Soft Matter

PAPER

Publ

ishe

d on

07

Febr

uary

201

4. D

ownl

oade

d by

Tre

nt U

nive

rsity

on

16/1

0/20

14 0

6:43

:44.

View Article OnlineView Journal | View Issue

Department of Chemical Engineering, Nat

Taiwan. E-mail: ljchen@ntu.edu.tw

Cite this: Soft Matter, 2014, 10, 3394

Received 24th October 2013Accepted 4th February 2014

DOI: 10.1039/c3sm52719k

www.rsc.org/softmatter

3394 | Soft Matter, 2014, 10, 3394–340

Evaporation of water droplets on soft patternedsurfaces

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

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.

Further evaporation would induce the wetting transition from the Cassie to the Wenzel state (due to the

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 dailylife. The evaporation of sessile drops plays an important role invarious applications, such as microuidics, lab-on-a-chipapplication, combustion, ink-jet printing, pesticide sprayingand so on.

In 1977, Picknett and Bexon investigated the evaporation ofsessile drops and distinguished three modes of evaporation,that is, constant contact angle mode, constant contact areamode and mixed mode.1 Usually, at the early stage of thedrop evaporation process, the contact angle decreases andthe contact area remains constant, which is called a constantcontact area or constant contact radius (CCR) mode. When thecontact angle keeps decreasing down to its receding contactangle, the contact line starts to recede and the constant contactangle (CCA) mode takes over. In other words, the contact radiusdecreases and the contact angle remains constant. Toward theend of evaporation, both contact radius and contact angle maydecrease simultaneously and that is termed the mixed mode.They also worked on the evaporation rate by a mass prole andthe theoretical analysis can obtain a reasonable prediction.1

ional Taiwan University, Taipei 10617,

3

Bourges-Monnier and Shanahan studied the evaporation ofwater and n-decane on various substrates.2 They classied theevaporation process into four stages, and proposed a model todetermine the diffusion coefficient of the vapor in air. The rststage of evaporation corresponds to a saturated atmosphere andthe other three stages correspond to the CCR, CCA and mixedmodes.2

McHale and coworkers3–6 have studied the evaporation ofsessile drops on different surfaces, including at surfaces withthe initial contact angle greater than 90� and less than 90� andalso working on patterned surfaces. They found that, for atsurfaces, when the initial contact angle is less than 90�, the CCRmode dominates and when the initial contact angle is largerthan 90�, the CCA mode dominates. They also suggested thatthe CCA mode is due to the local saturated vapor created nearthe contact line.6 In addition, McHale et al. worked on the SU-8textured superhydrophobic surface.3 They found that the evap-oration initially proceeded in the CCR mode and then followedby stepwise retreatment associated with the lattice structure ofthe substrate. They studied not only the evolution of contactangle and contact radius but also the evaporation rate consid-ering the diffusion model and the spherical geometry for theCCR and CCA modes. It has been pointed out by Kulinich andFarzaneh that the contact angle hysteresis is the main factoraffecting drop evaporation.7 The evaporation process of a sessiledrop on a high-hysteresis surface follows the CCR mode and in

This journal is © The Royal Society of Chemistry 2014

Fig. 1 SEM image of the surface structure with a mm � a mm squarepillars 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.

Paper Soft Matter

Publ

ishe

d on

07

Febr

uary

201

4. D

ownl

oade

d by

Tre

nt U

nive

rsity

on

16/1

0/20

14 0

6:43

:44.

View Article Online

contrast, that of a low-hysteresis surface follows the CCA mode.It is also observed that water evaporates faster on the high-hysteresis surface.7

Evaporation of sessile drops on rough surfaces can alsotrigger the wetting transition from the Cassie state to theWenzel state. McHale3 had observed a few cases that the wettingtransition happened abruptly with a sharp step-like decrease incontact angle and a step-like increase in contact radius. Reyssatet al. deposited a water droplet on the hydrophobic surfacesdecorated with regular micropillars.8 During evaporation, thedrop transferred from the Cassie state to the Wenzel state. Theysuggested that the reason is due to the deformation of theinterface below the drop. When evaporating, the drop curvaturedecreases and the Laplace pressure increases. The increasingpressure would enforce the deformation of the liquid–vaporinterface below the drop and while the liquid–vapor interfacetouches the ground surface, the wetting transition happens. Bythis hypothesis, they proposed a simple criterion to determinewhen the transition would happen. Tsai et al. also studied theevaporation-triggered wetting transition on hydrophobicsurfaces and it is observed how the Cassie state transferred intothe Wenzel state from the observation of the bottom view.9 Theyused the surface energy minimization to predict the critical sizeat wetting transition and got a nice consistency with theexperimental results.

It is interesting to note that a sessile droplet can deform anelastic surface due to the surface tension and capillary pres-sure.10–13 As a consequence, the elasticity of the substrate wouldhave a strong effect on contact angle hysteresis, wettingbehavior, and evaporation.14–19 It was found that the contactangle hysteresis is larger for the soer surfaces. That is, theadvancing and receding contact angles become larger andsmaller, respectively, for the soer surfaces. Recently, theevaporation of sessile water drops on so at polydimethylsi-loxane (PDMS) surfaces has been examined and found that thetotal evaporation time is shorter for the soer surfaces.15,16 Thebiocompatible elastomer PDMS has been widely used inbiomedical applications, such as microuidic devices, mockarteries, etc.20–26 In addition, we have demonstrated that thewetting transition from the Cassie state to the Wenzel stateoccurs on the so pillar-like patterned PDMS surfaces due tothe collapse of pillars.14 Consequently, the pillars may collapseduring the evaporation, that certainly induces the change ofevaporation mode. In this study, the water evaporation on theso pillar-like patterned PDMS surfaces is carefully examined toinvestigate how the soness of pillars would inuence theevaporation mechanism and the wetting behavior.

2. Experimental procedure2.1 Preparation of the patterned substrates

The patterned silicon master was prepared by photolithographyand further modied by a self-assembled octadecyltri-chlorosilane (Aldrich) monolayer to further minimize its surfaceenergy.27–30 Themixture of polydimethylsiloxane (PDMS, Sylgard184, Dow corning, USA), a prepolymer base and a curing agent(10 : 1, 20 : 1 or 30 : 1 by mass) was poured onto the patterned

This journal is © The Royal Society of Chemistry 2014

silicon masters. Aer thermal curing at 70 �C for 18 hours, aregular pillar-like PDMS substrate was obtained by peeling offthe PDMS mold from the patterned silicon master.14 Themicrostructure of the regular pillar-like PDMS substrate isillustrated in Fig. 1 with a mm � a mm square pillars separatedby a distance d mm and the pillar height h mm. The surfacetopology of this patterned PDMS substrate was examined byusing 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 Instru-ments, USA) was used to measure the Young's moduli of the atPDMS substrates prepared at three different mixing ratios of thebase to the curing agent (10 : 1, 20 : 1, and 30 : 1 by mass). TheYoung's moduli for these three substrates range from 3.87 to0.17 MPa, as listed in Table 1. In addition, the advancing andreceding contact angles of water on these at PDMS substratesare determined by the embedded needle method21–23 andreported in Table 1. The PDMS substrate becomes soer byincreasing the mixing ratio and the advancing and recedingcontact angles get larger and smaller, respectively.14,15

For simplicity, the PDMS-10 : 1, PDMS-20 : 1 and PDMS-30 : 1 substrates are used hereaer to stand for the regularpillar-like patterned PDMS substrates prepared at the mixingratio 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 : 1substrate, all the pillars underneath the drop would collapseaer the evaporation. Therefore, the PDMS-30 : 1 substrate wascovered by water and aer the evaporation all the pillars wouldcollapse. This patterned substrate of collapsed pillars isabbreviated as the PDMS-collapsed-pillars substrate hereaer.

2.2 Evaporation

We used pipette to place a 6 mL water droplet on the PDMSsubstrate at an ambient environment and observed the evapo-ration process of the sessile drop from top view and side view.Water was puried by double distillation and then followed by aPURELAB Maxima Series (ELGA, LabWater) purication systemwith the resistivity always better than 18.2 MU cm. For all the

Soft Matter, 2014, 10, 3394–3403 | 3395

Table 1 Young's moduli, advancing (qa) and receding (qr) contactangles of water on the flat PDMS substrates prepared at differentmixing 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 3.87 � 0.17 108 � 2 81 � 4PDMS 20 : 1 0.56 � 0.06 112 � 2 56 � 2PDMS 30 : 1 0.17 � 0.02 116 � 1 49 � 8

Soft Matter Paper

Publ

ishe

d on

07

Febr

uary

201

4. D

ownl

oade

d by

Tre

nt U

nive

rsity

on

16/1

0/20

14 0

6:43

:44.

View Article Online

evaporation experiments, the temperature and relativehumidity were in the range of 25 � 2 �C and 53% � 2%,respectively. A homemade enhanced video-microscopy systemincorporated with a digital image analysis was used to observethe 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 theevaporation process. The images of side view (i.e., drop prole)were used to extract the information of contact angles andcontact radii by the digital image analysis. An optical micro-scope (Olympus, BXFM) was applied to observe the evolution ofwater drop evaporation from top view. Each condition wasrepeated at least three times to ensure the reproducibility.

2.3 Advancing/receding contact angle measurement byusing an embedded needle method

The homemade enhanced video-microscopy system incorpo-rated with a digital image analysis was also used to perform theadvancing and receding contact angle measurements. Initially,we placed the prepared PDMS substrate in the environmentalchamber (Rame-hart instrument co.) and a needle was posi-tioned inside the chamber. Then a syringe pump (Orion, Sage,model M362) was turned on to generate a water droplet on thesubstrate. Aer this drop-forming step, water was againcontinuously and slowly pumped into (or sucked from) thedroplet and simultaneously the evolution of the water dropletwas recorded to further measure the advancing (or receding)contact angle via the enhanced video-microscopy system. Theexperimental details can be found in our previous studies.28–30

The rate of water pumping and suction through the needle toperform the advancing and receding contact angle measure-ment, respectively, was always kept lower than 0.03 mL min�1.

Fig. 2 The definition of (a) viewing angle, (b) contact radii, contactangles and reference point.

3. Results and discussion

PDMS substrates with the same patterned structure butdifferent ratios of the base to the curing agent were used toexamine the inuences of soness on the evaporation mecha-nism. In this study, the experiments of evaporation of watersessile drops were performed on four different substrates:PDMS-10 : 1, PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars. The viewing angle along the side of the square array isdened to be 0�, and the viewing angle along the diagonal of thesquare array is dened to be 45�, as illustrated in Fig. 2(a). Thecenter of the contact diameter in the very rst frame of an

3396 | Soft Matter, 2014, 10, 3394–3403

evaporation process is dened as the reference point and thecontact diameter is separated into two radii: contact radius onthe le hand side (rl) and on the right hand side (rr), as illus-trated in Fig. 2(b). The coordinates of the reference point is xedthroughout the evaporation process that enable us to observethe asymmetric evaporation process. In addition, the contactangles on the le hand side (ql) and on the right hand side (qr) ofa drop are also dened in Fig. 2(b).

Fig. 3 shows the evolution of contact angle and contactradius during the evaporation process on four differentsubstrates along two viewing angles 0� and 45�. Initially, thedrop stands on the top of the pillars, that is, in the Cassie state,and the initial contact angle is around 145�, except the PDMS-collapsed-pillars substrate. The evaporation starts with theconstant contact radius (CCR) mode: the contact angledecreases, the contact line is pinned and the contact radiusremains almost constant. For example, onemay see evolution ofcontact angle and contact radius as a function of time for thePDMS-20 : 1 substrate in the region of CCR mode specied bygreen long dashed line shown in Fig. 3(a) and (b). Once thereceding 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 remainsalmost constant, as one can see the region of CCA modeobserved on the PDMS-20 : 1 substrate specied in-between twovertical green long dashed lines shown in Fig. 3(a) and (b).Finally, in the third mode observed on the PDMS-10 : 1, PDMS-20 : 1 and PDMS-collapsed-pillars substrates, both contactradius and contact angle decrease, as shown in Fig. 3(a) and (b)again, that is, the mixedmode. We will come back to discuss theevaporation mechanism aer the CCA mode observed on thePDMS-30 : 1 substrate later on.

Table 2 lists the advancing/receding contact angle atdifferent viewing angles 0� and 45� obtained from embeddedneedle measurement and from evaporation. According to theresults of embedded needle measurements, the advancingcontact angles (qa) for the substrates of three different so-nesses are essentially the same around 155� and the recedingcontact angle (qr) becomes smaller when the substrate is soer.On the other hand, the advancing and receding contact anglesfor 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 tocompare the receding contact angle determined fromembedded needle measurement to that determined from the

This journal is © The Royal Society of Chemistry 2014

Fig. 3 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 regionsof 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 evaporationprocess. For certain droplets, the contact line is pinned at one side and only the other side shrinks andmoves inwards. That is, the relative contactradius may decrease even become negative, as curve 2 (PDMS-20 : 1) shown in (d).

Table 2 Advancing and receding contact angles of water on the patterned PDMS substrates

By embedded needle measurement By evaporation

qa qr qr,evap qr,evap,maxi qr,evap,mini

Viewing angle 0�

PDMS-10 : 1 153.7 � 3.8 135.2 � 2.2 132.4 � 5.4 136.8 � 2.2 128.0 � 3.3PDMS-20 : 1 155.4 � 4.0 124.0 � 2.8 123.2 � 3.4 125.6 � 2.8 120.8 � 1.8PDMS-30 : 1 154.9 � 1.6 120.4 � 1.8 120.2 � 3.5 122.2 � 2.1 118.2 � 3.7PDMS-collapsed-pillars 144.1 � 6.7 5.1 � 2.5

Viewing angle 45�

PDMS-10 : 1 153.0 � 6.2 132.8 � 1.9 129.1 � 7.3 135.0 � 4.6 123.3 � 3.6PDMS-20 : 1 151.3 � 6.3 122.1 � 4.9 124.9 � 6.1 130.0 � 4.1 119.8 � 1.5PDMS-30 : 1 151.2 � 4.5 118.8 � 1.6 120.4 � 3.5 124.3 � 2.4 117.7 � 1.8PDMS-collapsed-pillars 142.3 � 4.6 10.6 � 4.8

Paper Soft Matter

Publ

ishe

d on

07

Febr

uary

201

4. D

ownl

oade

d by

Tre

nt U

nive

rsity

on

16/1

0/20

14 0

6:43

:44.

View Article Online

evaporation process in the CCA mode. Note that the contactangle on the patterned surfaces in the CCA mode does notmaintain constant but varies periodically. The contact angledecreases down to its receding contact angle (a minimumcontact angle reached right before the contact line jumpinginwards), then the contact angle suddenly jumps to a highervalue and the contact radius reduces stepwise, as shown inFig. 4–6. Then the contact angle decreases again to anotherreceding contact angle and the relative contact radius main-tains to be almost constant before another jump. Strictlyspeaking, the evaporation mechanism switches back to the CCRmode. However, the contact angle increases around 5� or lessfor each jump, as shown in Fig. 4–6. In spite of this short termCCR mode for each jumping period, the time window ranging

This journal is © The Royal Society of Chemistry 2014

from dashed line A to dashed line B shown in Fig. 4–6 is iden-tied as the CCAmode. For each jumping period, the minimumcontact angle, as pointed out by a black arrow shown in Fig. 4, isconsidered as the receding contact angle. Consequently, thereexist many receding contact angles, as the minimum contactangles for each jumping cycle identied by black arrows shownin Fig. 4, in the CCA mode for each evaporation process.These receding contact angles are not constant. Table 2 liststhe maximum (qr,evap,maxi), minimum (qr,evap,mini) and average(qr,evap) receding contact angles determined from the evapora-tion process in the CCA mode. Overall, the average recedingcontact angle (qr,evap) determined from evaporation has a goodagreement with the receding contact angle (qr) determined byembedded needle measurement, as shown in Table 2. It should

Soft Matter, 2014, 10, 3394–3403 | 3397

Fig. 4 Evolution of (a) contact angle and (b) contact radius of a waterdrop deposited on the PDMS-10 : 1 substrate during the evaporationprocess from the viewing angle of 0�. Blue (1) and green (2) lines standfor the contact radius and contact angle on the right and left handsides of the drop, respectively. It is obviously observed that the contactline on the right hand side is pinned while that of the left hand siderecedes in the early stage of the CCAmode. Black dashed line A pointsout the occurrence of transition from the CCR mode to the CCAmode. Red dashed line B indicates the occurrence of wetting transitionfrom the Cassie state to the Wenzel state.

Fig. 5 Evolution of (a) contact angle and (b) contact radius of a waterdrop deposited on the PDMS-20 : 1 substrate during the evaporationprocess from the viewing angle of 0�. Blue (1) and green (2) lines standfor the contact radius and contact angle on the right and left handsides of the drop, respectively. It is obviously observed that the contactline on the right hand side is pinned most of the time while that of theleft hand side recedes. Black dashed line A points out the occurrenceof transition from the CCR mode to the CCA mode. Red dashed line Bindicates the occurrence of wetting transition from the Cassie state tothe Wenzel state.

Soft Matter Paper

Publ

ishe

d on

07

Febr

uary

201

4. D

ownl

oade

d by

Tre

nt U

nive

rsity

on

16/1

0/20

14 0

6:43

:44.

View Article Online

be pointed out that the receding contact angle is the keyfactor to determine the occurrence of the transition betweenthe CCR and CCA modes. Furthermore, the soer thesubstrate is, the smaller the receding contact angle is. Thusthe soer substrate would stay in the CCR mode for a longertime to reduce the contact angle down to its receding contactangle.

Now we take a close look at the CCA mode, as shown inFig. 4–6, observed on PDMS-10 : 1, PDMS-20 : 1 and PDMS-30 : 1 substrates, respectively. In the CCA mode, the contactangle reaches the receding contact angle, the contact radiussuddenly decreases and the contact angle jumps simulta-neously. Both the contact angle and the contact radius thenslowly decrease until that the contact angle reaches anotherreceding contact angle. This step-by-step retreatment is peri-odically repeated and somehow related to the patterned squarepillar-like substrate. It should be noted that the water droplet isstanding on top of the pillars to begin with. That is, the waterdroplet falls into the Cassie state during the evaporationprocess in the CCR and CCA modes. When the three-phase

3398 | Soft Matter, 2014, 10, 3394–3403

contact line recedes, it jumps inwards from one pillar to thenext nearby pillar. Therefore the contact radius does notsmoothly decrease but decreases stepwise. This is also known asthe slip-jump-stick behavior. Table 3 lists the average distanceretreated per jumping step during the evaporation process fromdifferent viewing angles. The average retreated distance perjumping step along the viewing angle 0� (L0) is about 29 mmwhich is consistent with the unit length of the patternedstructure (a + d). In the direction of the viewing angle 45�, theaverage retreated distance per jumping step (L45) is 21 mm,

consistent with half of the diagonal unit length�aþ dffiffiffi

2p

�. This

observation implies that stepwise reduction in contact radius isdirectly related to a row-to-row jumping of contact line retreat-ment, as schematically illustrated in Fig. 7. From the viewingangle of 0�, the contact line stands parallel to the square arrayand recedes from one row to the next, as schematically shown inFig. 7(a). From the viewing angle of 45�, the contact line alsostands on the row but along the diagonal direction of the squarearray, thus it jumps half of the diagonal unit length everyretreatment, as shown in Fig. 7(b).

This journal is © The Royal Society of Chemistry 2014

Fig. 6 Evolution of (a) contact angle and (b) contact radius of a waterdrop deposited on the PDMS-30 : 1 substrate during the evaporationprocess from the viewing angle of 0�. Blue (1) and green (2) lines standfor the contact radius and contact angle on the right and left handsides of the drop, respectively. It is obviously observed that the contactline on the left hand side is pinned while that of the right hand siderecedes. Black dashed line A points out the occurrence of transitionfrom the CCR mode to the CCA mode. Red dashed lines B and Cindicate the occurrence of wetting transition from the Cassie state tothe Wenzel state on the right and left hand sides of the drop,respectively.

Table 3 Average distance retreated per jumping step in the CCAmode

SubstrateL0 (mm)(viewing angle 0�)

L45 (mm)(viewing angle 45�)

PDMS-10 : 1 28.8 � 0.3 21.5 � 1.2PDMS-20 : 1 29.1 � 0.4 21.2 � 0.4PDMS-30 : 1 28.4 � 0.7 19.7 � 1.5

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� duringthe evaporation process.

Paper Soft Matter

Publ

ishe

d on

07

Febr

uary

201

4. D

ownl

oade

d by

Tre

nt U

nive

rsity

on

16/1

0/20

14 0

6:43

:44.

View Article Online

It should be pointed out that the contact line retreatment isnot necessarily a symmetric movement due to the pinning of thecontact line on some defects. We deliberately analyzed thecontact radius of the drop in terms of a relative distance fromthe starting center of the drop, the reference point dened inFig. 1(b). It is interesting to nd out that usually one side ismore 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, asshown in Fig. 6, the contact line on the right hand side (blue

This journal is © The Royal Society of Chemistry 2014

curve) jumps 6 times but that on the le hand side (green curve)jumps only once on the PDMS-30 : 1 substrate. This indicatesthat the contact line on the right hand side is more favorable tomove and the contact lines on both sides do not have to recedesimultaneously. Sometimes the contact line is pinned at oneside and only the other side exhibits the slip-jump-stickbehavior. This phenomenon is probably related to the surfacewhich is not perfectly homogeneous, for example, there aresome defects on the surface or the different roughnesses on thetop of the micropillars.

At the end of the CCA mode, a wetting transition fromthe Cassie state to the Wenzel state occurs consistently on thePDMS-10 : 1, PDMS-20 : 1 and PDMS-30 : 1 substrates, as thered dashed line B marked in Figs. 4–6, respectively. It is inter-esting to note that when the wetting transition occurs, there is aslight increase in the contact radius and a sudden decrease inthe contact angle. Aer this wetting transition, the contactradius seems to be pinned again and gradually decreases. Forthe hardest PDMS-10 : 1 substrate, the wetting transitionhappens at the very end of the evaporation process, as shown inFig. 3 and 4. As the substrate becomes soer, the wettingtransition happens earlier. It is believed that the early transitionis due to the so texture, in which the pillars are not strongenough to bear the increasing Laplace pressure during evapo-ration. The most obvious evidence is that for the soest PDMS-30 : 1 substrate the micropillars collapse aer the evaporationprocess. Through the optical microscope observation from thetop view, we can see that before the wetting transition, themicropillars stand upright well. During evaporation in the CCRand CCA modes, the micropillars remain intact. The micro-pillars collapse when the wetting transition from the Cassie tothe Wenzel state happens, as shown in Fig. 8(a). The wettingtransition oen occurs at somewhere close to the contact line ordefects and then water impales from the top of pillars into thebottom of the substrate and ows from one side to the other. Atthis moment, the micropillars are also pushed down by thewater ow leaking from the Cassie droplet and nally the wholedroplet transits into the Wenzel state.14 This observation can befurther conrmed by the experimental data of evolution ofcontact angle and contact radius of a water drop on the PDMS-30 : 1 substrate during the evaporation process from the sideview observation, as shown in Fig. 6. That is, a slight increase in

Soft Matter, 2014, 10, 3394–3403 | 3399

Fig. 8 (a) The optical microscope images of the PDMS-30 : 1substrate during the wetting transition from the Cassie state to theWenzel state. Initially, the pillars stood upright well and the water dropwas in the Cassie state. At a moment the pillars were pushed down bythe water flow leaking from the Cassie droplet, and finally the droplettransited into the Wenzel state and all the pillars under the dropletcollapsed. The whole process, from the start of collapse of the firstpillar to the end of collapse of all the pillars in the image, took about 45seconds. (The image size is about 0.58 mm � 0.58 mm.) (b) Variationof contact diameter of the sessile drop on the PDMS-30 : 1 substrateas a function of time during evaporation. (c) Optical microscope imageof a circular “stain” (collapsed pillars) left on the PDMS-30 : 1 substrateafter the evaporation process. The diameter of the circular stain (redsolid line shown in (c)) is consistent with the wetting transition pointillustrated in the evolution of contact diameter, as the red dashed lineshown in (b).

Fig. 9 (a) The overall process of the evaporation on PDMS-collapsedpillars. Blue line is referred to contact angle and green line representsrelative contact radius. (b) A series of top view images through thewater droplet sitting on PDMS-collapsed pillars. In the beginning, therewas air trapped inside. As time passed by, the bubbles graduallydecreased. At 500 seconds, all the bubbles almost disappeared.

Soft Matter Paper

Publ

ishe

d on

07

Febr

uary

201

4. D

ownl

oade

d by

Tre

nt U

nive

rsity

on

16/1

0/20

14 0

6:43

:44.

View Article Online

contact radius and a sudden decrease in contact angle are rstobserved at 3285 s on the right hand side (blue curves) of thewater drop, as the red dashed line B marked in Fig. 6. And then65 s later, another increase in contact radius and suddendecrease in contact angle are observed at 3350 s on the le handside (green curves) of the water drop, as the red dashed line Cmarked in Fig. 6.

Consequently, aer the evaporation process, there is acircular “stain” le on the PDMS-30 : 1 substrate due to thosecollapsed pillars, as shown in Fig. 8(c). The pattern of thecollapsed pillars is related to the water ow, in which thedirection of collapse of pillars is the same as the direction ofthe water ow.14 See the movie in the ESI of ref. 14 for the detailof the impregnating process of the water ow penetrating in-between the pillars and the direction of collapse of pillars.14 It isnoticed that, during wetting transition, the penetration of wateris not limited to one spot (defect) only. Usually there are twospots (defects) or more simultaneously impaled by water, and itprobably depends on the number and the location of thedefects. Thus the pattern of the collapsed pillars might bevariable, but the pillars at the outer ring, which is at theboundary between the collapsed pillars and the intact pillars,always collapse towards inside due to the shrinkage and surfacetension of the drop. Because of some defects on the surface, thedimension of the circular stain is not uniform and therefore we

3400 | Soft Matter, 2014, 10, 3394–3403

cannot specically determine the relationship between thesoness and the wetting transition. However, the dimension ofthe circular stain of collapsed pillars is consistent with thecontact diameter of the wetting transition point, as shown inFig. 8(b) and (c). Consequently, the circular stain of collapsedpillars is the ngerprint of the wetting transition from theCassie state to the Wenzel state.

We also performed the experiments of evaporation of asessile drop on the PDMS-collapsed-pillars substrate. It wasfound that the evaporation on this PDMS-collapsed-pillarssubstrate is quite different from that of the other patternedsubstrates. Fig. 9(a) shows the evolution of contact angle andcontact radius in the evaporation process of a sessile drop onthe PDMS-collapsed-pillars substrate. It is obvious that thecontact radius increases and the contact angle decreases at thebeginning stage of the evaporation process. An optical micro-scope was applied to delineate the origin of this phenomenonfrom the top view observation. A series of top view images areshown in Fig. 9(b). There are lots of air bubbles trapped amongthe collapsed pillars initially when a water drop is gentlydeposited onto the PDMS-collapsed-pillars substrate. The sizeof bubbles decreases along with time and eventually all thetrapped bubbles disappear. The water drop completely wets thePDMS-collapsed-pillars substrate and becomes a Wenzel drop.Therefore the initial increase and decrease in the contact radiusand contact angle, respectively, are simply due to the relaxationof the wetting process to eliminate air bubbles trapped insidethe deposited water drop on the substrate. Aer the trapped airbubbles are removed, as one can observe in Fig. 9(a), theevaporation process of the water droplet on the PDMS-collapsed-pillars substrate follows the CCR mode, then the CCAmode, and nally the mixed mode sequentially.

This journal is © The Royal Society of Chemistry 2014

Paper Soft Matter

Publ

ishe

d on

07

Febr

uary

201

4. D

ownl

oade

d by

Tre

nt U

nive

rsity

on

16/1

0/20

14 0

6:43

:44.

View Article Online

It is hard to determine the receding contact angle for thePDMS-collapsed-pillars substrate either by embedded needlemeasurement or by evaporation. For example, in Fig. 3(a), itseems to have a receding contact angle at 30� along the viewingangle of 0�. On the other hand, there is no obvious CCA modeobserved along the viewing angle of 45�, as shown in Fig. 3(c).The receding contact angles determined by embedded needlemeasurement are as low as 5.1� and 10.6� along the viewingangle of 0� and 45�, respectively, smaller than that observedfrom the evaporation process (Fig. 3(a)).

The evaporation process of a sessile drop on the PDMS-collapsed-pillars substrate is similar to the evaporation processaer the CCA mode on the soest PDMS-30 : 1 substrate, asshown in Fig. 3(a) and (b). It is reasonable for them to have thesimilar tendency, because both substrates are fabricated withexactly the same mixing ratio of the prepolymer base to thecuring agent and at last the water drops are in the Wenzel statewith collapsed pillars. Whenever the contact area is completelywetted, the contact line seems to be pinned again and thecontact angle gradually reduces, as the feature of the CCRmode.However, it is hard to recognize whether there are anotherreceding contact angles in the Wenzel state due to the graduallydiminishing and attening drop as well as the limit of resolu-tion. It is even harder for the PDMS-10 : 1 and PDMS-20 : 1substrates to be recognized that there is another CCR mode andreceding contact angle in the Wenzel state, since the initial sizeof the droplet in the Wenzel state is already too small to analyze.

According to the theory of drop evaporation,1,15,31 the evap-oration rate can be described by the diffusion model with thef(q) factor:

� dV

dt¼ 4pD

rL

�3V

pb

�13ðcs � cNÞf ðqÞ (1)

b ¼ 2 � 3 cos q + cos3 q (2)

f ðqÞ ¼ 0:00008957þ 0:6333qþ 0:1160q2 � 0:08878q3 þ 0:01033q4 for 0:175# q#p¼ 0:6366qþ 0:09591q2 � 0:06144q3 for 0# q\0:175 radians

(3)

where V is the drop volume, t is time (s), D is the diffusivity(m2 s�1), cs is the concentration of vapor at the liquid–vaporinterface (kg m�3), and cN is the concentration of vapor atinnite distance (kg m�3).

In the CCA mode, because of the constant value of contactangle, f(q) is also constant. Eqn (1) could be integrated by timeand found that the V2/3 is proportional to t.

V ¼ V0

�1� t

tCCA

�32; (4)

where Vo is the initial drop volume and tCCA is the total evapo-ration time in the CCA mode.1,15,31

However, in the CCR mode, only numerical solution can befound and it has been observed that the volume decreaseslinearly with time in the CCR mode.1,15,32

This journal is © The Royal Society of Chemistry 2014

V ¼ V0

�1� t

tCCR

�; (5)

where Vo is the initial drop volume and tCCR is the total evapo-ration 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 wellas to determine the transition point between the CCA and CCRmodes. The experimental data of drop volumes were obtainedfrom the side view images by integration of the drop prole andassuming that the dropwas composed of symmetric discs. Fig. 10shows the experimental results and theoretical calculations ofvolume change during the evaporation process. The curves forthe PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillarssubstrates have been displaced vertically for the ease of visuali-zation. That is, the initial drop volume of the system for thePDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars substrateswere shied downward by, respectively, one, two and three unitsin the log scale, as shown in Fig. 10. The solid line stands for ourexperimental results. The dotted line and dashed line are thetheoretical calculations for the CCR and CCAmodes, respectively.Generally, eqn (4) and (5) can well describe our experimentaldata. As the substrate becomes soer, the time duration of theCCR mode becomes longer. Eqn (4) ts well in the CCA mode,although in our observation the contact angle does not reallymaintain constant. Note that at the later stage of evaporation theWenzel state dominates, since the size of the droplet in theWenzel state is too small to analyze the results of PDMS-10 : 1and PDMS-20 : 1 substrates; the result of the PDMS-30 : 1substrate is chosen for further discussion. Fig. 11 shows thevariation of the volume and contact diameter of sessile drops onthe PDMS-30 : 1 substrate as a function of time. Aer the wettingtransition from the Cassie state to the Wenzel state occurs, thedynamic behavior of the evaporation process closely followsthe CCR mode. Thus the experimental data of drop volume fromthe beginning of the Wenzel state can be well described by eqn

(5), as blue dashed-and-dotted line shown in Fig. 11. It is obviousthat this second CCR mode only lasts for relatively a short periodof time, from 3303 to 4373 s, compared to the rst CCR mode(yellow dashed-and-dotted line), from 0 to 2587 s. Right aer thesecond CCRmode, another CCAmode takes over, as blue dashedline shown in Fig. 11, consistent with the results of the evapo-ration process of a sessile drop on the PDMS-collapsed-pillarssubstrate. Finally, it is interesting to nd out that the evaporationprocess of a sessile drop on the soest PDMS-30 : 1 substrate isidentied to exhibit four stages sequentially: CCR / CCA /

CCR / CCA. When the evaporation process of the sessile dropfalls in the rst CCR and CCA modes, the sessile drop is in theCassie state. Aer the sessile drop transitions into the Wenzelstate, the second sequence of the CCR and CCA modes isobserved in the evaporation mechanism.

Soft Matter, 2014, 10, 3394–3403 | 3401

Fig. 11 Variation of drop volume (black solid line) and contact diam-eter (green solid line) as a function of time during the evaporationprocess of a water drop on the PDMS-30 : 1 substrate along theviewing angle of 0�. Dashed-and-dotted and dashed lines representthe theoretical calculation results of the evaporation process,respectively, in the CCR mode and in the CCA mode. Yellow and bluecolors stand for the theoretical calculation results of the drop in theCassie state and in the Wenzel state, respectively. Red solid line Apoints out the occurrence of transition from the CCRmode to the CCAmode in the Cassie state. Red solid line B indicates the occurrence ofwetting transition from the Cassie state to the Wenzel state and thetransition from the CCA mode to the CCR mode. Red solid line Cpoints out the occurrence of transition from the CCRmode to the CCAmode in the Wenzel state.

Fig. 10 The experiment and theoretical calculations of volumechange with time (a) from the viewing angle of 0� (b) from the viewingangle of 45�. Solid line stands for the experimental results, dashed-and-dotted line is the theoretical calculation of the CCRmode and thedashed 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. Thecurves for the PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillarssubstrates have been displaced vertically for ease of visualization.

Soft Matter Paper

Publ

ishe

d on

07

Febr

uary

201

4. D

ownl

oade

d by

Tre

nt U

nive

rsity

on

16/1

0/20

14 0

6:43

:44.

View Article Online

Finally, Fig. 10 also demonstrates that the total evaporationtime for four different substrates is in the order of PDMS-10 : 1 >PDMS-20 : 1 > PDMS-30 : 1 > PDMS-collapsed-pillars. In otherwords, a water droplet on the so patterned substrate evaporatesfaster than that of the hard patterned substrate, consistent withthe nding for at PDMS substrates.15 Furthermore, we alsoperformed the evaporation experiments of 6 mL water droplets onthe at PDMS (30 : 1) substrate to examine the effect of thesurface pattern on the evaporation process. It is interesting tond out that the total evaporation time for three differentsubstrates of same elasticity (at a xed mixing ratio 30 : 1) is inthe order of PDMS-30 : 1 > at PDMS (30 : 1) > PDMS-collapsed-pillars. That is, the water droplet on the at PDMS (30 : 1)substrate evaporates faster than that of the PDMS-30 : 1substrate, consistent with a recent study on hard surfaces,33 butslower than that of the PDMS-collapsed-pillars substrate.

As pointed out by Lopes and Bonaccurso,15 a water dropletcompletely evaporates in CCR mode much faster than that inCCA mode with a same initial condition. Therefore, as thesubstrate becomes soer, the receding contact angle becomessmaller, the time duration in CCR mode becomes longer, and

3402 | Soft Matter, 2014, 10, 3394–3403

the evaporation becomes faster. The receding contact angles ofthese three substrates of same elasticity are in the order ofPDMS-30 : 1 > at PDMS (30 : 1) > PDMS-collapsed-pillars, asgiven in Tables 1 and 2. That is, the smaller the receding contactangle is, the faster the evaporation is.

4. Conclusions

In this study, the evaporation of sessile drops on four differentsubstrates: PDMS-10 : 1, PDMS-20 : 1, PDMS-30 : 1 and PDMS-collapsed-pillars are carefully examined. Three modes (CCR, CCAand mixed mode) can be distinguished during evaporation ofsessile drops on the PDMS-10 : 1, PDMS-20 : 1, and PDMS-collapsed-pillars substrates. The CCR mode comes at rst, andwhen the receding contact angle is attained, the CCA mode takesover. Finally, both contact radius and contact angle decrease andthe mixed mode appears till the end of evaporation.

The soness of the patterned substrate has a great effect onthe receding contact angle: the soer the substrate is, thesmaller the receding contact angle is. Therefore, with the sameinitial condition, a sessile drop on the soest PDMS-30 : 1substrate will stay in the CCR mode for the longest time due tothe smallest receding contact angle. The contact angle of thesessile drop does maintain to be almost constant in the CCAmode during the evaporation and the three-phase-contact-lineof the sessile drop exhibits the slip-jump-stick behavior peri-odically accompanied by the stepwise decrease of contactradius. The average slip-jump-stick distance is directly relatedto the patterned structure: from the viewing angle of 0�, theaverage distance per slip-jump-stick is just a unit length ofthe patterned structure (a + d); from the viewing angle of 45�,the average distance per slip-jump-stick is about half of the unit

This journal is © The Royal Society of Chemistry 2014

Paper Soft Matter

Publ

ishe

d on

07

Febr

uary

201

4. D

ownl

oade

d by

Tre

nt U

nive

rsity

on

16/1

0/20

14 0

6:43

:44.

View Article Online

of diagonal�aþ dffiffiffi

2p

�. The CCA mode ends when the wetting

transition from the Cassie state to the Wenzel state occurs.While the substrate is soer, the wetting transition happensearlier because the soer pillars relatively cannot stand theincreasingly high Laplace pressure. Especially for the soestPDMS-30 : 1 substrate, the micropillars collapsed to induce theearly wetting transition and ended up remaining a roundedmark. Right aer the wetting transition, the sessile drop is inthe Wenzel state and further evaporation resumes the CCRmode followed by the CCA mode sequentially. Consider theevaporation rate, a water droplet on the at substrate evaporatesfaster than that of the patterned substrate and the water dropleton the soer patterned surface evaporates faster.

Nomenclature

a

This jo

The dimension of pillar [mm], dened in Fig. 1

cs The concentration of vapor at the liquid–vapor interface

[kg m�3]

cN The concentration of vapor at innite distance [kg m�3] d The distance between two pillars [mm], dened in Fig. 1 D The diffusivity [m2 s�1] f(q) A function of contact angle q, dened by eqn (3) h The pillar height [mm], dened in Fig. 1 rl Relative contact radius on the le hand side of a drop,

dened in Fig. 2(b)

rr Relative contact radius on the right hand side of a drop,

dened in Fig. 2(b)

t Time [s] tCCA The total evaporation time in CCA mode [s] tCCR The total evaporation time in CCR mode [s] V The drop volume Vo The initial drop volume ql Contact angle on the le hand side of the drop, dened in

Fig. 2(b)

qr Contact angle on the right hand side of the drop, dened

in Fig. 2(b)

q Contact angle [radians].

Acknowledgements

This work was supported by the National Science Council ofTaiwan.

References

1 R. G. Picknett and R. Bexon, J. Colloid Interface Sci., 1977, 61,336–350.

2 C. Bourges-Monnier and M. E. R. Shanahan, Langmuir, 1995,11, 2820–2829.

3 G. McHale, S. Aqil, N. J. Shirtcliffe, M. I. Newton andH. Y. Erbil, Langmuir, 2005, 21, 11053–11060.

urnal is © The Royal Society of Chemistry 2014

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, SoMatter, 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, Viscoelasticeffects 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.

Soft Matter, 2014, 10, 3394–3403 | 3403