Sliding behavior of water droplets on line-patterned

hydrophobic surfaces

Shunsuke Suzuki a,b, Akira Nakajima a,b,*, Kouichi Tanaka a,Munetoshi Sakai b, Ayako Hashimoto b, Naoya Yoshida b,c,

Yoshikazu Kameshima a,b, Kiyoshi Okada a

a Department of Metallurgy and Ceramic Science, Graduate School of Science and Engineering,

Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japanb Kanagawa Academy of Science and Technology, 308 East, Kanagawa Science Park, 3-2-1 Sakado,

Takatsu-ku, Kawasaki-shi, Kanagawa 213-0012, Japanc Center for Collaborative Research, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan

Received 27 April 2007; received in revised form 19 July 2007; accepted 20 July 2007

Available online 1 August 2007

Abstract

We prepared line-patterned hydrophobic surfaces using fluoroalkylsilane (FAS) and octadecyltrimethoxysilane (ODS) then investigated the

effect of line direction on sliding behavior of water droplets by direct observation of the actual droplet motion during sliding. Water droplets slide

down with a periodic large deformation of the contact line and sliding velocity fluctuation that occurred when they crossed over the 500-mm ODS

line regions in FAS regions on a Si surface tilted at 358. These behaviors are less marked for motion on a 100-mm line surface, or on lines oriented

parallel to the slope direction. Smaller droplets slide down with greater displacement in the line direction on 500-mm line patterning when the lines

were rotated at 138 in-plane for the slope direction. This sliding behavior depended on the droplet size and rotation angle, and is accountable by the

balance between gravitational and retentive forces.

# 2007 Elsevier B.V. All rights reserved.

www.elsevier.com/locate/apsusc

Applied Surface Science 254 (2008) 1797–1805

PACS : Surface patterning; 81.65.Cf; In liquid–solid interfaces; 68.08.Bc; Photolithography; 85.40.Hp

Keywords: Wetting; Silane; Hydrophobicity; Coatings; Surface patterning; Photolithography

1. Introduction

Hydrophobic coating technology has played an important

role in various industrial applications for protection against

wetting, greasy dirt, snow adherence, rusting, and friction [1–

5]. A solid surface’s hydrophobicity can be evaluated from two

aspects: static hydrophobicity and dynamic hydrophobicity [6].

The water-droplet contact angle is commonly used as a criterion

for evaluating static hydrophobicity. For assessing dynamic

hydrophobicity, the sliding angle (the angle at which a water

droplet of a certain mass begins to slide down an inclined plate)

* Corresponding author at: Department of Metallurgy and Ceramic Science,

Graduate School of Science and Engineering, Tokyo Institute of Technology,

2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan.

E-mail address: anakajim@ceram.titech.ac.jp (A. Nakajima).

0169-4332/$ – see front matter # 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.apsusc.2007.07.171

or contact-angle hysteresis (the difference between advancing

and receding contact angles) has been commonly employed as a

criterion [7–14]. However, neither of those criteria represents

information related to water-shedding properties such as sliding

acceleration, and the droplet shape during practical sliding.

That information is crucial for representation of the realistic

sliding behavior of droplets. Recently, reports of relationships

between surface properties and sliding acceleration or droplet

shape during sliding have gradually increased [15–22].

Various surface composition patterns using self-assembled

monolayers (SAMs) were fabricated recently using photo-

lithography [22–27]; wettability on such surfaces has been

investigated extensively [22,26–31]. Those studies revealed

that such surfaces exhibit anisotropy in static and dynamic

hydrophobicity [27,31]. However, most of those studies

examined the sliding behavior for parallel and orthogonal

directions to the patterned lines; experimental analyses of the

S. Suzuki et al. / Applied Surface Science 254 (2008) 1797–18051798

effects of line direction on sliding behavior of water droplets

remain insufficient. Moreover, analyses based on the direct

observation of practical droplet motion during sliding, not the

instant of sliding, such as the sliding angle, are quite limited.

For this study, we prepared line-patterned hydrophobic

coatings using silane and photolithography technique with

various microstructures. Then, the sliding behaviors of a water

droplet on those surfaces were recorded using a high-speed

camera system. We changed the line direction against the slope

direction by in-plane rotation. Then, we directly observed the

water-droplet motion to investigate the effect of the alignment

of hydrophobic patterning on sliding behavior.

2. Experimental

2.1. Sample preparation

Sample substrates were cut from Si(1 0 0) wafers (Aki Corp.,

Miyagi, Japan) to 8 cm � 8 cm. These substrates were cleaned

using acetone and 10% HF solution to remove the heterogeneous

oxide surface layer [32]. Vacuum ultraviolet light (VUV) was

then irradiated (l = 172 nm with a power density of around

7 mW cm�2, UEM20-172; Ushio Inc.) to the substrates for

15 min in air to obtain Si–OH terminated surfaces, which reacted

with organosilanes [33,34]. Organosilane coating was carried out

using chemical vapor deposition (CVD) method. The pre-treated

substrates were set into a Petri dish together with 0.02 cm3

of heptadecafluoro-1,1,2,2-tetrahydrodecyltrimethoxysilane

(CF3(CF2)7CH2CH2Si(OCH3)3 (FAS, TSL8233; GE Toshiba

Silicones, Tokyo, Japan) in a glove box filled with dry N2. The

Petri dish was covered with a glass cap and heated in an oven at

423 K for 1 h under N2 atmosphere. After coating, substrates

were rinsed using acetone and toluene, and then dried at 353 K.

Subsequently, VUV was irradiated to the coating through a

photomask for 12 min under 100 Pa of air. The line and space

widths of photomasks with periodic lines were 100/100 mm or

500/500 mm. Hereafter, these samples are denoted as 500 mm

line-surface and 100 mm line-surface. The sample was rinsed

again using acetone and toluene. The water-contact angle of the

irradiated area was less than 58. The FAS/Si–OH line patterned

surface was coated with octadecyltrimethoxysilane (ODS,

CH3(CH2)17Si(OCH3)3 Aldrich Chemical Co. Inc., Milwaukee,

WI, U.S.A.) using the same procedure as that for FAS coating.

For comparison, plain FAS and ODS coatings were

fabricated on Si substrates. The FAS coating was applied on

cleaned Si. Then, ODS was coated on the Si surface after

decomposition of the FAS coating at the same condition as that

for patterning.

2.2. Evaluation

The coating surface was observed using scanning electron

microscope (FE-SEM, S-4500; Hitachi Ltd., Japan) without a

conductive coating. The static contact angle of a 4-mg water

droplet on plain FAS and ODS coatings was evaluated using a

sessile drop method with a commercial contact-angle meter

(Dropmaster DM-500; Kyowa Interface Science Co. Ltd.,

Japan). The contact angle was measured at five different points.

The sliding angle of a 30-mg water droplet on plain surfaces

was measured using the DM-500 automatic sliding system. The

advancing and receding contact angle values were also

measured at the sliding angle.

Water-droplets were evaluated for their sliding behaviors

(sliding distance, sliding velocity, and advancing–receding

contact angles during sliding) using a high-speed digital camera

system (512 PCI; Photron Ltd., and Dipp -Motion, -Macro;

Ditect Co. Ltd., Japan). The patterned samples with line-pitch

of 100 mm or 500 mm were set on the slope surface, which was

tilted 358 from a horizontal position. Droplets’ sizes were 20–

45 mg. They were started to slide by gentle upward removal of

the needle of the micro-syringe from the droplet. Image

recording was carried out from two different directions to

provide a side view and a top view. A water-droplet sliding

image was recorded at 250–1000 frames per second (fps). The

camera for the side view was located at the side of the slope

tilted 358. The sliding distance and advancing–receding contact

angles were evaluated from a recorded sliding image. The top

viewing position was the upside of the slope, normal to the

slope (Fig. 1(a)). The patterned sample was rotated in-plane at

the angle of F, which was determined by the direction of the

patterned line and slope (Fig. 1(b)). In this study, F was

changed from 08 to 908.

3. Results

The static contact angle of a 4-mg water droplet and sliding

angle of a 30-mg water droplet on plain ODS and FAS coatings

were, respectively, 988 and 178 (ODS), and 1078 and 118 (FAS).

The advancing and receding contact angles at that sliding angle

were, respectively, 101 � 18 and 84 � 18 on plain ODS, and

118 � 18 and 102 � 18 on plain FAS. A water droplet weighing

more than 30 mg can slide with positive constant acceleration

on plain ODS or FAS coatings at 358.Fig. 2 shows FE-SEM micrographs of the FAS surface with

periodic line-patterns of ODS regions. The bright region

corresponds to ODS; the dark region corresponds to FAS [25].

These micrographs show the ODS line as wider than that of the

FAS. The width ratios of FAS/ODS were estimated as 0.98 and

0.87, respectively, from micrographs for 500 mm (Fig. 2(a)) and

100 mm (Fig. 2(b)).

Fig. 3 presents the respective sliding velocities of advancing

and receding edges, vA and vR, and dynamic advancing and

receding contact angles for the sliding direction, uA and uR,

against the position of respective edges of a 25-mg water

droplet on (a) a 500 mm line-surface and (b) a 100 mm line-

surface at F = 908. This alignment provided the periodically

fluctuating velocity and deformation to the sliding droplets.

However, these fluctuations on a 500 mm line-surface were

more marked than those on a 100 mm line-surface. The

fluctuation interval of uA, uR, vA, and vR on a 500 mm line-

surface was roughly about 1 mm, which corresponds to the

width of a pair of the ODS line and the FAS line.

Fig. 4 shows the time dependence of the dynamic contact-

angle hysteresis (H = cosuR � cosuA) of a 25-mg droplet

Fig. 2. FE-SEM micrographs of the FAS surface periodically line-patterned by

ODS region with line/space of (a) 500/500 mm and (b) 100/100 mm. The ODS

and FAS regions are shown respectively as white and black.

Fig. 1. Schematic illustration for evaluation of water droplets’ sliding behavior

on these surfaces: (a) alignment of sample and high-speed cameras, (b)

alignment of samples and a droplet.

S. Suzuki et al. / Applied Surface Science 254 (2008) 1797–1805 1799

sliding on 500 mm and 100 mm line-surfaces at (a) F = 08 and

(b) F = 908. For F = 08, a water droplet slide with constant

velocity and exhibited almost no fluctuations in uA or uR.

Therefore, H was almost constant. For F = 908, fluctuation of

contact-angle hysteresis on a 500 mm line-surface was more

marked than that on a 100 mm line-surface.

Fig. 5 presents sequential photographs (200-ms intervals) of

a sliding 25-mg water droplet on (a) 500 mm and (b) 100 mm

line-surfaces. The line direction was rotated at F = 138 and 158in-plane, respectively, against the slope direction on the y-axis

(see Fig. 1(b)). On a 500 mm line-surface, the advancing and

receding side of the contact line of the droplet did not overcome

any interface of ODS–FAS lines during sliding; the droplet

completely slide down on the same lines. Therefore, the actual

sliding direction of the droplet corresponded with the line

direction, which was F = 138. On a 100 mm sample, a 25-mg

water droplet slide down almost directly with the slope

direction.

Fig. 6 shows the respective sliding behaviors of droplets with

various masses on the 500 mm line-surface rotated in-plane at

F = 138. Each droplet exhibited a different sliding direction

(different b in Fig. 1(b)) on the surface. Fig. 7 displays the

sequential outlines of a 35-mg water droplet shown in Fig. 6(b).

The ODS and FAS regions are shown respectively as gray and

white lines. A 35-mg droplet always moved on three or four

FAS and ODS lines. In such a situation, uA always became

greater than 908 and uR sometimes became greater than 908.Consequently, the outline did not coincide completely with the

three-phase contact line. However, characteristic deformation

is visible at the receding side (upper right side) of the droplet

before and after passing over the interface between ODS and

FAS lines, which corresponds to (A), (B), and (C) droplets

shown in the figure.

In that deformation, the receding edge moves on the

interfaces for the orthogonal direction to lines: (A) FAS to

ODS, (B) ODS to FAS, and (C) FAS to ODS. The length of the

receding contact line on the ODS region becomes greatest in the

(A) stage. Stage (B) shows the outline of the droplet after its

receding contact line surmounted the FAS–ODS interface. It is

noteworthy that the advancing contact line (lower left side of

the contact line) did not overcome any interface from situations

(A) to (B). Consequently, the contact-angle hysteresis for the

Fig. 4. Dynamic contact-angle hysteresis of the droplet sliding on a 500 mm

and a 100 mm line-surface against time, t, at (a) F = 08 and (b) F = 908.

Fig. 3. Sliding velocities of advancing and receding edges, vA and vR, and

dynamic contact angles for the sliding direction, uA and uR, against the position

of respective edges of a 25-mg water droplet sliding on (a) a 500 mm line-

surface and (b) a 100 mm line-surface rotated at F = 908 in the slope plane

(tilting with 358).

S. Suzuki et al. / Applied Surface Science 254 (2008) 1797–18051800

orthogonal direction in stage (A) is greater than that for stage

(B). During sliding of the droplet from stage (A) to stage (B), it

slide down in the y direction with a slight displacement to the x

direction. This movement can be evaluated as vector a, which

links the bottom edges of the droplets in the figure. For

movement of a droplet from stage (B) to stage (C), the contact

line advances orthogonally and overcomes the ODS–FAS

interface; the practical sliding direction is shown as vector b in

the figure. Vector c, which represents the practical sliding

direction of the droplet for the unit period, is obtainable by

resolving vectors a and b. For a 35-mg water droplet, the

displacement angle, b, between the y axis and vector c (see

Fig. 1) was about 48. This displacement angle was calculated

for several periods after sliding more than 4 cm on the patterned

sample. Fig. 8 depicts b against m evaluated from the sliding

behavior shown in Figs. 5 and 6 for droplets sliding on the

500 mm line-surface. Larger droplets showed smaller b.

Fig. 9 shows the sliding behavior of 25-mg water droplets on

a 500 mm line-surface rotated at (a) F = 358 and (b) F = 558 on

the slope tilted at 358. At this higher rotation angle, a 25-mg

droplet overcame the interface between lines and slide down

with a displacement angle of almost b = 0.

4. Discussion

In this study, the ODS line region was produced on the

surface after decomposition of FAS coating using photolitho-

graphy techniques. The widths of the prepared lines differed

from the ideal values (1/1). The discrepancy between the

measured and ideal values probably results from VUV

spreading at a slight distance between the photomask and

the sample substrate.

From the static and dynamic contact angles, the advancing

and receding contact line of the droplet can be pinned at the

interface from ODS to FAS. On the other hand, the practical

sliding behavior of the droplet implies that the advancing

contact line is also pinned at the FAS–ODS interface, as shown

from droplet (A) to (B) in Fig. 7. A plausible explanation of the

Fig. 6. Sliding behavior of droplets with various masses on a 500 mm line-surface

rotated at F = 138 on a slope tilted at 358. Droplet masses are, respectively, (a)

30 mg, (b) 35 mg, and (c) 45 mg. The image-recording interval is 200 ms.

Fig. 5. Sequential photographs of a 25-mg water droplet taken each 200 ms

from the top position to the sample surface tilted at 358: (a) droplet sliding on a

500 mm line-surface rotated in-plane at F = 138, (b) droplet sliding on a

100 mm line-surface rotated at F = 158.

S. Suzuki et al. / Applied Surface Science 254 (2008) 1797–1805 1801

pinning of FAS–ODS interface is the existence of a chemically

heterogeneous region. Using similar patterning techniques,

Song et al. [22] demonstrated the existence of hydrophilic

defect at the chemical interface attributable to the difference of

rigidity and length of a silane molecule. They reported that this

defect affects the sliding angle of water droplets on the

hydrophobic–hydrophobic line-patterned surface. Although

detailed surface analysis is required, an identical defect might

exist in this surface and affect the motion of the three-phase

line.

For a droplet to slide downward, the gravitational force must

overcome retentive forces. Eq. (1) has been derived and revised

Fig. 8. Plots of the displacement angle, b, and the averaged sliding acceleration

to the slope direction, y axis, [ay] evaluated for the unit period of sliding

behavior against droplet mass, m, on a 500 mm line-surface (a = 358, F = 138).

Fig. 7. Sequential images of the outline of a 35-mg water droplet shown in

Fig. 6. The ODS and FAS regions are shown respectively, as colored and white

columns. (a) Outline for 20 ms. Herein, the right side of the receding outline

shows interface (A) from FAS to ODS, (B) from ODS to FAS, and (C) from FAS

to ODS. (b) Magnified images of the outline of droplets at (A), (B), and (C)

positions.

S. Suzuki et al. / Applied Surface Science 254 (2008) 1797–18051802

for the retentive force, FR, necessary to overcome the interfacial

forces and move a droplet [35]:

FR ¼ kwgLVðcos uR � cosuAÞ; (1)

where k is a coefficient derived from the droplet shape, w is the

droplet width, and gLV is the liquid–vapor surface energy. This

equation implies that the retentive force is greatest when the

contact-angle hysteresis reaches its largest value.

On the periodical line-patterned surface, the dynamic contact

angle hysteresis of a water droplet depends on the microstructure.

Greater deformation can produce larger contact angle hysteresis.

A water droplet sliding along with ODS–FAS interfaces, i.e.

F = 0, showed no large fluctuations in the shape and exhibited

constant velocity (Fig. 4(a)), suggesting that the retentive force

for sliding was almost constant. When a water droplet slides

orthogonally downward, i.e. F = 908, a water droplet must

overcome each interface between the ODS–FAS lines. In Fig. 3,

the period of the motion of the advancing and receding edges

roughly corresponds to the line width: 1 mm on the 500 mm line-

surface and 200 mm on the 100 mm line-surface. Several peaks in

sliding velocity between these main periods are attributable to the

viscoelastic motion of the water droplet. Detailed analyses

revealed that the advancing and receding contact edges overcome

the boundary between FAS and ODS at different timings, and that

medium-sized valleys appear in vA and vR at the timing when

these edges overcome the boundary between FAS and ODS. This

result implies that the sticking of one edge can affect the motion

of another edge. The water droplet should have limited

elongation and shrinkage because of its size and the attainable

contact angle on the chemically patterned surface. This motion of

the droplet induces a small vibration on the surface shape of the

droplet because of its viscoelastic property, thereby producing

the several small peaks and valleys in vA and vR. The 500 mm

line-surface provides wider fluctuating velocity and larger

deformation than 100 mm patterning, as shown in Figs. 3 and

4(b). Similar line width dependence was reported by Song et al.

[22]. This result is attributable to the degree of the deformation of

the three-phase contact line. In this study, the bumpy shape of the

contact line is more remarkable on the 500 mm line-surface than

on the 100 mm line-surface. Results of a previous study [14]

showed that the length and arrangement of the three-phase

contact line affects the water droplets’ sliding angle. For an

isotropic continuous three-phase-contact line, it is expected that a

shorter length is advantageous for sliding. With FAS–ODS

patterning at F = 908, the line pitch of 100 mm is insufficiently

Fig. 9. Sliding behavior of 25-mg droplets sliding on a 500 mm line-surface on

a slope tilted at 358, which is rotated in-plane at (a) F = 358 and (b) F = 558.The image interval is 200 ms.

S. Suzuki et al. / Applied Surface Science 254 (2008) 1797–1805 1803

large to deform the three-phase contact line of 25–45 mg water

droplets.

The displacement angle (b) of water droplets during sliding

on the 500 mm line-surface depends on the droplet mass

(Figs. 6 and 8). However, this directional dependence is less

remarkable on the 100 mm line-surface. Droplets’ movements

are governed by the balance between gravitational and retentive

forces, which is proportional to the contact-angle hysteresis, as

described in Eq. (1). The gravitational force for the droplet

sliding on the tilted plane is described as mgsina, where m is the

droplet mass, g is the gravitational acceleration, and a is the tilt

angle. The retentive force will increase with increasing droplet

size proportionally to the length of the contact line, m�1/3, but

the gravitational force will also increase proportionally to the

droplet volume, m, suggesting that the increase rate of the

gravitational force is greater than that of the retentive force with

increasing droplet size. Consequently, if the gravitational force

for sliding is large, as it is for a large droplet mass, the contact

line overcomes the chemical interface; thereby, a smaller b

value is expected on line-patterned surfaces. Very recently, a

few reports predicted the possibility of using chemical stripes to

sort droplets [36] or microcapsules [37] from a computational

simulation. Our practical results shown in Fig. 8 indicate that

the water droplets are sortable by size according to their mass.

The retentive force, FR, for a sliding droplet derived from

Eq. (1) is simplified to the following equation using the droplet

contact radius, r0, with a circular contact area of

FR ¼ k0r0gLVH; (2)

where k0 is a coefficient depending on the droplet shape. The

relationship between the contact angle u and r0 is given as

r0 ¼�

3V=p

ð2þ cos uÞð1� cos uÞ2�1=3

sin u; (3)

where V is the droplet volume [22]. Eq. (2) was derived for the

circular contact line. Therefore, the k0 includes information

related to distortion from the circular contact shape of the

droplet. The evaluated elongation (L/W; here, L is the length of

parallel direction to lines, W is the width of orthogonal direction

to lines) was 1.1–1.2 for a water droplet of 25–45 mg sliding on

the surface that had been chemically patterned with 500 mm

pitch of ODS–FAS (F = 138, tilted at 358). The fluctuations of

the elongation of the droplet before and after overcoming the

chemical interface are within 0.1. It is considered that these

values are not so large. Consequently, the retentive force is

evaluated sufficiently from Eq. (2).

When the line-patterned surface is rotated at F, the retentive

force for the orthogonal direction (FR(?)) and that for the

parallel direction (FR(//)) to the lines are estimated using the

following equation:

FRð==;?Þ ¼ Kð==;?Þr0gLVHð==;?Þ; (4)

where K(//,?) are coefficients related respectively to the parallel

(//) and orthogonal (?) directions to the lines. The coefficients’

values depend on the droplet shape. The H(//,?�) are contact-

angle hysteresis values for respective directions.

Fig. 10 shows a schematic illustration on the force model for

a sliding droplet on a surface with periodic line regions with the

rotation angle of F. Fig. 10 shows the retentive forces for the

orthogonal and parallel directions. The equations for a droplet’s

motion on the x and y axes are

max ¼ FRð? Þ cos F� FRð==Þ sin F for the x axis; and (5)

may ¼ mg sin a� FRð? Þ sin F� FRð==Þ cos F for the y axis:

(6)

Therein, m is the droplet mass, and ax and ay, respectively

represent the sliding acceleration of droplets for the x and y

axes; FR(//,?) represents the retentive forces derived from

Eq. (4). Eqs. (5) and (6) represent the sliding acceleration for

the x and y axis, as determined by the balance of the gravity

force and retentive force for the orthogonal and parallel

directions. The results shown in Fig. 4 show that the contact

angle hysteresis that is orthogonal to line (H(?)) has a periodical

Fig. 11. Averaged contact-angle hysteresis, [H(//,?)], and sliding acceleration

for the slope direction, [ay], as evaluated from the sliding behavior of a water

droplet on a 500-mm line-surface tilted at 358 at F = 08 and 908.

Table 1

K(//) and K(?) at F = 08, 908, K0(//) and K0(?) at F = 138; and K0(?)/K(?) for water

droplet masses, m, of 30–45 mg

Droplet mass;

m (mg)

F = 08K(//)

F = 908K(?)

F = 138 K0(?)/

K(?)K0(//) K0(?)

30 2.09 2.21 2.22 0.504 0.228

35 2.19 2.23 2.21 0.499 0.223

45 2.26 2.28 2.09 0.519 0.227

Fig. 10. Schematic illustration of the driving and retentive forces acting on a

sliding droplet on a surfacewith periodic line regions rotated at F in surface plane.

S. Suzuki et al. / Applied Surface Science 254 (2008) 1797–18051804

fluctuation over a wide range. For that reason, the sliding

accelerations of droplets can vary from a negative value to a

positive value.

The average retentive force is estimated using the average

contact-angle hysteresis for a unit period from Eq. (2), as

½FRð==;?Þ� ¼ Kð==;?Þr0gLV½Hð==;?Þ�: (7)

The average sliding acceleration of droplets for the y axis,

[ay], is also identified for m. For the unit period, dynamic

equations can be derived as

m½ax� ¼ ½FRð? Þ�cos F� ½FRð==Þ�sin F for the x axis; and

(8)

m½ay� ¼ mg sin a� ½FRð? Þ�sin F

� ½FRð==Þ�cos F for the y axis: (9)

The displacement angle of a droplet, b, is determined by the

balance of resulting forces for the x and y axes for a unit period.

tan b ¼ ½ax�=½ay� (10)

This relationship is reasonable when the fluctuation of

instantaneous acceleration is sufficiently small and periodical.

Fig. 11 shows the arithmetic means of contact-angle

hysteresis, [H(//,?)], at F = 0 and 908 for the unit period

against m. The [H(//)] is almost identical to [H(?)], although the

instantaneous value of [H(?)] fluctuated widely by periodic

deformation. The averaged sliding acceleration of droplet

sliding at F = 0 and 908, [ay], is also plotted in this figure From

these results, K(?) and K(//) are calculable for the slope direction

given by Eq. (9), as listed in Table 1. The difference of K(?) and

K(//) values originates from the droplet deformation, either

along the chemical interfaces or orthogonal to them. We can

estimate the sliding behavior at any F using Eqs. (8) and (9),

and the sliding direction for the unit period from Eq. (10).

However, an experimental difficulty exists in measuring the

change of actual contact-angle values of a water droplet sliding

along with or across several chemical interfaces. Here, the

average retentive forces of a droplet sliding parallel and

orthogonal to periodic lines’ direction, [FR(//)] and [FR(?)],

were easily estimated using the averaged contact-angle

hysteresis obtained at F = 08, 908 [H(// from F=0)], and [H(?

from F=90)] from the following equation:

½FRð==;?Þ� ¼ K 0ð==;?Þr0gLV½Hð==;? from F¼0;90Þ�; (11)

in which K0(//,?) are coefficients, relating not only to the droplet

shape, but also to the deviation originated from using the

averaged contact-angle hysteresis obtained at F = 08, 908instead of the actual values. At F = 138 on a 500 mm line-

surface, the averaged sliding acceleration for the y-axis slope

direction, [ay], is depicted in Fig. 8, which is evaluated by the

practical sliding behavior of the sliding water droplet. The K0(//,?) are calculable, as listed in Table 1, from Eqs. (3), (8), (9),

(10), and (11). For a 25-mg droplet, K0(//,?) cannot be calculated

because [ay] was 0. The calculated values of K0(//) are almost

identical to those of K(//). However, the K0(?) value is smaller

than K(//). The values of K0(?)/K(?) for all droplets almost equal

ca. 0.225, which is sin 138. The averaged contact-angle hyster-

esis values are expected to be proportional to the droplet mass,

m, which is related to the gravitational force, as shown in

Fig. 11. At F = 08, 908, the direction of the gravitational force,

S. Suzuki et al. / Applied Surface Science 254 (2008) 1797–1805 1805

mgsin358, coincides with the slope direction. On the other hand,

the driving force in the orthogonal direction for lines at F = 138decreased to sin138, suggesting that the magnitude of deforma-

tion can be decreased to the same ratio. This deviation is

expected to appear in the value of K0(?)/K(?).

For greater displacement of droplets to the x direction, which

gives greater b, it is important to optimize the balance between

the gravitational force and retentive force. From Eq. (8), droplets

are not expected to displace a larger range to the x direction at a

larger rotation angle because cosF will decrease and sinF will

increase with increasing F. At larger F, the driving force will

increase in the orthogonal direction, suggesting that the droplet

can readily overcome the interface with a greater driving force.

Actually, a 25-mg droplet can readily overcome the interfaces on

500-mm line-surface at F = 358, 558, although the droplet cannot

overcome the interface at F = 138 (see Fig. 5(a) and Fig. 9). The

length and continuity of the underlying receding contact line

decrease with increasing F, indicating that the droplet would

overcome the interface because of decreasing contact angle

hysteresis for the orthogonal direction. These trends depend on

the line-patterning microstructure and contrasting hydrophobi-

city between lines.

5. Conclusion

For this study, we prepared line-patterned surfaces using FAS

and ODS. Subsequently, using direct observation of the practical

droplet motion during sliding, we investigated the effects of the

line direction on water droplets’ sliding behavior. Water droplets

slide downward with a periodic large deformation of the contact

line and sliding velocity fluctuation when it vertically crossed

over the 500-mm ODS line regions in FAS regions on a Si surface

tilted at 358. These behaviors are less pronounced for the parallel

direction to lines or a 100 mm line-surface. Smaller droplets slide

down with greater displacement in the line direction on 500 mm

line patterning when the lines were rotated at 138 for the slope

direction in-plane. This sliding behavior depends on the droplet

size and rotation angle. For that reason, the droplets’ different

sliding behaviors represent different balances that pertain

between gravitational and retention forces.

Acknowledgement

This work was supported in part by Research Fellowships of

the Japan Society for the Promotion of Science for Young

Scientists (JSPS Research Fellow 2005-08586).

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