop, respectively.
Table 3
Average distance retreated per jumping step in the CCA
mode
Substrate
L0 (mm) (viewing angle 0 )
L45 (mm) (viewing angle 45 )
PDMS-10 : 1 PDMS-20 : 1 PDMS-30 : 1
28.8 0.3 29.1 0.4 28.4 0.7
21.5 1.2 21.2 0.4 19.7 1.5
It should be pointed out that the contact line retreatment is not necessarily a symmetric movement due to the pinning of the contact line on some defects. We deliberately analyzed the contact radius of the drop in terms of a relative distance from the starting center of the drop, the reference point dened in Fig. 1(b). It is interesting to nd out that usually one side is more favorable to slide than the other side, as shown in Fig. 4–6. For example, at the same time period from 2500 to 3150 s, as shown in Fig. 6, the contact line on the right hand side (blue
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curve) jumps 6 times but that on the le hand side (green curve) jumps only once on the PDMS-30 : 1 substrate. This indicates that the contact line on the right hand side is more favorable to move and the contact lines on both sides do not have to recede simultaneously. Sometimes the contact line is pinned at one side and only the other side exhibits the slip-jump-stick behavior. This phenomenon is probably related to the surface which is not perfectly homogeneous, for example, there are some defects on the surface or the different roughnesses on the top of the micropillars. At the end of the CCA mode, a wetting transition from the Cassie state to the Wenzel state occurs consistently on the PDMS-10 : 1, PDMS-20 : 1 and PDMS-30 : 1 substrates, as the red dashed line B marked in Figs. 4–6, respectively. It is interesting to note that when the wetting transition occurs, there is a slight increase in the contact radius and a sudden decrease in the contact angle. Aer this wetting transition, the contact radius seems to be pinned again and gradually decreases. For the hardest PDMS-10 : 1 substrate, the wetting transition happens at the very end of the evaporation process, as shown in Fig. 3 and 4. As the substrate becomes soer, the wetting transition happens earlier. It is believed that the early transition is due to the so texture, in which the pillars are not strong enough to bear the increasing Laplace pressure during evaporation. The most obvious evidence is that for the soest PDMS30 : 1 substrate the micropillars collapse aer the evaporation process. Through the optical microscope observation from the top view, we can see that before the wetting transition, the micropillars stand upright well. During evaporation in the CCR and CCA modes, the micropillars remain intact. The micropillars collapse when the wetting transition from the Cassie to the Wenzel state happens, as shown in Fig. 8(a). The wetting transition oen occurs at somewhere close to the contact line or defects and then water impales from the top of pillars into the bottom of the substrate and ows from one side to the other. At this moment, the micropillars are also pushed down by the water ow leaking from the Cassie droplet and nally the whole droplet transits into the Wenzel state.14 This observation can be further conrmed by the experimental data of evolution of contact angle and contact radius of a water drop on the PDMS30 : 1 substrate during the evaporation process from the side view observation, as shown in Fig. 6. That is, a slight increase in
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Fig. 8 (a) The optical microscope images of the PDMS-30 : 1 substrate during the wetting transition from the Cassie state to the Wenzel state. Initially, the pillars stood upright well and the water drop was in the Cassie state. At a moment the pillars were pushed down by the water flow leaking from the Cassie droplet, and finally the droplet transited into the Wenzel state and all the pillars under the droplet collapsed. The whole process, from the start of collapse of the first pillar to the end of collapse of all the pillars in the image, took about 45 seconds. (The image size is about 0.58 mm 0.58 mm.) (b) Variation of contact diameter of the sessile drop on the PDMS-30 : 1 substrate as a function of time during evaporation. (c) Optical microscope image of a circular “stain” (collapsed pillars) left on the PDMS-30 : 1 substrate after the evaporation process. The diameter of the circular stain (red solid line shown in (c)) is consistent with the wetting transition point illustrated in the evolution of contact diameter, as the red dashed line shown in (b).
contact radius and a sudden decrease in contact angle are rst observed at 3285 s on the right hand side (blue curves) of the water drop, as the red dashed line B marked in Fig. 6. And then 65 s later, another increase in contact radius and sudden decrease in contact angle are observed at 3350 s on the le hand side (green curves) of the water drop, as the red dashed line C marked in Fig. 6. Consequently, aer the evaporation process, there is a circular “stain” le on the PDMS-30 : 1 substrate due to those collapsed pillars, as shown in Fig. 8(c). The pattern of the collapsed pillars is related to the water ow, in which the direction of collapse of pillars is the same as the direction of the water ow.14 See the movie in the ESI of ref. 14 for the detail of the impregnating process of the water ow penetrating inbetween the pillars and the direction of collapse of pillars.14 It is noticed that, during wetting transition, the penetration of water is not limited to one spot (defect) only. Usually there are two spots (defects) or more simultaneously impaled by water, and it probably depends on the number and the location of the defects. Thus the pattern of the collapsed pillars might be variable, but the pillars at the outer ring, which is at the boundary between the collapsed pillars and the intact pillars, always collapse towards inside due to the shrinkage and surface tension of the drop. Because of some defects on the surface, the dimension of the circular stain is not uniform and therefore we
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cannot specically determine the relationship between the soness and the wetting transition. However, the dimension of the circular stain of collapsed pillars is consistent with the contact diameter of the wetting transition point, as shown in Fig. 8(b) and (c). Consequently, the circular stain of collapsed pillars is the ngerprint of the wetting transition from the Cassie state to the Wenzel state. We also performed the experiments of evaporation of a sessile drop on the PDMS-collapsed-pillars substrate. It was found that the evaporation on this PDMS-collapsed-pillars substrate is quite different from that of the other patterned substrates. Fig. 9(a) shows the evolution of contact angle and contact radius in the evaporation process of a sessile drop on the PDMS-collapsed-pillars substrate. It is obvious that the contact radius increases and the contact angle decreases at the beginning stage of the evaporation process. An optical microscope was applied to delineate the origin of this phenomenon from the top view observation. A series of top view images are shown in Fig. 9(b). There are lots of air bubbles trapped among the collapsed pillars initially when a water drop is gently deposited onto the PDMS-collapsed-pillars substrate. The size of bubbles decreases along with time and eventually all the trapped bubbles disappear. The water drop completely wets the PDMS-collapsed-pillars substrate and becomes a Wenzel drop. Therefore the initial increase and decrease in the contact radius and contact angle, respectively, are simply due to the relaxation of the wetting process to eliminate air bubbles trapped inside the deposited water drop on the substrate. Aer the trapped air bubbles are removed, as one can observe in Fig. 9(a), the evaporation process of the water droplet on the PDMScollapsed-pillars substrate follows the CCR mode, then the CCA mode, and nally the mixed mode sequentially.
(a) The overall process of the evaporation on PDMS-collapsed pillars. Blue line is referred to contact angle and green line represents relative contact radius. (b) A series of top view images through the water droplet sitting on PDMS-collapsed pillars. In the beginning, there was air trapped inside. As time passed by, the bubbles gradually decreased. At 500 seconds, all the bubbles almost disappeared.
Fig. 9
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It is hard to determine the receding contact angle for the PDMS-collapsed-pillars substrate either by embedded needle measurement or by evaporation. For example, in Fig. 3(a), it seems to have a receding contact angle at 30 along the viewing angle of 0 . On the other hand, there is no obvious CCA mode observed along the viewing angle of 45 , as shown in Fig. 3(c). The receding contact angles determined by embedded needle measurement are as low as 5.1 and 10.6 along the viewing angle of 0 and 45 , respectively, smaller than that observed from the evaporation process (Fig. 3(a)). The evaporation process of a sessile drop on the PDMScollapsed-pillars substrate is similar to the evaporation process aer the CCA mode on the soest PDMS-30 : 1 substrate, as shown in Fig. 3(a) and (b). It is reasonable for them to have the similar tendency, because both substrates are fabricated with exactly the same mixing ratio of the prepolymer base to the curing agent and at last the water drops are in the Wenzel state with collapsed pillars. Whenever the contact area is completely wetted, the contact line seems to be pinned again and the contact angle gradually reduces, as the feature of the CCR mode. However, it is hard to recognize whether there are another receding contact angles in the Wenzel state due to the gradually diminishing and attening drop as well as the limit of resolution. It is even harder for the PDMS-10 : 1 and PDMS-20 : 1 substrates to be recognized that there is another CCR mode and receding contact angle in the Wenzel state, since the initial size of the droplet in the Wenzel state is already too small to analyze. According to the theory of drop evaporation,1,15,31 the evaporation rate can be described by the diffusion model with the f(q) factor:
1 dV 4pD 3V 3 ¼ ðcs cN Þf ðqÞ dt rL pb b ¼ 2 3 cos q + cos3 q
(1)
(2)
t V ¼ V0 1 CCR ; t
where Vo is the initial drop volume and tCCR is the total evaporation time in the CCR mode.1,15,32 Our experimental data of drop volume (V) as a function of time (t) are tted to eqn (4) and (5) to determine tCCA and tCCR, as well as to determine the transition point between the CCA and CCR modes. The experimental data of drop volumes were obtained from the side view images by integration of the drop prole and assuming that the drop was composed of symmetric discs. Fig. 10 shows the experimental results and theoretical calculations of volume change during the evaporation process. The curves for the PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrates have been displaced vertically for the ease of visualization. That is, the initial drop volume of the system for the PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrates were shied downward by, respectively, one, two and three units in the log scale, as shown in Fig. 10. The solid line stands for our experimental results. The dotted line and dashed line are the theoretical calculations for the CCR and CCA modes, respectively. Generally, eqn (4) and (5) can well describe our experimental data. As the substrate becomes soer, the time duration of the CCR mode becomes longer. Eqn (4) ts well in the CCA mode, although in our observation the contact angle does not really maintain constant. Note that at the later stage of evaporation the Wenzel state dominates, since the size of the droplet in the Wenzel state is too small to analyze the results of PDMS-10 : 1 and PDMS-20 : 1 substrates; the result of the PDMS-30 : 1 substrate is chosen for further discussion. Fig. 11 shows the variation of the volume and contact diameter of sessile drops on the PDMS-30 : 1 substrate as a function of time. Aer the wetting transition from the Cassie state to the Wenzel state occurs, the dynamic behavior of the evaporation process closely follows the CCR mode. Thus the experimental data of drop volume from the beginning of the Wenzel state can be well described by eqn
f ðqÞ ¼ 0:00008957 þ 0:6333q þ 0:1160q2 0:08878q3 þ 0:01033q4 for 0:175 # q # p ¼ 0:6366q þ 0:09591q2 0:06144q3 for 0 # q\0:175 radians where V is the drop volume, t is time (s), D is the diffusivity (m2 s1), cs is the concentration of vapor at the liquid–vapor interface (kg m3), and cN is the concentration of vapor at innite distance (kg m3). In the CCA mode, because of the constant value of contact angle, f(q) is also constant. Eqn (1) could be integrated by time and found that the V2/3 is proportional to t. 3 t 2 V ¼ V0 1 CCA ; t
(4)
where Vo is the initial drop volume and tCCA is the total evaporation time in the CCA mode.1,15,31 However, in the CCR mode, only numerical solution can be found and it has been observed that the volume decreases linearly with time in the CCR mode.1,15,32
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(5)
(3)
(5), as blue dashed-and-dotted line shown in Fig. 11. It is obvious that this second CCR mode only lasts for relatively a short period of time, from 3303 to 4373 s, compared to the rst CCR mode (yellow dashed-and-dotted line), from 0 to 2587 s. Right aer the second CCR mode, another CCA mode takes over, as blue dashed line shown in Fig. 11, consistent with the results of the evaporation process of a sessile drop on the PDMS-collapsed-pillars substrate. Finally, it is interesting to nd out that the evaporation process of a sessile drop on the soest PDMS-30 : 1 substrate is identied to exhibit four stages sequentially: CCR / CCA / CCR / CCA. When the evaporation process of the sessile drop falls in the rst CCR and CCA modes, the sessile drop is in the Cassie state. Aer the sessile drop transitions into the Wenzel state, the second sequence of the CCR and CCA modes is observed in the evaporation mechanism.
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Fig. 11 Variation of drop volume (black solid line) and contact diameter (green solid line) as a function of time during the evaporation process of a water drop on the PDMS-30 : 1 substrate along the viewing angle of 0 . Dashed-and-dotted and dashed lines represent the theoretical calculation results of the evaporation process, respectively, in the CCR mode and in the CCA mode. Yellow and blue colors stand for the theoretical calculation results of the drop in the Cassie state and in the Wenzel state, respectively. Red solid line A points out the occurrence of transition from the CCR mode to the CCA mode in the Cassie state. Red solid line B indicates the occurrence of wetting transition from the Cassie state to the Wenzel state and the transition from the CCA mode to the CCR mode. Red solid line C points out the occurrence of transition from the CCR mode to the CCA mode in the Wenzel state.
Fig. 10 The experiment and theoretical calculations of volume change with time (a) from the viewing angle of 0 (b) from the viewing angle of 45 . Solid line stands for the experimental results, dashedand-dotted line is the theoretical calculation of the CCR mode and the dashed line is the theoretical calculation of the CCA mode. The red, green, blue and orange lines represent the PDMS-10 : 1, PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrates, respectively. The curves for the PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrates have been displaced vertically for ease of visualization.
Finally, Fig. 10 also demonstrates that the total evaporation time for four different substrates is in the order of PDMS-10 : 1 > PDMS-20 : 1 > PDMS-30 : 1 > PDMS-collapsed-pillars. In other words, a water droplet on the so patterned substrate evaporates faster than that of the hard patterned substrate, consistent with the nding for at PDMS substrates.15 Furthermore, we also performed the evaporation experiments of 6 mL water droplets on the at PDMS (30 : 1) substrate to examine the effect of the surface pattern on the evaporation process. It is interesting to nd out that the total evaporation time for three different substrates of same elasticity (at a xed mixing ratio 30 : 1) is in the order of PDMS-30 : 1 > at PDMS (30 : 1) > PDMS-collapsedpillars. That is, the water droplet on the at PDMS (30 : 1) substrate evaporates faster than that of the PDMS-30 : 1 substrate, consistent with a recent study on hard surfaces,33 but slower than that of the PDMS-collapsed-pillars substrate. As pointed out by Lopes and Bonaccurso,15 a water droplet completely evaporates in CCR mode much faster than that in CCA mode with a same initial condition. Therefore, as the substrate becomes soer, the receding contact angle becomes smaller, the time duration in CCR mode becomes longer, and
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the evaporation becomes faster. The receding contact angles of these three substrates of same elasticity are in the order of PDMS-30 : 1 > at PDMS (30 : 1) > PDMS-collapsed-pillars, as given in Tables 1 and 2. That is, the smaller the receding contact angle is, the faster the evaporation is.
4. Conclusions In this study, the evaporation of sessile drops on four different substrates: PDMS-10 : 1, PDMS-20 : 1, PDMS-30 : 1 and PDMScollapsed-pillars are carefully examined. Three modes (CCR, CCA and mixed mode) can be distinguished during evaporation of sessile drops on the PDMS-10 : 1, PDMS-20 : 1, and PDMScollapsed-pillars substrates. The CCR mode comes at rst, and when the receding contact angle is attained, the CCA mode takes over. Finally, both contact radius and contact angle decrease and the mixed mode appears till the end of evaporation. The soness of the patterned substrate has a great effect on the receding contact angle: the soer the substrate is, the smaller the receding contact angle is. Therefore, with the same initial condition, a sessile drop on the soest PDMS-30 : 1 substrate will stay in the CCR mode for the longest time due to the smallest receding contact angle. The contact angle of the sessile drop does maintain to be almost constant in the CCA mode during the evaporation and the three-phase-contact-line of the sessile drop exhibits the slip-jump-stick behavior periodically accompanied by the stepwise decrease of contact radius. The average slip-jump-stick distance is directly related to the patterned structure: from the viewing angle of 0 , the average distance per slip-jump-stick is just a unit length of the patterned structure (a + d); from the viewing angle of 45 , the average distance per slip-jump-stick is about half of the unit
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aþd pffiffiffi . The CCA mode ends when the wetting 2 transition from the Cassie state to the Wenzel state occurs. While the substrate is soer, the wetting transition happens earlier because the soer pillars relatively cannot stand the increasingly high Laplace pressure. Especially for the soest PDMS-30 : 1 substrate, the micropillars collapsed to induce the early wetting transition and ended up remaining a rounded mark. Right aer the wetting transition, the sessile drop is in the Wenzel state and further evaporation resumes the CCR mode followed by the CCA mode sequentially. Consider the evaporation rate, a water droplet on the at substrate evaporates faster than that of the patterned substrate and the water droplet on the soer patterned surface evaporates faster.
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of diagonal
Nomenclature a cs cN d D f(q) h rl rr t tCCA tCCR V Vo ql qr q
The dimension of pillar [mm], dened in Fig. 1 The concentration of vapor at the liquid–vapor interface [kg m3] The concentration of vapor at innite distance [kg m3] The distance between two pillars [mm], dened in Fig. 1 The diffusivity [m2 s1] A function of contact angle q, dened by eqn (3) The pillar height [mm], dened in Fig. 1 Relative contact radius on the le hand side of a drop, dened in Fig. 2(b) Relative contact radius on the right hand side of a drop, dened in Fig. 2(b) Time [s] The total evaporation time in CCA mode [s] The total evaporation time in CCR mode [s] The drop volume The initial drop volume Contact angle on the le hand side of the drop, dened in Fig. 2(b) Contact angle on the right hand side of the drop, dened in Fig. 2(b) Contact angle [radians].
Acknowledgements This work was supported by the National Science Council of Taiwan.
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