Colloids and Surfaces A: Physicochem. Eng. Aspects 248 (2004) 101–104

Contact angle hysteresis on rough hydrophobic surfaces

Bo He, Junghoon Lee, Neelesh A. Patankar∗

Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, B224 Evanston, IL 60208-3111, USA

Received 9 April 2004; accepted 8 September 2004

Abstract

In this short note, we report a quantitative investigation of the hysteresis of the Cassie and Wenzel drops on a given rough surface. TheCassie drop shows much less hysteresis compared to a Wenzel drop and is therefore preferred in applications involving moving droplets. Theexperimental measurements are compared with the various theoretical models for the apparent contact angles and recommendations are made.© 2004 Elsevier B.V. All rights reserved.

Keywords:Contact angle hysteresis; Advancing angle; Receding angle; Self-cleaning surface; Lotus effect; Roughness induced superhydrophobicity

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. Introduction

Surface roughness amplifies hydrophobicity. Superhy-rophobic surfaces are good self-cleaning surfaces like somelant leaves, e.g., lotus. Water drops are almost spherical on

hese plant leaves and can easily roll off, cleaning the surfacen the process[1]. This is usually referred to as the Lotusffect. The key ingredients for these applications are, a largeontact angle of the fluid drop on the rough surface (i.e.,uperhydrophobic) and the ability of the drop to roll off orove easily (i.e., low hysteresis) on the rough surface. Su-erhydrophobic surfaces are also desirable for channel flowsince it can reduce resistance to the flow[2].

It is now known that there are typically two states in whichdrop can reside on a given rough surface[3,4]. The drop

ither sits on the peaks of the surface roughness (to be referredo as a drop with a composite contact) or it wets the groovesto be referred to as a drop with a wetted contact), dependingn how it is formed. The drop that sits on the peaks has ‘airockets’ along its contact with the substrate.

The apparent contact angle of the drop that wets the

shown that, of the two possible states, the one with a loweparent contact angle has lower energy. Geometric paramof the surface roughness determine whether Cassie or Wdrop has lower energy[7,8]. We verified our predictions bperforming experiments[4].

It is known from the experiments with Lotus leaves[1]that a Cassie drop rolls easily, i.e., it shows less hysteThus, it is important to design superhydrophobic roughfaces such that a Cassie drop is formed. A Wenzel drop,if superhydrophobic, is expected to show much largerteresis due to the wetting of the grooves[9,10]. Johnson anDettre [11] hypothesized based on the principle of enebarriers that the Cassie drop should have lower contacthysteresis compared to a Wenzel drop. This was qualitasupported by their experiments with roughened wax sur[12]. Current microfabrication technology permits more ctrolled experiments where the roughness of the surface cquantified in terms of the geometric parameters. Both Cand Wenzel drops can be formed on the same rough sudepending on how a drop is formed[3,4]. Hence, it is of interest to study hysteresis of these drops on the same s

rooves is given by Wenzel’s formula[5] while the appar-nt contact angle of a drop that sits on the roughness peaks isiven by Cassie’s formula[6]. Theoretical analysis[7,8] has

15.

unlike previous studies[12].In this note, we quantify the hysteresis of Cassie and

Wenzel drops on a given rough surface. Experiments wereconducted to measure the advancing and receding con-t e ofp rge

d.

∗ Corresponding author. Tel.: +1 847 491 3021; fax: +1 847 491 39E-mail address:n-patankar@northwestern.edu (N.A. Patankar).

927-7757/$ – see front matter © 2004 Elsevier B.V. All rights reserveoi:10.1016/j.colsurfa.2004.09.006

act angles on a given rough hydrophobic surface madoly(dimethylsiloxane) (PDMS). The Wenzel drop has la

102 B. He et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 248 (2004) 101–104

hysteresis. We compare the experimental measurements withvarious theoretical models for the apparent contact angles.This sheds some light on the microscopic view of the ad-vancing and receding fronts of a drop.

2. Experimental

The rough substrate made of PDMS was fabricated usingsoft lithography technique[13]. A mold made of the negative-tone UV photoresist (MicroChem Corporation, SU8-25,Newton, MA) was generated using MA6 mask aligner in thecontact mode (SUSS MicroTech Inc., Tempe, AZ). The pro-cessing parameters were empirically tuned to achieve the de-sired SU-8 layer thickness, which is 30�m (Detailed SU8process procedure can be found in[14]). A curing agentand PDMS prepolymer (Sylgard 184 Silicone Elastomer Kit,Dow Corning, Midland, MI)[15] were thoroughly mixed ina 1:10 weight ratio and stirred to ensure the complete mixingbetween two parts. The liquid mixture was left in air for 2–3 hto degas the air bubbles. Then it was cured at 80◦C for 1 h ina vacuum oven. After curing, the PDMS replica was peeledfrom the mold and cut with a razor into small pieces. Ourfabrication process is presented in greater detail in[4].

The contact angle measurement was carried out by a go-n A)t t on asd rop isf singt n ad-v Thea e in-c 0R uctedb ps.T olumer anglem thes d byd

3

illars.Ag entswH acta enzed

orre-s anglec vanc-i ace.

Fig. 1. An SEM image of a typical microfabricated rough surface.

They were 115 and 88◦, respectively. Here ‘flat’ implies thatthe surface is not roughened by microfabrication. Microscop-ically (i.e., on length scales much smaller that the 10�m scaleof the microfabricated roughness) the PDMS surface may notbe perfectly smooth and may have heterogeneities that giverise to its advancing and receding angles.

Fig. 2shows the contact angle measurements, of a Cassiedrop, for increasing volumes on a rough substrate. When asmall drop is deposited on the surface, it typically forms acontact angle between the advancing and receding values forthe rough substrate. As the drop volume is increased the ap-parent contact angle increases until it reaches the maximumstatic angle. We define this the advancing contact angle of therough surface. Once the advancing value of the contact angleis reached, further increase in volume does not significantlychange the apparent angle of the drop. Microscopically, theincrease in the apparent angle with volume could be due tothe pinning of the contact line on the substrate. Once theadvancing contact angle is reached, the contact line moves(rather than pinning) thus resulting in no significant changein the apparent contact angle of the drop. Thus,Fig. 2givesan advancing angle between 152 and 153◦ for a Cassie dropon the rough substrate.

Fig. 2 also shows a plot of the receding contact anglemeasurements for a Cassie drop. The volume reduction isb ngle

F e drop.T nd thed

iometer (AST Products Inc., VCA Optima XE, Boston, Mhat takes and analyzes the image of a sessile dropleurface. A droplet with small volume (2–7�L) was gentlyeposited on the substrate to ensure that a Cassie d

ormed[4]. The drop volume was increased in steps uhe automatic dispensing syringe. The contact line is aancing front due to the increase in the drop volume.dvancing contact angle was measured after each volumrement. The drop volume was increased up to about 1�L.eceding contact angle measurements were then condy removing fixed amount water from the droplet in stehe apparent contact angle was measured after each veduction step. The advancing and receding contacteasurements for the Wenzel drop were carried out in

ame way except that a wetted contact is initially formeropping the water droplet from some height[4].

. Results and discussion

The rough substrate is an ordered array of square ptypical microfabricated surface is shown inFig. 1. The

eometric parameters for the surface used for the experimere:a= 22.7�m, b= 28.7�m, H= 30�m, wherea, b andare defined inFig. 1. The advancing and receding cont

ngle measurements were made for both Cassie and Wrops as discussed in the previous section.

A surface typically has an advancing contact angle cponding to an advancing front and a receding contactorresponding to a receding front. We measured the adng and receding contact angles of a ‘flat’ PDMS surf

l

egun from the last drop obtained in the advancing a

ig. 2. Advancing and receding contact angle measurement of a Cassihe plot indicates a hysteresis loop for the apparent contact angle arop volume.

B. He et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 248 (2004) 101–104 103

Fig. 3. Advancing contact angle measurement of a Wenzel drop.

measurements. Once again we see an initial decrease in theapparent contact angle of the drop, with decreasing volume, isfollowed by an almost constant value. The receding contactangle for the Cassie drop is thus found to be about 132◦.The difference between the advancing and receding valuesis a measure of the hysteresis. This is also evident from ahysteresis loop defined by the plots for the advancing andreceding angle measurements (Fig. 2).

Fig. 3shows that the advancing contact angle for the Wen-zel drop on the same rough surface is between 142 and 143◦.No conclusions could be drawn regarding the receding con-tact angle (Fig. 4) of a Wenzel drop. The apparent contactangle kept decreasing with decreasing volume up the small-est drop volume we could handle. As inFigs. 2 and 3, wedid not get a constant apparent angle with decrease in thedrop volume. The results imply that the Wenzel drop, dueto the wetting of the grooves, exhibits very large hysteresis.Therefore, it is undesirable for applications involving dropletmotion. Cassie drops are preferred due to significantly lesshysteresis.

Next, we investigate models to predict the advancing andreceding contact angles of drops on rough surfaces. To thisend, few comments are in order. The contact angle hysteresisof the roughened surface considered here can be attributed totwo aspects, first is the effect of hysteresis at the microscopics ngleso f ther tables erenta

The influence of the first effect can be accounted for byconsidering the advancing and receding angles of the surfacematerial in the respective Cassie and Wenzel formulas to getthe apparent angles of the artificially roughened surface. Thisis done below. This is reasonable, because, microscopicallythe front is advancing or receding during the experiments.However, the apparent angles, so estimated, will representenergy minima based on the advancing and receding anglesof the surface material.

To estimate the second effect, following e.g., the hypoth-esis of Johnson and Dettre[11], will involve the estimationof the energy barriers of the artificially roughened surface.This is not considered in the current work mainly, because,quantitative models to relate energy barriers to contact anglehysteresis are not well established. Note that the second ef-fect will represent deviations of the advancing and recedingangles in addition to those represented by the first effect.

In this work, we will consider the first effect and enquirehow these predictions compare with the experimental mea-surements. The following Cassie formula is of interest

cosθcadv = f cosθf

adv + f − 1 (1)

wheref is the area fraction of the peaks of the square pillarson the horizontal surface,f=a2/(a+b)2 = 0.1950. Subscript‘c Notetpt y theC ace.T g for-w S).I ents[

dropc

c

wT of1 ther t liner a thinfi ingb gc

c

i-m Bicoe yt er

cale i.e., the influence of advancing and receding af the PDMS surface itself, and second is the effect ooughness geometry that gives rise to additional metastates in which a drop can get trapped thus leading to diffdvancing and receding angles[11].

Fig. 4. Receding contact angle measurement of a Wenzel drop.

adv’ denotes advancing angle and superscriptscandf denoteomposite contact and the PDMS surface, respectively.hatθf

adv= 115◦ for PDMS. Eq.(1) givesθcadv= 152.5◦ com-

ared to the experimental value between 152 and 153◦. Thus,he advancing angle of a Cassie drop is well predicted bassie formula with the advancing angle for the flat surfhis is reasonable since an advancing front is also movinard microscopically on the surface material (here PDM

t can be verified that the data from previous experim3,4] are also well represented by Eq.(1).

Modeling of the receding contact angle of the Cassiean be done analogous to Eq.(1).

osθcrec = f cosθf

rec + f − 1 (2)

here subscript ‘rec’ denotes receding angle andθfrec= 88◦.

his givesθcrec= 143◦ compared to an experimental value

32◦. Patankar[7] proposed another model to estimateeceding contact angle for Cassie drops. As the contacecedes, it is assumed that the droplet leaves behindlm of liquid on the peaks of the pillars instead of leavehind a dry surface (as assumed in Eq.(2)). The recedinontact angle in this case is given by

osθcrec = 2f − 1 (3)

Eq. (3) givesθcrec= 127.6◦ which is closer to the exper

ental value. It may be noted that the experiments oft al. [3] also agree with Eq.(3) better. It is therefore likel

hat the mechanism implied by Eq.(3) plays some role in theceding contact angle of Cassie drops.

104 B. He et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 248 (2004) 101–104

The advancing contact angle of the Wenzel drop can bepredicted by Wenzel’s formula

cosθwadv = r cosθf

adv (4)

where superscriptw denotes a wetted contact andr is the solidroughness, defined as the ratio of the actual solid–liquid con-tact area to the contact area projected on the horizontal plane.Thus,r = ((a+b)2 + 4aH)/(a+b)2 = 2.0311 for our rough sur-face. Eq.(4) givesθw

adv= 149◦ compared to the experimentalvalue of 142◦.

Models for the receding contact angle of a Wenzel dropon a rough surface are not evident. Even when a Wenzel dropsimply deposited on a rough surface shows hydrophobicity,we conclude that the hysteresis is significant due to the wet-ting of the grooves.

4. Conclusions

In this note, we measure the advancing and receding con-tact angles of Cassie and Wenzel drops on a given rough sur-face. The Cassie drop shows much less hysteresis comparedto a Wenzel drop and is therefore preferred in applicationsinvolving moving droplets. The uniqueness of this work isa quantitative study of the hysteresis of Cassie and Wenzeld g andr wn inF loopi ersust not

observed primarily because no receding contact angle couldbe defined for this case. The experimental measurements arecompared with the various theoretical models for the apparentcontact angles and recommendations are made.

Acknowledgment

This work has been supported by DARPA (SymBioSys)grant (contract # N66001-01-C-8055) with Dr. Anantha Kr-ishnan as monitor.

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[ et,

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