Morphology of Evaporating Sessile Microdroplets on Lyophilic

Subscriber access provided by University of Michigan-Flint

Interfaces: Adsorption, Reactions, Films, Forces, Measurement Techniques, Charge Transfer, Electrochemistry, Electrocatalysis, Energy Production and Storage

Morphology of Evaporating Sessile Microdroplets on Lyophilic Elliptical Patches José Manuel Encarnación Escobar, Diana Garcia-Gonzalez, Ivan Devic, Xuehua Zhang, and Detlef Lohse Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b03393 • Publication Date (Web): 09 Jan 2019 Downloaded from http://pubs.acs.org on January 10, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Morphology of Evaporating Sessile Microdroplets on Lyophilic Elliptical Patches José M. Encarnación Escobar,†,k Diana Garc´ıa-González ,†,‡,k Ivan Dević ,† Xuehua Zhang,∗,¶ and Detlef Lohse∗,† †Department of Physics of Fluids, University of Twente, Enschede, The Netherlands ‡Max Planck Institute for Polymer Research, Mainz, Germany ¶Department of Chemical & Materials Engineering, University of Alberta, Edmonton, Alberta, Canada §Max Plank Institute for Dynamics and Self-Organization, Göttingen, Germany kBoth authors contributed equally to this work E-mail: [email protected]; [email protected]

1

Abstract

2

The evaporation of droplets occurs in a large variety of natural and technolog-

3

ical processes such as medical diagnostics, agriculture, food industry, printing, and

4

catalytic reactions. We study the different droplet morphologies adopted by an evapo-

5

rating droplet on a surface with an elliptical patch with a different contact angle. We

6

perform experiments to observe these morphologies and use numerical calculations to

7

predict the effect of the patched surfaces. We observe that tuning the geometry of

8

the patches offers control over the shape of the droplet. In the experiments, the drops

9

of various volumes are placed on elliptical chemical patches of different aspect ratios

10

and imaged in 3D using laser scanning confocal microscopy, extracting the droplet’s

11

shape. In the corresponding numerical simulations, we minimize the interfacial free

1

ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

12

energy of the droplet, employing Surface Evolver. The numerical results are in good

13

qualitative agreement with our experimental data and can be used for the design of

14

micro-patterned structures, potentially suggesting or excluding certain morphologies

15

for particular applications. However, the experimental results show the effects of pin-

16

ning and contact angle hysteresis, which are obviously absent in the numerical energy

17

minimization. The work culminates with a morphology diagram in the aspect ratio vs

18

relative volume parameter space, comparing the predictions with the measurements.

19

Introduction

20

The use of patterned surfaces to control the behavior of liquid drops is not only a re-

21

current phenomenon in nature, but it is also useful in various industrial and scientific

22

applications. For instance, the observation of nature inspired the use of patterned sur-

23

faces for water harvesting applications 1 as well as the fabrication of anti-fogging 2 and

24

self-cleaning materials 3 . The geometry of droplets and the substrates in which they lay

25

can affect their adhesion, as can their evaporation and other important properties 4–6 .

26

The interest in wetting motivated by applications covers a wide range of scales and

27

backgrounds from microfluidics 7–9 to catalytic reactors 10 , including advanced printing

28

techniques 11,12 ; improved heat transfer 13,14 ; nano-architecture 15–17 ; droplet-based di-

29

agnostics 18 or anti-wetting surfaces 19–21 . Aside from all the practical significance, we

30

have to add the interest on wetting fundamentals 22 , including contact angle hystere-

31

sis and dynamics 23–25 ; contact line dynamics 26 ; nanobubbles and nanodroplets 27–29 ;

32

spreading dynamics 30,31 ; and complex surfaces 32,33 .

33

34

Due to the complexity of the field, most previous studies have restricted themselves

35

to considering geometries with constant curvature as straight stripes or constant cur-

36

vature geometries, namely circumferences. In this work we will study the behavior

37

of evaporating drops on lyophobized substrates that have lyophilic elliptical patches.

38

The elliptical shape for the patches is chosen as a transitional case between a circular

2


Page 2 of 39

Page 3 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

39

patch 34 and a single stripe 35–38 , having the uniqueness of a perimeter with non-constant

40

curvature. When a drop is placed on a homogeneous substrate, the minimization of

41

surface energy leads to a spherical cap shape. This is traditionally described by the

42

Young-Laplace, Wenzel, or, for pillars or patterns with length scales much smaller

43

than the drop, Cassie-Baxter relations 39–42 , which reasonably apply to homogeneous

44

substrates or substrates with sufficiently small and homogeneously distributed hetero-

45

geneities 43–45 , which are not the focus of this study.

46

Our previous work (Dević et al. 46 ) based on Surface Evolver and Monte Carlo cal-

47

culations showed that, when a droplet rests on an elliptical patch, four distinguishable

48

morphologies are found, depending on the volume of the drop and the aspect ratio of

49

the patch. These morphologies were termed 46 A, B, C and D, see figure 1. When a

50

large enough droplet evaporates on an elliptical patch, the first morphology found is D.

51

In this case, the droplet completely wets the ellipse with a part of its contact line out-

52

side the ellipse and the rest pinned to the contour of the patch. After a certain volume

53

loss, the droplet adopts either morphology B or C - depending on the geometry of the

54

patch. In morphology B, a part of the droplet’s contact line remains outside the patch

55

while the rest is already inside the patch. In contrast, the contact line of a droplet

56

adopting morphology C follows the perimeter of the ellipse. The final morphology to

57

be found for evaporating drops is morphology A, characterized by a part of its contact

58

line following the perimeter of the ellipse and the rest of the contact line laying inside

59

it.

60

Methods

61

In this paper we perform corresponding experiments and numerical simulations, per-

62

formed again with Surface Evolver using the experimental parameters. Both the ex-

63

periments and the calculations are performed for Bond numbers below unity to avoid

64

the effects of gravity. Moreover, the experiments are performed at room temperature

65

with a relative humidity of 38±2% in a closed and controlled environment, ensuring

3


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1: Scheme of the morphologies of a droplet as seen from the top as expected from the calculations by Dević et al. 46

Figure 2: Left: Coordinate system employed in this paper. θ1 and θ2 are, respectively, the Young’s angles of the lyophobic (white) and lyophilic (red) regions. R(φ) is the distance from the center of the ellipse to the contact line of the droplet (blue), and a and b are the major and minor axis respectively. S indicates the vertical section. Right: Experimental results: Top view images taken during the evaporation of various droplets on ellipses with different sizes and aspect ratios, the red contours represent the elliptical patches on the surface. A) Morphology A, droplet on an ellipse of aspect ratio b/a=0.61 and semi-major axis a=512±16µm. B) Morphology B, droplet on an ellipse of aspect ratio b/a=0.43 and semi-major axis a=392±20µm. C) Morphology C, droplet on an ellipse of aspect ratio b/a=0.98 and semi-major axis a=410±20µm. D) Morphology D, droplet on an ellipse of aspect ratio b/a=0.69 and semi-major axis a=411±20µm.

4


Page 4 of 39

Page 5 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

66

that the evaporation driven volume change is slow enough so that the droplets evolve

67

in quasi-static equilibrium. The effects of humidity, evaporative cooling, and evapo-

68

ration driven flows do not have any important effects. However, for heated or cooled

69

substrates or more volatile liquids this situation may change. Unlike the gravitational

70

and evaporative effects, the effects of the inhomogeneities of the substrate —like pin-

71

ning and contact angle hysteresis— are unavoidable in our experiments while they are

72

absent from the Surface Evolver calculations.

73

Preparation of substrates with lyophilic elliptical patches

74

The patched substrates were prepared via photolithography followed by chemical va-

75

por deposition (CVD) of a mono layer of trimethylchlorosilane (TMCS). The 100 x

76

100 mm2 chromium on glass photo-mask used was designed with an array of ellipses

77

of aspect ratios varying from 0.3 to 1 and sizes varying from a=320µm to b=2500µm,

78

see figure 3 (a), and fabricated in the MESA+ Institute clean room facilities of the

79

University of Twente, using laser writing technology. The substrates were glass slides

80

(20 × 60 mm2 ) of 170 µm thickness, which is optimal for confocal microscopy. The

81

photolithography steps of the fabrication, outlined in figure 3 (b), were performed in

82

a cleanroom environment. First, the substrates were pre-cleaned in a nitric acid bath

83

(NOH3 , purity 99%) followed by water rinsing and nitrogen drying. Subsequently,

84

we dehydrated the substrate (120◦ C, 5 min). After dehydration, we spin-coated the

85

photoresist (Olin OiR, 17 µm), pre-baked it (95◦ C, 90 s) and proceeded with the align-

86

ment of the photomask and UV irradiation (4 s, 12 mW/cm2 ). Once the photoresist

87

was cured, we developed and post-baked it (120◦ C, 10 min). Finally, the substrates

88

were taken outside the clean-room environment for the CVD ( 2 h, 0.1 MPa) of a

89

TMCS monolayer (Sigma Aldrich, purity ≥ 99%) to lyophobize the exterior of the el-

90

lipses. The photoresist was later stripped away by rinsing the substrates with acetone,

91

cleaned with isopropanol and dried using pressurized nitrogen.

5


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a) Design Photomask

Page 6 of 39

b) 1

Pre-cleaning with NOH3 Developement photoresist Glass Substrate 4 Spin-coating photoresist

2

Photoresist

CVD deposition of TMCS 5 TMCS

UV light through photomask

5 mm

6

3

TMCS elliptical patches TMCS

Figure 3: a) Array of ellipses of aspect ratios varying from 0.3 to 1 and sizes varying from a=320 µm to b=2500 µm fabricated on the photomask. b) Simplified steps of the substrates’ fabrication in the order indicated by the numbers. 92

Experimental data acquisition and analysis

93

For all the measurements, we used droplets of ultrapure (Milli-Q) water dyed with

94

Rhodamine 6G at a concentration of 0.2 µg/ml. The droplet was deposited cover-

95

ing the lyophilic patch and imaged by laser scanning confocal microscopy (LSCM) in

96

three dimensions during the evaporation process. After deposition of the droplet, the

97

substrate was covered to avoid external perturbations.

98

In figure 4, we show four examples of three-dimensional reconstructions of a stack

99

of scans with increasing heights taken under LSCM. For each scan, we detected the

100

surface of the drop using a threshold algorithm, allowing for the three-dimensional

101

reconstruction of the drop. Using this data we calculate the local contact angle at

102

every point detected on the contact line. For the measurement of the contact angle θ,

103

we extract the height profile along the contact line. This can be achieved, as sketched

104

in figure 2, by identifying the tangent to each point of the contact line at an angle

105

φ and finding the points belonging simultaneously to its normal plane S and to the

106

surface of the droplet.

107

We extracted three-dimensional images of evaporating water droplets using LSCM.

108

From the three-dimensional data we measured the local contact angle along the three-

109

phase contact line through the azimuthal angle φ. Figure 2, right, shows top views

110

of various evaporating droplets as examples of each of the morphologies introduced

6


Page 7 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

111

previously. The lyophilic elliptical islands of the substrate are highlighted by red curves.

112

We adopted a cylindrical coordinate system with its origin at the center of the

113

ellipse. The polar axis was fixed to be in the direction of one of the major semi-axes a as

114

shown in figure 2 (left). We set the large semi-axis (a) of the ellipse as the characteristic

115

length scale for this system and the aspect ratio of the ellipses b/a to characterize the

116

geometry of the patch. The relative volume of the droplets is normalized as V /a3 .

Figure 4: Three-dimensional reconstruction of the shape extracted from the LSCM data collected for four different droplets adopting morphologies A, B, C and D respectively as performed for the extraction of the contact angle along the contact line with the shape of the elliptical patch, highlighted in red lines. Repeatability is subjected to the initial position of the droplet and pinning of the contact line which can affect the symmetry of the shape as well as delay the transition between phases as compared to the predictions. In figure 6 all the morphologies observed during the experiments are shown.

117

Calculations

118

We compute the surface energy minimization using Surface Evolver, a free software

119

package used for minimization of the interfacial free energy developed by Brakke 47 , to

120

extract the droplet’s shape and local contact angle as in the previous work by Dević

121

et al. 46 . An initial shape of the droplet and the characteristic interfacial tensions of

122

the surfaces are given to Surface Evolver as an input. The software minimizes the

123

surface energy by an energy gradient descent method. Since hysteresis is not captured

7


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

124

by our simulations, we compared each group of experimental results with two different

125

calculations: one considering the receding contact angles for the two regions, and the

126

other considering the advancing contact angle for the lyophilic part.

127

To perform the calculations, we measured the contact angles of both the lyophilic

128

and lyophobic parts of our patches. To do this, we treated two separated substrates ho-

129

mogeneously in the same manner as in these two regions. We measured the advancing

130

and receding contact angles on both substrates. Respectively for the lyophobic (sub-

131

script 1) and lyophilic surfaces (subscript 2), the advancing contact angles measured

132

were θa1 = 85±3◦ and θa2 = 33±4◦ , and the receding contact angles were θr1 = 49±3◦

133

and θr2 = 15 ± 4◦ . During the experiments, we observed variations between 5% and

134

10% of the contact angle due to occasional pinning events.

135

Results

136

In this section, we present the results of our experiments and the Surface Evolver cal-

137

culations for each of the observed morphologies. In Figure 5, each row presents one

138

of the morphologies shown previously in Figure 4. For each morphology, we show

139

the normalized footprint radii R/a next to the local contact angles θ, both along the

140

azimuthal coordinate φ. In each of the plots we overlay experimental and computa-

141

tional results. The red and blue markers represent the calculations done considering

142

the lyophilic contact angle θ2 = 33◦ and θ2 = 15◦ , respectively. In the plots of the

143

normalized footprint radii we plot the position of the patch contour (black curve).

144

To follow the chronological sequence of our evaporating experiments, we present

145

the results starting from morphology D (largest droplet volume) and finishing with

146

morphology A (smallest droplet volume). Finally, in figure 6 we present the morphology

147

diagrams predicted by the Surface Evolver calculations (colored areas) and compare

148

those with the results of all our experiments (colored markers).

8


Page 8 of 39

Page 9 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

149

Morphology type D

150

In figure 5 (a and b), we can see an example of an experiment in which morphology

151

D was found. The normalized footprint radius R/a and the contact angle are plotted

152

along the azimuthal coordinate. From the figure, we observe reasonable agreement

153

between Surface Evolver calculations and experiments. However, the existence of inho-

154

mogeneities introduces pinning and hence, a delay in the movement of the contact line.

155

This delay translates into an experimental radius larger than that predicted by the

156

Surface Evolver calculations. Despite this mismatch of the contact line, consequence

157

of individual pinning events of the contact line, we obtain reasonable agreement with

158

the contact angle calculations.

159

Morphology type C

160

Morphology C appeared for ellipses of higher aspect ratio b/a as compared to morphol-

161

ogy B. Additionally, when evaporating, the drop reaches morphology C always through

162

morphology D, implying that any pinning event of the contact line outside the ellipse

163

prevents morphology C. Indeed, the transition from morphology D to C was always

164

found in a later stage of evaporation than predicted by theory, i.e., for lower volumes

165

(see figure 6 (b)).

166

In figure 5 (c and d), we show a droplet of volume V /a3 =0.37 placed on a high

167

aspect ratio ellipse (b/a=0.98). The results of the calculations predict morphology C

168

and contact angles between the receding and the advancing ones. The contact angle

169

and the contact line show always good agreement with the Surface Evolver calculations.

170

This is expected as it is the closer case to the trivial spherical cap shape.

171

Morphology type B

172

The experimental data shown in figure 5 e and f, are particularly interesting as this

173

case presents a strong asymmetry in the radius caused by a sharp pinning point which

174

can be identified at φ ≈ 120◦ (indicated by an arrow in figure 5 e). Unlike the radius,

9


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

175

the contact angle shows a symmetric behavior. We found that pinning leads to an

176

asymmetric behavior in this morphology for all our experiments but, besides the asym-

177

metry forced by pinning, the experiments agree with the Surface Evolver calculations.

178

The good match for the angle can be explained considering that the contact angle at

179

every point of the contact line –far enough from the ellipse contour– is dictated by the

180

chemistry of the surrounding substrate.

181

Morphology type A

182

The experimental results showed morphology type A as predicted by the calculations

183

for θ2 = 15◦ , with a part of the contact line pinned at the boundaries of the ellipse and

184

the rest of the contact line inside the ellipse. Note that, in the calculations for the higher

185

receding contact angle (θ2 = 33◦ ), the results predict a spherical cap shape with radius

186

R < b. However, our results for the contact angle were not in good agreement with

187

either of the Surface Evolver calculations, but rather an intermediate state between

188

them, subjected to the irregularities of the edge (see figure 5 g and h. This can be

189

due to imperfections of the coating in the edges of the ellipse. The high portion of

190

the contact line that remains pinned at the boundary between the lyophilic and the

191

lyophobic parts appeared to be very sensitive to the quality of the patch rim.

10


Page 10 of 39

Page 11 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 5: Normalized footprint radius R/a and contact angle θ along the azimuthal coordinate φ (as defined in figure 2). Experimental results for the four different morphologies (green). From top to bottom; morphology D (V /a3 = 0.40, b/a = 0.69, and a = 411±20µm); morphology C (V /a3 = 0.37, b/a = 0.98, and a = 410 ± 20 µm); morphology B (V /a3 = 0.30, b/a = 0.43, and a = 392 ± 20 µm); and morphology A (V /a3 = 0.08, b/a = 0.60, and a = 512 ± 16 µm). Results of the numerical simulations considering the lyophilic contact angles θ2 = 15◦ (blue) and θ2 = 33◦ (red). The black curve in the radius plot shows the contour of the elliptical patch. 11


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

192

Morphology Diagrams

193

Figure 6 presents two morphology diagrams showing all the morphological regions

194

and transitions predicted by the Surface Evolver calculations (as color shaded areas),

195

together with the experimental results (colored markers). In this figure, morphology

196

E is added, to illustrate the transition to the case in which the ellipse does not have

197

an effect, as in that case the droplet is smaller than the ellipse minor axis. Using

198

the receding contact angle for the calculations (see figure 6(a)) is, in principle, the

199

most logical method for calculating the shape of evaporating droplets. However, the

200

experimental results show a behavior that falls between the results calculated for both

201

limits of contact angle hysteresis.

202

In fact, for the first transitions (from morphology D to B and to C), the calculations

203

done considering the hysteresis limits θr1 = 49 ± 4◦ and θa2 = 33 ± 4◦ show better

204

qualitative agreement with our experiments than those done considering both receding

205

angles. For these morphologies, in which part of the contact line lays on the lyophobic

206

area, the overall angle of the drop is kept higher by the influence of the high contact

207

angle of the lyophobic area θ1 = θr1 = 49 ± 4◦ , bringing it to the maximum angle

208

possible for the lyophilic patch θ2 = θa2 = 33 ± 4◦ . For the same reason, the transitions

209

from morphologies B and C to morphology A, in which the contact line has to travel

210

along the lyophilic patch, show better agreement with the calculations performed for

211

θ2 = θr2 = 15 ± 4◦ . The experiments also show that the transitions occur for smaller

212

droplet volumes as compared to those predicted. This delay can be observed if, for

213

a fixed aspect ratio b/a, we follow down the vertical line in the decreasing volume

214

direction. This effect is forced by pinning, which acts to favor larger radii morphologies.

215

Moreover, during the calculations we found that, for certain lyophilicity differences,

216

we can exclude morphologies from the diagram. In our case, the calculations that

217

were computed considering θ2 = θr2 = 15◦ (see figure 6(a)) predict the absence of

218

morphology B.

12


Page 12 of 39

Page 13 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 6: Morphology diagrams in aspect ratio b/a vs relative volume V /a3 phase space showing the morphologies A, B, C, D and E. (a) Experimental results displayed together with the computational results considering θ2 = θr2 = 15◦ (b) Experimental results displayed with the computational results considering θ2 = θa2 = 33◦ . The main features for A-D are indicated in figure 4, while E shows the case in which the droplet is small enough to adopt the trivial spherical cap shape inside the patch. The color shadowed regions represent the morphologies obtained with our calculations. Green, yellow, dark blue, red and light blue regions represent respectively the regions where morphologies D,C, B, A and E where found in our calculations and the colored markers show the experimental points specified in the legend.

13


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

219

Conclusions

220

We have performed experiments to validate the Surface Evolver calculations, and these

221

showed good agreement. We observe how the effect of substrate heterogeneities, in-

222

cluding pinning and contact angle hysteresis, can affect the accuracy of our surface

223

minimization calculations. These heterogeneities seem mostly to affect the symmetry

224

and the transitions in the morphology diagrams. With this study, we show the ro-

225

bustness of the contact angle predictions which contrast with the sensitivity that radii

226

predictions have to pinning. The reason is that the radius depends on the mobility of

227

the contact line and therefore on pinning, even when a different morphology would be

228

energetically more efficient, while the contact angle is forced by the chemistry of the

229

substrate in the vicinity of the contact line, making it more robust.

230

According to our results, we conclude that the knowledge of the hysteresis limits can

231

be used for improving the predictions of Surface Evolver calculations. In general, the

232

morphologies found experimentally show good repeatability However, the morphologies

233

adopted by the droplets are always subjected to the effect of pinning, which influences

234

the droplet’s symmetry and delays its transition to the next morphology. This effect

235

shifts the experimental transitions to smaller volumes than those predicted by our

236

calculations, as shown in the morphology diagram. We expect this effect to be opposite

237

for growing droplets but that remains an open question and it is beyond the scope of

238

the present study, as it would require a different experimental setup. Finally, the

239

exploration of lyophilicity differences between the patches and the surroundings have

240

shown the feasibility of excluding morphologies from the phase diagram, which is an

241

interesting result with bearing on the design of micro-patterned structures for various

242

applications.

14


Page 14 of 39

Page 15 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

243

Langmuir

References

244

(1) Zhai, L.; Berg, M. C.; Cebeci, F. C ¸ .; Kim, Y.; Milwid, J. M.; Rubner, M. F.;

245

Cohen, R. E. Patterned Superhydrophobic Surfaces: Toward a Synthetic Mimic

246

of the Namib Desert Beetle. Nano Lett. 2006, 6, 1213–1217.

247

(2) Gao, X.; Yan, X.; Yao, X.; Xu, L.; Zhang, K.; Zhang, J.; Yang, B.; Jiang, L.

248

The Dry-Style Antifogging Properties of Mosquito Compound Eyes and Artificial

249

Analogues Prepared by Soft Lithography. Adv.Mater. 2007, 19, 2213–2217.

250

(3) Barthlott, W.; Neinhuis, C. Purity of the sacred lotus, or escape from contami-

251

252

253

nation in biological surfaces. Planta 1997, 202, 1–8. (4) Paxson, A. T.; Varanasi, K. K. Self-similarity of contact line depinning from textured surfaces. Nat. Commun. 2013, 4, 1492.

254

(5) Sáenz, P. J.; Wray, A. W.; Che, Z.; Matar, O. K.; Valluri, P.; Kim, J.; Sefiane, K.

255

Dynamics and universal scaling law in geometrically-controlled sessile drop evap-

256

oration. Nat. Commun. 2017, 8, 14783.

257

258

259

260

(6) Stauber, J. M.; Wilson, S. K.; Duffy, B. R.; Sefiane, K. On the lifetimes of evaporating droplets. J. Fluid Mech. 2014, 744, R2. (7) Lauga, E.; Brenner, M. P.; Stone, H. A. Handbook of Experimental Fluid Dynamics; Springer, 2007; pp 1219–1240.

261

(8) Debuisson, D.; Senez, V.; Arscott, S. SU-8 micropatterning for microfluidic

262

droplet and microparticle focusing. Micromech. Microeng. 2011, 21, 065011.

263

(9) Lee, T.; Charrault, E.; Neto, C. Interfacial slip on rough, patterned and soft

264

surfaces: A review of experiments and simulations. Adv. Colloid Interface Sci.

265

2014, 210, 21 – 38.

266

(10) Clausen, B. S.; Schiøtz, J.; Gr˚ abæk, L.; Ovesen, C. V.; Jacobsen, K. W.;

267

Nørskov, J. K.; Topsøe, Wetting/ non-wetting phenomena during catalysis: Ev-

15


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

268

idence from in situ on-line EXAFS studies of Cu-based catalysts. Top. Catal.

269

1994, 1, 367–376.

270

(11) Soltman, D.; Smith, B.; Kang, H.; Morris, S. J. S.; Subramanian, V. Methodology

271

for Inkjet Printing of Partially Wetting Films. Langmuir 2010, 26, 15686–15693.

272

(12) Lim, J. A.; Lee, W. H.; Lee, H. S.; Lee, J. H.; Park, Y. D.; Cho, K. Self-

273

organization of ink-jet-printed triisopropylsilylethynyl pentacene via evaporation-

274

induced flows in a drying droplet. Adv. Functional Mat. 2008, 18, 229–234.

275

(13) Cho, H. J.; Preston, D. J.; Zhu, Y.; Wang, E. N. Nanoengineered materials for

276

277

278

liquid-vapour phase-change heat transfer. Nat. Rev. Mat. 2017, 2, 16092. (14) Patankar, N. A. Supernucleating surfaces for nucleate boiling and dropwise condensation heat transfer. Soft Matter 2010, 6, 1613–1620.

279

(15) Han, W.; Lin, Z. Learning from ”Coffee Rings”: Ordered Structures Enabled by

280

Controlled Evaporative Self-Assembly. Angew. Chem. Int. Edit. 2012, 51, 1534–

281

1546.

282

(16) Mar´ın, A. G.; Gelderblom, H.; Susarrey-Arce, A.; van Houselt, A.; Lefferts, L.;

283

Gardeniers, J. G. E.; Lohse, D.; Snoeijer, J. H. Building microscopic soccer balls

284

with evaporating colloidal fakir drops. Proc. Nat. Acad. Sci. 2012, 109, 16455–

285

16458.

286

(17) Yang, H.; Wang, Y.; Song, Y.; Qiu, L.; Zhang, S.; Li, D.; Zhang, X. Assembling

287

of graphene oxide in an isolated dissolving droplet. Soft Matter 2012, 8, 11249–

288

11254.

289

(18) Hsiao, A. Y.; Tung, Y.-C.; Kuo, C.-H.; Mosadegh, B.; Bedenis, R.; Pienta, K. J.;

290

Takayama, S. Micro-ring structures stabilize microdroplets to enable long term

291

spheroid culture in 384 hanging drop array plates. Biomed. Microdevices 2012,

292

14, 313–323.

16


Page 16 of 39

Page 17 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

293

(19) Tadanaga, K.; Katata, N.; Minami, T. Formation process of super-water-repellent

294

Al2O3 coating films with high transparency by the sol-gel method. J. Am. Ceram.

295

Soc. 1997, 80, 1040–1042.

296

(20) Paven, M.; Papadopoulos, P.; Sch¨ ottler, S.; Deng, X.; Mailänder, V.; Vollmer, D.;

297

Butt, H.-J. Super liquid-repellent gas membranes for carbon dioxide capture and

298

heart-lung machines. Nat. Commun. 2013, 4, 2512.

299

300

301

(21) Butt, H.-J.; Vollmer, D.; Papadopoulos, P. Super liquid-repellent layers: The smaller the better. Adv. Colloid Interface Sci. 2015, 222, 104–109. (22) de Gennes, P. G.; Brochard-Wyart, F.; Quéré, D. Capillarity and wetting

302

phenomena: drops, bubbles, pearls, waves; Springer: New York, 2004.

303

(23) Quéré, D. Wetting and roughness. Annu. Rev. Mater. Sci. 2008, 38, 71–99.

304

(24) Marmur, A. Contact Angle Hysteresis on Heterogeneous Smooth Surfaces. J. Coll.

305

306

307

308

309

310

311

312

313

Interf. Sci. 1994, 168, 40 – 46. (25) Qiao, S.; Li, Q.; Feng, X.-Q. Sliding friction and contact angle hysteresis of droplets on microhole-structured surfaces. The Eur. Phys. J. E 2018, 41, 25. (26) Pompe, T.; Herminghaus, S. Three-phase contact line energetics from nanoscale liquid surface topographies. Phys. Rev. Lett. 2000, 85, 1930–1933. (27) Lohse, D.; Zhang, X. Surface nanobubble and surface nanodroplets. Rev. Mod. Phys. 2015, 87, 981–1035. (28) Rauscher, M.; Dietrich, S. Wetting Phenomena in Nanofluidics. Ann. Rev. Mater. Res. 2008, 38, 143–172.

314

(29) Mendez-Vilas, A.; Jodar-Reyes, A. B.; Gonzalez-Martin, M. L. Ultrasmall Liq-

315

uid Droplets on Solid Surfaces: Production, Imaging, and Relevance for Current

316

Wetting Research. Small 2009, 5, 1366–1390.

17


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

317

318

319

320

321

322

323

324

325

326

(30) Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Wetting and spreading. Rev. Mod. Phys. 2009, 81, 739–805. (31) Kant, P.; Hazel, A. L.; Dowling, M.; Thompson, A. B.; Juel, A. Controlling droplet spreading with topography. Phys. Rev. Fluids 2017, 2, 094002. (32) Herminghaus, S.; Brinkmann, M.; Seemann, R. Wetting and Dewetting of Complex Surface Geometries. Ann. Rev. Mater. Res. 2008, 38, 101–121. (33) Lenz, P.; Lipowsky, R. Morphological Transitions of Wetting Layers on Structured Surfaces. Phys. Rev. Lett. 1998, 80, 1920–1923. (34) Extrand, C. W. Contact Angles and Hysteresis on Surfaces with Chemically Heterogeneous Islands. Langmuir 2003, 19, 3793–3796.

327

(35) Darhuber, A. A.; Troian, S. M.; Miller, S. M.; Wagner, S. Morphology of liquid

328

microstructures on chemically patterned surfaces. J. Appl. Phys. 2000, 87, 7768–

329

7775.

330

331

(36) Brinkmann, M.; Lipowsky, R. Wetting morphologies on substrates with striped surface domains. J. Appl. Phys. 2002, 92, 4296–4306.

332

(37) Ferraro, D.; Semprebon, C.; Tóth, T.; Locatelli, E.; Pierno, M.; Mistura, G.;

333

Brinkmann, M. Morphological Transitions of Droplets Wetting Rectangular Do-

334

mains. Langmuir 2012, 28, 13919–13923.

335

(38) Jansen, H. P.; Bliznyuk, O.; Kooij, E. S.; Poelsema, B.; Zandvliet, H. J. W.

336

Simulating Anisotropic Droplet Shapes on Chemically Striped Patterned Surfaces.

337

Langmuir 2012, 28, 499–505.

338

339

340

(39) Young, T. An Essay on the Cohesion of Fluids. Philos. T. R. Soc. of Lon. 1805, 95, 65–87. (40) Cassie, A. B. D. Contact Angles. Discuss. Faraday Soc. 1948, 3, 11–16.

18


Page 18 of 39

Page 19 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

341

342

343

344

345

346

347

348

349

350

Langmuir

(41) Cassie, A. B. D.; Baxter, S. Wettability of Porous Surfaces. Trans. Faraday Soc. 1944, 40, 546–551. (42) Wenzel, R. N. Resistance of solid surfaces to wetting by water. Ind. Eng. Chem. 1936, 28. (43) Gao, L.; McCarthy, T. J. How Wenzel and Cassie Were Wrong. Langmuir 2007, 23, 3762–3765. (44) Marmur, A.; Bittoun, E. When Wenzel and Cassie Are Right: Reconciling Local and Global Considerations. Langmuir 2009, 25, 1277–1281. (45) McHale, G. Cassie and Wenzel: Were They Really So Wrong? Langmuir 2007, 23, 8200–8205.

351

(46) Dević, I.; Soligno, G.; Dijkstra, M.; Roij, R. v.; Zhang, X.; Lohse, D. Sessile

352

Nanodroplets on Elliptical Patches of Enhanced Lyophilicity. Langmuir 2017,

353

33, 2744–2749.

354

(47) Brakke, K. A. The surface evolver. Experiment. Math. 1992, 1, 141–165.

19


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Morphology of Evaporating Sessile Microdroplets on Lyophilic Elliptical Patches José M. Encarnación Escobar,†,k Diana Garc´ıa-González ,†,‡,k Ivan Dević ,† Xuehua Zhang,⇤,¶ and Detlef Lohse⇤,† †Department of Physics of Fluids, University of Twente, Enschede, The Netherlands ‡Max Planck Institute for Polymer Research, Mainz, Germany ¶Department of Chemical & Materials Engineering, University of Alberta, Edmonton, Alberta, Canada §Max Plank Institute for Dynamics and Self-Organization, Göttingen, Germany kBoth authors contributed equally to this work E-mail: [email protected]; [email protected]

1

Abstract

2

The evaporation of droplets occurs in a large variety of natural and technolog-

3

ical processes such as medical diagnostics, agriculture, food industry, printing, and

4

catalytic reactions. We study the di↵erent droplet morphologies adopted by an evapo-

5

rating droplet on a surface with an elliptical patch with a di↵erent contact angle. We

6

perform experiments to observe these morphologies and use numerical calculations to

7

predict the e↵ect of the patched surfaces. We observe that tuning the geometry of

8

the patches o↵ers control over the shape of the droplet. In the experiments, the drops

9

of various volumes are placed on elliptical chemical patches of di↵erent aspect ratios

10

and imaged in 3D using laser scanning confocal microscopy, extracting the droplet’s

11

shape. In the corresponding numerical simulations, we minimize the interfacial free

1


Page 20 of 39

Page 21 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

12

energy of the droplet, employing Surface Evolver. The numerical results are in good

13

qualitative agreement with our experimental data and can be used for the design of

14

micro-patterned structures, potentially suggesting or excluding certain morphologies

15

for particular applications. However, the experimental results show the e↵ects of pin-

16

ning and contact angle hysteresis, which are obviously absent in the numerical energy

17

minimization. The work culminates with a morphology diagram in the aspect ratio vs

18

relative volume parameter space, comparing the predictions with the measurements.

19

Introduction

20

The use of patterned surfaces to control the behavior of liquid drops is not only a re-

21

current phenomenon in nature, but it is also useful in various industrial and scientific

22

applications. For instance, the observation of nature inspired the use of patterned sur-

23

faces for water harvesting applications 1 as well as the fabrication of anti-fogging 2 and

24

self-cleaning materials 3 . The geometry of droplets and the substrates in which they lay

25

can a↵ect their adhesion, as can their evaporation and other important properties 4–6 .

26

The interest in wetting motivated by applications covers a wide range of scales and

27

backgrounds from microfluidics 7–9 to catalytic reactors 10 , including advanced printing

28

techniques 11,12 ; improved heat transfer 13,14 ; nano-architecture 15–17 ; droplet-based di-

29

agnostics 18 or anti-wetting surfaces 19–21 . Aside from all the practical significance, we

30

have to add the interest on wetting fundamentals 22 , including contact angle hystere-

31

sis and dynamics 23–25 ; contact line dynamics 26 ; nanobubbles and nanodroplets 27–29 ;

32

spreading dynamics 30,31 ; and complex surfaces 32,33 .

33

34

Due to the complexity of the field, most previous studies have restricted themselves

35

to considering geometries with constant curvature as straight stripes or constant cur-

36

vature geometries, namely circumferences. In this work we will study the behavior

37

of evaporating drops on lyophobized substrates that have lyophilic elliptical patches.

38

The elliptical shape for the patches is chosen as a transitional case between a circular

2


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

39

patch 34 and a single stripe 35–38 , having the uniqueness of a perimeter with non-constant

40

curvature. When a drop is placed on a homogeneous substrate, the minimization of

41

surface energy leads to a spherical cap shape. This is traditionally described by the

42

Young-Laplace, Wenzel, or, for pillars or patterns with length scales much smaller

43

than the drop, Cassie-Baxter relations 39–42 , which reasonably apply to homogeneous

44

substrates or substrates with sufficiently small and homogeneously distributed hetero-

45

geneities 43–45 , which are not the focus of this study.

46

Our previous work (Dević et al. 46 ) based on Surface Evolver and Monte Carlo cal-

47

culations showed that, when a droplet rests on an elliptical patch, four distinguishable

48

morphologies are found, depending on the volume of the drop and the aspect ratio of

49

the patch. These morphologies were termed 46 A, B, C and D, see figure 1. When a

50

large enough droplet evaporates on an elliptical patch, the first morphology found is D.

51

In this case, the droplet completely wets the ellipse with a part of its contact line out-

52

side the ellipse and the rest pinned to the contour of the patch. After a certain volume

53

loss, the droplet adopts either morphology B or C - depending on the geometry of the

54

patch. In morphology B, a part of the droplet’s contact line remains outside the patch

55

while the rest is already inside the patch. In contrast, the contact line of a droplet

56

adopting morphology C follows the perimeter of the ellipse. The final morphology to

57

be found for evaporating drops is morphology A, characterized by a part of its contact

58

line following the perimeter of the ellipse and the rest of the contact line laying inside

59

it.

60

Methods

61

In this paper we perform corresponding experiments and numerical simulations, per-

62

formed again with Surface Evolver using the experimental parameters. Both the ex-

63

periments and the calculations are performed for Bond numbers below unity to avoid

64

the e↵ects of gravity. Moreover, the experiments are performed at room temperature

65

with a relative humidity of 38±2% in a closed and controlled environment, ensuring

3


Page 22 of 39

Page 23 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 1: Scheme of the morphologies of a droplet as seen from the top as expected from the calculations by Dević et al. 46

Figure 2: Left: Coordinate system employed in this paper. ✓1 and ✓2 are, respectively, the Young’s angles of the lyophobic (white) and lyophilic (red) regions. R( ) is the distance from the center of the ellipse to the contact line of the droplet (blue), and a and b are the major and minor axis respectively. S indicates the vertical section. Right: Experimental results: Top view images taken during the evaporation of various droplets on ellipses with di↵erent sizes and aspect ratios, the red contours represent the elliptical patches on the surface. A) Morphology A, droplet on an ellipse of aspect ratio b/a=0.61 and semi-major axis a=512±16µm. B) Morphology B, droplet on an ellipse of aspect ratio b/a=0.43 and semi-major axis a=392±20µm. C) Morphology C, droplet on an ellipse of aspect ratio b/a=0.98 and semi-major axis a=410±20µm. D) Morphology D, droplet on an ellipse of aspect ratio b/a=0.69 and semi-major axis a=411±20µm.

4


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

66

that the evaporation driven volume change is slow enough so that the droplets evolve

67

in quasi-static equilibrium. The e↵ects of humidity, evaporative cooling, and evapo-

68

ration driven flows do not have any important e↵ects. However, for heated or cooled

69

substrates or more volatile liquids this situation may change. Unlike the gravitational

70

and evaporative e↵ects, the e↵ects of the inhomogeneities of the substrate —like pin-

71

ning and contact angle hysteresis— are unavoidable in our experiments while they are

72

absent from the Surface Evolver calculations.

73

Preparation of substrates with lyophilic elliptical patches

74

The patched substrates were prepared via photolithography followed by chemical va-

75

por deposition (CVD) of a mono layer of trimethylchlorosilane (TMCS). The 100 x

76

100 mm2 chromium on glass photo-mask used was designed with an array of ellipses

77

of aspect ratios varying from 0.3 to 1 and sizes varying from a=320µm to b=2500µm,

78

see figure 3 (a), and fabricated in the MESA+ Institute clean room facilities of the

79

University of Twente, using laser writing technology. The substrates were glass slides

80

(20 ⇥ 60 mm2 ) of 170 µm thickness, which is optimal for confocal microscopy. The

81

photolithography steps of the fabrication, outlined in figure 3 (b), were performed in

82

a cleanroom environment. First, the substrates were pre-cleaned in a nitric acid bath

83

(NOH3 , purity 99%) followed by water rinsing and nitrogen drying. Subsequently,

84

we dehydrated the substrate (120 C, 5 min). After dehydration, we spin-coated the

85

photoresist (Olin OiR, 17 µm), pre-baked it (95 C, 90 s) and proceeded with the align-

86

ment of the photomask and UV irradiation (4 s, 12 mW/cm2 ). Once the photoresist

87

was cured, we developed and post-baked it (120 C, 10 min). Finally, the substrates

88

were taken outside the clean-room environment for the CVD ( 2 h, 0.1 MPa) of a

89

TMCS monolayer (Sigma Aldrich, purity

90

lipses. The photoresist was later stripped away by rinsing the substrates with acetone,

91

cleaned with isopropanol and dried using pressurized nitrogen.

99%) to lyophobize the exterior of the el-

5


Page 24 of 39

Page 25 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

a) Design Photomask

b) 1

Pre-cleaning with NOH3 Developement photoresist Glass Substrate 4 Spin-coating photoresist

2

Photoresist

CVD deposition of TMCS 5 TMCS

UV light through photomask

5 mm

6

3

TMCS elliptical patches TMCS

Figure 3: a) Array of ellipses of aspect ratios varying from 0.3 to 1 and sizes varying from a=320 µm to b=2500 µm fabricated on the photomask. b) Simplified steps of the substrates’ fabrication in the order indicated by the numbers. 92

Experimental data acquisition and analysis

93

For all the measurements, we used droplets of ultrapure (Milli-Q) water dyed with

94

Rhodamine 6G at a concentration of 0.2 µg/ml. The droplet was deposited cover-

95

ing the lyophilic patch and imaged by laser scanning confocal microscopy (LSCM) in

96

three dimensions during the evaporation process. After deposition of the droplet, the

97

substrate was covered to avoid external perturbations.

98

In figure 4, we show four examples of three-dimensional reconstructions of a stack

99

of scans with increasing heights taken under LSCM. For each scan, we detected the

100

surface of the drop using a threshold algorithm, allowing for the three-dimensional

101

reconstruction of the drop. Using this data we calculate the local contact angle at

102

every point detected on the contact line. For the measurement of the contact angle ✓,

103

we extract the height profile along the contact line. This can be achieved, as sketched

104

in figure 2, by identifying the tangent to each point of the contact line at an angle

105

and finding the points belonging simultaneously to its normal plane S and to the

106

surface of the droplet.

107

We extracted three-dimensional images of evaporating water droplets using LSCM.

108

From the three-dimensional data we measured the local contact angle along the three-

109

phase contact line through the azimuthal angle

110

of various evaporating droplets as examples of each of the morphologies introduced

6

. Figure 2, right, shows top views


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

111

previously. The lyophilic elliptical islands of the substrate are highlighted by red curves.

112

We adopted a cylindrical coordinate system with its origin at the center of the

113

ellipse. The polar axis was fixed to be in the direction of one of the major semi-axes a as

114

shown in figure 2 (left). We set the large semi-axis (a) of the ellipse as the characteristic

115

length scale for this system and the aspect ratio of the ellipses b/a to characterize the

116

geometry of the patch. The relative volume of the droplets is normalized as V /a3 .

Figure 4: Three-dimensional reconstruction of the shape extracted from the LSCM data collected for four di↵erent droplets adopting morphologies A, B, C and D respectively as performed for the extraction of the contact angle along the contact line with the shape of the elliptical patch, highlighted in red lines. Repeatability is subjected to the initial position of the droplet and pinning of the contact line which can a↵ect the symmetry of the shape as well as delay the transition between phases as compared to the predictions. In figure 6 all the morphologies observed during the experiments are shown.

117

Calculations

118

We compute the surface energy minimization using Surface Evolver, a free software

119

package used for minimization of the interfacial free energy developed by Brakke 47 , to

120

extract the droplet’s shape and local contact angle as in the previous work by Dević

121

et al. 46 . An initial shape of the droplet and the characteristic interfacial tensions of

122

the surfaces are given to Surface Evolver as an input. The software minimizes the

123

surface energy by an energy gradient descent method. Since hysteresis is not captured

7


Page 26 of 39

Page 27 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

124

by our simulations, we compared each group of experimental results with two di↵erent

125

calculations: one considering the receding contact angles for the two regions, and the

126

other considering the advancing contact angle for the lyophilic part.

127

To perform the calculations, we measured the contact angles of both the lyophilic

128

and lyophobic parts of our patches. To do this, we treated two separated substrates ho-

129

mogeneously in the same manner as in these two regions. We measured the advancing

130

and receding contact angles on both substrates. Respectively for the lyophobic (sub-

131

script 1) and lyophilic surfaces (subscript 2), the advancing contact angles measured

132

were ✓a1 = 85±3 and ✓a2 = 33±4 , and the receding contact angles were ✓r1 = 49±3

133

and ✓r2 = 15 ± 4 . During the experiments, we observed variations between 5% and

134

10% of the contact angle due to occasional pinning events.

135

Results

136

In this section, we present the results of our experiments and the Surface Evolver cal-

137

culations for each of the observed morphologies. In Figure 5, each row presents one

138

of the morphologies shown previously in Figure 4. For each morphology, we show

139

the normalized footprint radii R/a next to the local contact angles ✓, both along the

140

azimuthal coordinate . In each of the plots we overlay experimental and computa-

141

tional results. The red and blue markers represent the calculations done considering

142

the lyophilic contact angle ✓2 = 33 and ✓2 = 15 , respectively. In the plots of the

143

normalized footprint radii we plot the position of the patch contour (black curve).

144

To follow the chronological sequence of our evaporating experiments, we present

145

the results starting from morphology D (largest droplet volume) and finishing with

146

morphology A (smallest droplet volume). Finally, in figure 6 we present the morphology

147

diagrams predicted by the Surface Evolver calculations (colored areas) and compare

148

those with the results of all our experiments (colored markers).

8


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

149

Morphology type D

150

In figure 5 (a and b), we can see an example of an experiment in which morphology

151

D was found. The normalized footprint radius R/a and the contact angle are plotted

152

along the azimuthal coordinate. From the figure, we observe reasonable agreement

153

between Surface Evolver calculations and experiments. However, the existence of inho-

154

mogeneities introduces pinning and hence, a delay in the movement of the contact line.

155

This delay translates into an experimental radius larger than that predicted by the

156

Surface Evolver calculations. Despite this mismatch of the contact line, consequence

157

of individual pinning events of the contact line, we obtain reasonable agreement with

158

the contact angle calculations.

159

Morphology type C

160

Morphology C appeared for ellipses of higher aspect ratio b/a as compared to morphol-

161

ogy B. Additionally, when evaporating, the drop reaches morphology C always through

162

morphology D, implying that any pinning event of the contact line outside the ellipse

163

prevents morphology C. Indeed, the transition from morphology D to C was always

164

found in a later stage of evaporation than predicted by theory, i.e., for lower volumes

165

(see figure 6 (b)).

166

In figure 5 (c and d), we show a droplet of volume V /a3 =0.37 placed on a high

167

aspect ratio ellipse (b/a=0.98). The results of the calculations predict morphology C

168

and contact angles between the receding and the advancing ones. The contact angle

169

and the contact line show always good agreement with the Surface Evolver calculations.

170

This is expected as it is the closer case to the trivial spherical cap shape.

171

Morphology type B

172

The experimental data shown in figure 5 e and f, are particularly interesting as this

173

case presents a strong asymmetry in the radius caused by a sharp pinning point which

174

can be identified at

⇡ 120 (indicated by an arrow in figure 5 e). Unlike the radius,

9


Page 28 of 39

Page 29 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

175

the contact angle shows a symmetric behavior. We found that pinning leads to an

176

asymmetric behavior in this morphology for all our experiments but, besides the asym-

177

metry forced by pinning, the experiments agree with the Surface Evolver calculations.

178

The good match for the angle can be explained considering that the contact angle at

179

every point of the contact line –far enough from the ellipse contour– is dictated by the

180

chemistry of the surrounding substrate.

181

Morphology type A

182

The experimental results showed morphology type A as predicted by the calculations

183

for ✓2 = 15 , with a part of the contact line pinned at the boundaries of the ellipse and

184

the rest of the contact line inside the ellipse. Note that, in the calculations for the higher

185

receding contact angle (✓2 = 33 ), the results predict a spherical cap shape with radius

186

R < b. However, our results for the contact angle were not in good agreement with

187

either of the Surface Evolver calculations, but rather an intermediate state between

188

them, subjected to the irregularities of the edge (see figure 5 g and h. This can be

189

due to imperfections of the coating in the edges of the ellipse. The high portion of

190

the contact line that remains pinned at the boundary between the lyophilic and the

191

lyophobic parts appeared to be very sensitive to the quality of the patch rim.

10


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5: Normalized footprint radius R/a and contact angle ✓ along the azimuthal coordinate (as defined in figure 2). Experimental results for the four di↵erent morphologies (green). From top to bottom; morphology D (V /a3 = 0.40, b/a = 0.69, and a = 411±20µm); morphology C (V /a3 = 0.37, b/a = 0.98, and a = 410 ± 20 µm); morphology B (V /a3 = 0.30, b/a = 0.43, and a = 392 ± 20 µm); and morphology A (V /a3 = 0.08, b/a = 0.60, and a = 512 ± 16 µm). Results of the numerical simulations considering the lyophilic contact angles ✓2 = 15 (blue) and ✓2 = 33 (red). The black curve in the radius plot shows the contour of the elliptical patch. 11


Page 30 of 39

Page 31 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

192

Morphology Diagrams

193

Figure 6 presents two morphology diagrams showing all the morphological regions

194

and transitions predicted by the Surface Evolver calculations (as color shaded areas),

195

together with the experimental results (colored markers). In this figure, morphology

196

E is added, to illustrate the transition to the case in which the ellipse does not have

197

an e↵ect, as in that case the droplet is smaller than the ellipse minor axis. Using

198

the receding contact angle for the calculations (see figure 6(a)) is, in principle, the

199

most logical method for calculating the shape of evaporating droplets. However, the

200

experimental results show a behavior that falls between the results calculated for both

201

limits of contact angle hysteresis.

202

In fact, for the first transitions (from morphology D to B and to C), the calculations

203

done considering the hysteresis limits ✓r1 = 49 ± 4 and ✓a2 = 33 ± 4 show better

204

qualitative agreement with our experiments than those done considering both receding

205

angles. For these morphologies, in which part of the contact line lays on the lyophobic

206

area, the overall angle of the drop is kept higher by the influence of the high contact

207

angle of the lyophobic area ✓1 = ✓r1 = 49 ± 4 , bringing it to the maximum angle

208

possible for the lyophilic patch ✓2 = ✓a2 = 33 ± 4 . For the same reason, the transitions

209

from morphologies B and C to morphology A, in which the contact line has to travel

210

along the lyophilic patch, show better agreement with the calculations performed for

211

✓2 = ✓r2 = 15 ± 4 . The experiments also show that the transitions occur for smaller

212

droplet volumes as compared to those predicted. This delay can be observed if, for

213

a fixed aspect ratio b/a, we follow down the vertical line in the decreasing volume

214

direction. This e↵ect is forced by pinning, which acts to favor larger radii morphologies.

215

Moreover, during the calculations we found that, for certain lyophilicity di↵erences,

216

we can exclude morphologies from the diagram. In our case, the calculations that

217

were computed considering ✓2 = ✓r2 = 15 (see figure 6(a)) predict the absence of

218

morphology B.

12


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6: Morphology diagrams in aspect ratio b/a vs relative volume V /a3 phase space showing the morphologies A, B, C, D and E. (a) Experimental results displayed together with the computational results considering ✓2 = ✓r2 = 15 (b) Experimental results displayed with the computational results considering ✓2 = ✓a2 = 33 . The main features for A-D are indicated in figure 4, while E shows the case in which the droplet is small enough to adopt the trivial spherical cap shape inside the patch. The color shadowed regions represent the morphologies obtained with our calculations. Green, yellow, dark blue, red and light blue regions represent respectively the regions where morphologies D,C, B, A and E where found in our calculations and the colored markers show the experimental points specified in the legend.

13


Page 32 of 39

Page 33 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

219

Conclusions

220

We have performed experiments to validate the Surface Evolver calculations, and these

221

showed good agreement. We observe how the e↵ect of substrate heterogeneities, in-

222

cluding pinning and contact angle hysteresis, can a↵ect the accuracy of our surface

223

minimization calculations. These heterogeneities seem mostly to a↵ect the symmetry

224

and the transitions in the morphology diagrams. With this study, we show the ro-

225

bustness of the contact angle predictions which contrast with the sensitivity that radii

226

predictions have to pinning. The reason is that the radius depends on the mobility of

227

the contact line and therefore on pinning, even when a di↵erent morphology would be

228

energetically more efficient, while the contact angle is forced by the chemistry of the

229

substrate in the vicinity of the contact line, making it more robust.

230

According to our results, we conclude that the knowledge of the hysteresis limits can

231

be used for improving the predictions of Surface Evolver calculations. In general, the

232

morphologies found experimentally show good repeatability However, the morphologies

233

adopted by the droplets are always subjected to the e↵ect of pinning, which influences

234

the droplet’s symmetry and delays its transition to the next morphology. This e↵ect

235

shifts the experimental transitions to smaller volumes than those predicted by our

236

calculations, as shown in the morphology diagram. We expect this e↵ect to be opposite

237

for growing droplets but that remains an open question and it is beyond the scope of

238

the present study, as it would require a di↵erent experimental setup. Finally, the

239

exploration of lyophilicity di↵erences between the patches and the surroundings have

240

shown the feasibility of excluding morphologies from the phase diagram, which is an

241

interesting result with bearing on the design of micro-patterned structures for various

242

applications.

243

Acknowledgments

244

This work was supported by the Netherlands Center for Multiscale Catalytic En-

245

ergy Conversion (MCEC), an NWO Gravitation program funded by the Ministry of

246

Education, Culture and Science of the government of the Netherlands. DL also ac-

14


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

247

knowledges an ERC Advanced grant. We acknowledge the support of the Natural

248

Sciences and Engineering Research Council of Canada (NSERC).

249

References

250

(1) Zhai, L.; Berg, M. C.; Cebeci, F. C ¸ .; Kim, Y.; Milwid, J. M.; Rubner, M. F.;

251

Cohen, R. E. Patterned Superhydrophobic Surfaces: Toward a Synthetic Mimic

252

of the Namib Desert Beetle. Nano Lett. 2006, 6, 1213–1217.

253

(2) Gao, X.; Yan, X.; Yao, X.; Xu, L.; Zhang, K.; Zhang, J.; Yang, B.; Jiang, L.

254

The Dry-Style Antifogging Properties of Mosquito Compound Eyes and Artificial

255

Analogues Prepared by Soft Lithography. Adv.Mater. 2007, 19, 2213–2217.

256

(3) Barthlott, W.; Neinhuis, C. Purity of the sacred lotus, or escape from contami-

257

258

259

nation in biological surfaces. Planta 1997, 202, 1–8. (4) Paxson, A. T.; Varanasi, K. K. Self-similarity of contact line depinning from textured surfaces. Nat. Commun. 2013, 4, 1492.

260

(5) S´ aenz, P. J.; Wray, A. W.; Che, Z.; Matar, O. K.; Valluri, P.; Kim, J.; Sefiane, K.

261

Dynamics and universal scaling law in geometrically-controlled sessile drop evap-

262

oration. Nat. Commun. 2017, 8, 14783.

263

264

265

266

(6) Stauber, J. M.; Wilson, S. K.; Du↵y, B. R.; Sefiane, K. On the lifetimes of evaporating droplets. J. Fluid Mech. 2014, 744, R2. (7) Lauga, E.; Brenner, M. P.; Stone, H. A. Handbook of Experimental Fluid Dynamics; Springer, 2007; pp 1219–1240.

267

(8) Debuisson, D.; Senez, V.; Arscott, S. SU-8 micropatterning for microfluidic

268

droplet and microparticle focusing. Micromech. Microeng. 2011, 21, 065011.

269

(9) Lee, T.; Charrault, E.; Neto, C. Interfacial slip on rough, patterned and soft

15


Page 34 of 39

Page 35 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

270

surfaces: A review of experiments and simulations. Adv. Colloid Interface Sci.

271

2014, 210, 21 – 38.

272

(10) Clausen, B. S.; Schiøtz, J.; Gr˚ abæk, L.; Ovesen, C. V.; Jacobsen, K. W.;

273

Nørskov, J. K.; Topsøe, Wetting/ non-wetting phenomena during catalysis: Ev-

274

idence from in situ on-line EXAFS studies of Cu-based catalysts. Top. Catal.

275

1994, 1, 367–376.

276

(11) Soltman, D.; Smith, B.; Kang, H.; Morris, S. J. S.; Subramanian, V. Methodology

277

for Inkjet Printing of Partially Wetting Films. Langmuir 2010, 26, 15686–15693.

278

(12) Lim, J. A.; Lee, W. H.; Lee, H. S.; Lee, J. H.; Park, Y. D.; Cho, K. Self-

279

organization of ink-jet-printed triisopropylsilylethynyl pentacene via evaporation-

280

induced flows in a drying droplet. Adv. Functional Mat. 2008, 18, 229–234.

281

(13) Cho, H. J.; Preston, D. J.; Zhu, Y.; Wang, E. N. Nanoengineered materials for

282

283

284

liquid-vapour phase-change heat transfer. Nat. Rev. Mat. 2017, 2, 16092. (14) Patankar, N. A. Supernucleating surfaces for nucleate boiling and dropwise condensation heat transfer. Soft Matter 2010, 6, 1613–1620.

285

(15) Han, W.; Lin, Z. Learning from ”Co↵ee Rings”: Ordered Structures Enabled by

286

Controlled Evaporative Self-Assembly. Angew. Chem. Int. Edit. 2012, 51, 1534–

287

1546.

288

(16) Mar´ın, A. G.; Gelderblom, H.; Susarrey-Arce, A.; van Houselt, A.; Le↵erts, L.;

289

Gardeniers, J. G. E.; Lohse, D.; Snoeijer, J. H. Building microscopic soccer balls

290

with evaporating colloidal fakir drops. Proc. Nat. Acad. Sci. 2012, 109, 16455–

291

16458.

292

(17) Yang, H.; Wang, Y.; Song, Y.; Qiu, L.; Zhang, S.; Li, D.; Zhang, X. Assembling

293

of graphene oxide in an isolated dissolving droplet. Soft Matter 2012, 8, 11249–

294

11254.

16


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

295

(18) Hsiao, A. Y.; Tung, Y.-C.; Kuo, C.-H.; Mosadegh, B.; Bedenis, R.; Pienta, K. J.;

296

Takayama, S. Micro-ring structures stabilize microdroplets to enable long term

297

spheroid culture in 384 hanging drop array plates. Biomed. Microdevices 2012,

298

14, 313–323.

299

(19) Tadanaga, K.; Katata, N.; Minami, T. Formation process of super-water-repellent

300

Al2O3 coating films with high transparency by the sol-gel method. J. Am. Ceram.

301

Soc. 1997, 80, 1040–1042.

302

(20) Paven, M.; Papadopoulos, P.; Schöttler, S.; Deng, X.; Mailänder, V.; Vollmer, D.;

303

Butt, H.-J. Super liquid-repellent gas membranes for carbon dioxide capture and

304

heart-lung machines. Nat. Commun. 2013, 4, 2512.

305

306

307

(21) Butt, H.-J.; Vollmer, D.; Papadopoulos, P. Super liquid-repellent layers: The smaller the better. Adv. Colloid Interface Sci. 2015, 222, 104–109. (22) de Gennes, P. G.; Brochard-Wyart, F.; Quéré, D. Capillarity and wetting

308

phenomena: drops, bubbles, pearls, waves; Springer: New York, 2004.

309

(23) Quéré, D. Wetting and roughness. Annu. Rev. Mater. Sci. 2008, 38, 71–99.

310

(24) Marmur, A. Contact Angle Hysteresis on Heterogeneous Smooth Surfaces. J. Coll.

311

312

313

314

315

316

317

318

319

Interf. Sci. 1994, 168, 40 – 46. (25) Qiao, S.; Li, Q.; Feng, X.-Q. Sliding friction and contact angle hysteresis of droplets on microhole-structured surfaces. The Eur. Phys. J. E 2018, 41, 25. (26) Pompe, T.; Herminghaus, S. Three-phase contact line energetics from nanoscale liquid surface topographies. Phys. Rev. Lett. 2000, 85, 1930–1933. (27) Lohse, D.; Zhang, X. Surface nanobubble and surface nanodroplets. Rev. Mod. Phys. 2015, 87, 981–1035. (28) Rauscher, M.; Dietrich, S. Wetting Phenomena in Nanofluidics. Ann. Rev. Mater. Res. 2008, 38, 143–172.

17


Page 36 of 39

Page 37 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

320

(29) Mendez-Vilas, A.; Jodar-Reyes, A. B.; Gonzalez-Martin, M. L. Ultrasmall Liq-

321

uid Droplets on Solid Surfaces: Production, Imaging, and Relevance for Current

322

Wetting Research. Small 2009, 5, 1366–1390.

323

324

325

326

327

328

329

330

331

332

(30) Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Wetting and spreading. Rev. Mod. Phys. 2009, 81, 739–805. (31) Kant, P.; Hazel, A. L.; Dowling, M.; Thompson, A. B.; Juel, A. Controlling droplet spreading with topography. Phys. Rev. Fluids 2017, 2, 094002. (32) Herminghaus, S.; Brinkmann, M.; Seemann, R. Wetting and Dewetting of Complex Surface Geometries. Ann. Rev. Mater. Res. 2008, 38, 101–121. (33) Lenz, P.; Lipowsky, R. Morphological Transitions of Wetting Layers on Structured Surfaces. Phys. Rev. Lett. 1998, 80, 1920–1923. (34) Extrand, C. W. Contact Angles and Hysteresis on Surfaces with Chemically Heterogeneous Islands. Langmuir 2003, 19, 3793–3796.

333

(35) Darhuber, A. A.; Troian, S. M.; Miller, S. M.; Wagner, S. Morphology of liquid

334

microstructures on chemically patterned surfaces. J. Appl. Phys. 2000, 87, 7768–

335

7775.

336

337

(36) Brinkmann, M.; Lipowsky, R. Wetting morphologies on substrates with striped surface domains. J. Appl. Phys. 2002, 92, 4296–4306.

338

(37) Ferraro, D.; Semprebon, C.; Tóth, T.; Locatelli, E.; Pierno, M.; Mistura, G.;

339

Brinkmann, M. Morphological Transitions of Droplets Wetting Rectangular Do-

340

mains. Langmuir 2012, 28, 13919–13923.

341

(38) Jansen, H. P.; Bliznyuk, O.; Kooij, E. S.; Poelsema, B.; Zandvliet, H. J. W.

342

Simulating Anisotropic Droplet Shapes on Chemically Striped Patterned Surfaces.

343

Langmuir 2012, 28, 499–505.

18


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

344

345

(39) Young, T. An Essay on the Cohesion of Fluids. Philos. T. R. Soc. of Lon. 1805, 95, 65–87.

346

(40) Cassie, A. B. D. Contact Angles. Discuss. Faraday Soc. 1948, 3, 11–16.

347

(41) Cassie, A. B. D.; Baxter, S. Wettability of Porous Surfaces. Trans. Faraday Soc.

348

349

350

351

352

353

354

355

356

1944, 40, 546–551. (42) Wenzel, R. N. Resistance of solid surfaces to wetting by water. Ind. Eng. Chem. 1936, 28. (43) Gao, L.; McCarthy, T. J. How Wenzel and Cassie Were Wrong. Langmuir 2007, 23, 3762–3765. (44) Marmur, A.; Bittoun, E. When Wenzel and Cassie Are Right: Reconciling Local and Global Considerations. Langmuir 2009, 25, 1277–1281. (45) McHale, G. Cassie and Wenzel: Were They Really So Wrong? Langmuir 2007, 23, 8200–8205.

357

(46) Dević, I.; Soligno, G.; Dijkstra, M.; Roij, R. v.; Zhang, X.; Lohse, D. Sessile

358

Nanodroplets on Elliptical Patches of Enhanced Lyophilicity. Langmuir 2017,

359

33, 2744–2749.

360

(47) Brakke, K. A. The surface evolver. Experiment. Math. 1992, 1, 141–165.

19


Page 38 of 39

Page 39 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

For Table of Contents Use Only

20


Morphology of Evaporating Sessile Microdroplets on Lyophilic

Recommend Documents