International Journal of Multiphase Flow 129 (2020) 103352

Contents lists available at ScienceDirect

International Journal of Multiphase Flow

journal homepage: www.elsevier.com/locate/ijmulflow

Dynamic Wetting Behaviors of Water Droplets on Surfaces with Dual

Structures at the Nanoscale

Tae Woo Kwon

a , Kwang Ho Lee

a , Young Min Seo

b , Joonkyung Jang

c , Man Yeong Ha

a , ∗

a School of Mechanical Engineering, Pusan National University, 2 Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan, 46241, Korea b Rolls-Royce and Pusan National University Technology Centre in Thermal Management, Pusan National University, 2 Busandaehak-ro 63beon-gil,

Geumjeong-gu, Busan, 46241, Korea c Department of Nanoenergy Engineering, Pusan National University, 2 Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan, 46241, Korea

a r t i c l e i n f o

Article history:

Received 20 February 2020

Revised 18 May 2020

Accepted 19 May 2020

Available online 22 May 2020

Keywords:

Molecular dynamics

Dual structure

Water droplet

Contact angle

a b s t r a c t

Molecular dynamics simulations were carried out to investigate the static and dynamic wetting behaviors

of water droplets on surfaces with single and dual structures at the nanoscale. The effects of the surface

characteristic energy, pillar height, and applied force on the dynamic wetting behavior were considered

in this study. The dual structures were constructed by attaching small minor bump textures to the main

pillar structures. The dynamic behaviors of water droplets could be classified into four different groups

according to their dynamic shapes. The dynamic wetting behaviors were quantitatively evaluated accord-

ing to the contact angle hysteresis and the ratio of water molecules penetrating into the gaps between

pillars. As a result, the dual structures make the surface more hydrophobic in the dynamic state, as well

as the static state, compared to the single structures.

© 2020 Elsevier Ltd. All rights reserved.

1

a

i

c

p

t

l

b

d

l

u

Y

r

N

c

Y

t

s

B

d

v

d

(

2

e

h

d

o

e

w

i

t

t

a

n

d

2

t

a

s

t

h

0

. Introduction

Wetting is the ability of a liquid to maintain contact with

surface. Recently, the interest in wettability studies has been

ncreasing due to the technological applications, such as self-

leaning ( Li et al., 2018 ), drag reduction ( Ou et al., 2004 ), and oil

urification ( Wang et al., 2016 ). These studies generally quantify

he degree of wetting by measuring the contact angle of the

iquid droplet on a solid surface, which is determined by the force

alance among the liquid, solid, and vapor phases acting on the

roplet.

Early studies theoretically predicted the contact angle of a

iquid droplet on a solid surface. The contact angle of a liq-

id droplet on a perfectly smooth surface can be described by

oung’s equation ( Young, 1805 ). However, all real surfaces have

oughness because of the presence of structures ( Barthlott and

einhuis, 1997 , Watson et al., 2011 ), resulting in a considerable

hange in the contact angle. Wenzel ( Wenzel, 1936 ) modified

oung’s equation and derived an equation that describes the con-

act angle when a liquid droplet completely fills the gaps between

tructures on a smooth surface. Cassie and Baxter ( Cassie and

axter, 1944 ) derived the contact angle equation for when a liquid

roplet does not fill the gaps between the structures.

∗ Corresponding author.

E-mail address: myha@pusan.ac.kr (M.Y. Ha).

a

d

ttps://doi.org/10.1016/j.ijmultiphaseflow.2020.103352

301-9322/© 2020 Elsevier Ltd. All rights reserved.

Many experimental studies have considered the effect of

arious textures on a smooth solid surface on the static and

ynamic contact angle behaviors of a droplet on the surfaces

Martines et al., 2005 , Oner and McCarthy, 20 0 0 , Miwa et al.,

0 0 0 , Yoshimitsu et al., 2002 , Song et al., 2006 ). Martines

t al. ( Martines et al., 2005 ) experimentally investigated the

ydrophilicity, hydrophobicity, and sliding behaviors of water

roplets on nanoasperities with controlled dimensions. Forests

f hydrophilic and hydrophobic slender pillars were the most

ffective configurations for making a surface super-wettable and

ater-repellent, respectively.

Oner and McCarthy ( Oner and McCarthy, 20 0 0 ) experimentally

nvestigated the importance of structures of the three-phase con-

act line on the dynamic hydrophobicity of surfaces that have been

extured with various types of posts, such as square, rhombus, star,

nd indented-square posts. They showed the changes in the dy-

amic behavior of the water droplet according to the post height,

istance between posts, and their shape. Miwa et al. ( Miwa et al.,

0 0 0 ) carried out an experimental study and proposed an equa-

ion that describes the relationship between the contact angle

nd the sliding angle of a water droplet on a super-hydrophobic

urface with roughness. They also developed a super-hydrophobic

ransparent film with different surface roughness, which gave

lmost no resistance to the sliding of the water droplet.

Yoshimitsu et al. ( Yoshimitsu et al., 2002 ) fabricated a hy-

rophobic silicon wafer with pillar-like and groove structures

2 T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352

b

p

b

g

t

C

2

Z

n

w

e

v

s

f

P

r

p

t

r

(

i

t

h

p

o

c

t

s

a

2

r

d

T

s

d

r

v

b

2

t

t

c

t

U

b

p

a

p

a

l

t

p

t

a

J

a

1

to investigate the hydrophobic and sliding behaviors of a water

droplet on the surfaces. They showed that it is more effective to

design the surface with respect to the shape and extent of the

three-phase line than to increase the contact angles by merely

decreasing the solid-water contact area. Song et al. ( Song et al.,

2006 ) experimentally investigated the static and dynamic hy-

drophobic behaviors of water droplets on a line-patterned surface.

The surface was prepared using fluoroalkylsilances with different

molecular chain lengths. They showed that the sliding acceleration

of a water droplet on the patterned surface is governed by both

the chemical composition and the patterning structure.

In addition to these experimental studies ( Martines et al., 2005 ,

Oner and McCarthy, 20 0 0 , Miwa et al., 20 0 0 , Yoshimitsu et al.,

2002 , Song et al., 2006 ), many numerical studies ( Lundgren et al.,

2007 , Koishi et al., 2011 , Yong and Zhang, 2009 , Yoo et al., 2018 ,

Chai et al., 2009 , Hirvi and Pakkanee, 2008 , Jung et al., 2012 ,

Rahmawan et al., 2010 , Kwon et al., 2018 ) using molecular dy-

namics simulations have been carried out to investigate the static

and dynamic behaviors of nanoscale water droplets on a surface

textured with various structures. Lundgren et al. ( Lundgren et al.,

2007 ) performed molecular dynamics simulations to investigate

the static behavior of nanoscale water droplets on heterogeneously

patterned surfaces. They considered the effects of the relative sizes

of the domains and the droplets, the pillar width, and the gap be-

tween the pillars on the static behaviors of water droplets. They

showed the importance of the detailed topography and composi-

tion of the solid surface.

Koishi et al. ( Koishi et al., 2011 ) conducted a large-scale molec-

ular dynamics simulation study to measure the contact angle hys-

teresis of a nanodroplet of water placed on nanopillared surface.

They simulated the behavior of water droplet by systematically

varying the number of water molecules in the droplets. They mea-

sured the contact angle hysteresis by using a conventional defini-

tion, and a new definition which can be extended to estimate hys-

teresis between the Cassie and Wenzel state. This study found that

the contact-angle hysteresis in the Cassie state is weaker than that

in the Wenzel state, which is consistent with experimental obser-

vations.

Yong et al. ( Yong and Zhang, 2009 ) carried out molecular dy-

namics simulations to investigate the nanoscale wetting on groove-

patterned surfaces and compared their results with the Wenzel

and Cassie-Baxter continuum theories. For hydrophobic surfaces,

their computational results for the static contact angles obeyed the

predictions of Wenzel theory for wetted contacts and Cassie-Baxter

theory for composite contacts. However, for hydrophilic surfaces,

their results were higher than Wenzel’s prediction.

Yoo et al. ( Yoo et al., 2018 ) carried out molecular dynamics sim-

ulations to examine the static wetting characteristics of nanosize

water droplets on surfaces with various pillar surfaces according

to the surface fraction, surface energy, and pillar height. Chai et al.

( Chai et al., 2009 ) conducted molecular dynamics simulations to

investigate the static wetting characteristics of water droplets on

modified amorphous silica surfaces. They considered the effects of

different degrees of surface hydroxylation and silanization on the

transformation of the surface characteristics from hydrophilic to

hydrophobic.

Hirvi et al. ( Hirvi and Pakkanee, 2008 ) carried out molecular

dynamics simulations to investigate the dynamic wetting charac-

teristics of water droplets when they collide and slide on nanos-

tructured polyethylene and poly-polymer surfaces. They showed

that the final equilibrium shape and state of the water droplet de-

pend on the surface hydrophobicity but are independent of the ini-

tial velocity. They observed the Wenzel state of a water droplet on

the hydrophilic surface, and the water droplet bounced on a hy-

drophobic surface. Jung et al. ( Jung et al., 2012 ) conducted molec-

ular dynamic simulations and investigated the static and dynamic

ehaviors of water droplets on a corrugated surface with nanosize

illar-type structures with external forces applied. The dynamic

ehavior of the water droplets was classified into three different

roups, which depended on the static state of the water droplet,

he pillar characteristics, and the magnitude of the applied force.

Many previous studies ( Martines et al., 2005 , Oner and Mc-

arthy, 20 0 0 , Miwa et al., 20 0 0 , Yoshimitsu et al., 20 02 , Song et al.,

006 , Lundgren et al., 2007 , Koishi et al., 2011 , Yong and

hang, 2009 , Yoo et al., 2018 , Chai et al., 2009 , Hirvi and Pakka-

ee, 2008 , Jung et al., 2012 ) examined the static and dynamic

etting behaviors on the surface with the single structures. How-

ver, many surfaces encountered in nature, like lotus leaves, have

ery complex multiple structures that result in super-hydrophobic

urface characteristics. Rahmanwan et al. ( Rahmawan et al., 2010 )

abricated dual-scale rough surfaces which consist of microscale

DMS pillars covered with nanoscale wrinkles. This dual structure

esulted in super hydrophobic surface characteristics. Small micro-

illar spacing ratios resulted in a super hydrophobic surface with

he contact angle over 160 °, while larger micro-pillar spacing ratios

esulted in a less hydrophobic contact angle of 130 °. Kwon et al.

Kwon et al., 2018 ) conducted molecular dynamics simulations to

nvestigate the static behavior of water droplets on a surface tex-

ured with dual structures at the nanoscale. They compared the

ydrophobicity of dual structure with that of single structures and

roposed the surface adhesion energy as a fundamental measure

f wettability. These previous studies have researched the surface

haracteristics of multiple structures, but only in the static condi-

ion, not the dynamic condition. The dynamic wetting behaviors

howed different results compared to the static wetting behavior

s shown in previous studies ( Hirvi and Pakkanee, 2008 , Jung et al.,

012 ).

In the present study, molecular dynamics simulations were car-

ied out to investigate the dynamic wetting behaviors of water

roplets on a solid surface with dual structures at the nanoscale.

he dual structures were constructed by attaching small bumps to

ingle pillar structures. The dynamic wetting behaviors of water

roplets in the presence of an applied force were classified. The

esults of single and dual structures were compared in order to in-

estigate the effect of the dual structures on the dynamic wetting

ehavior of water droplets.

. Computational methodology

Molecular dynamics was used to simulate the behaviors of wa-

er droplets on rough surfaces. The molecular dynamics simula-

ions predict the physical movements of atoms and molecules by

alculating the potential energy function between them. The po-

ential energy function is expressed as follows:

total = U bond + U angle + U coulomb + U LJ (1)

There are two kinds of potential energy terms in this function:

onded and non-bonded terms. U bond and U angle are the bonded

otential terms, which model the interactions of covalently bonded

toms in the same molecule. U bond is the two-body spring bond

otential and describes the harmonic vibrational motion between

pair of covalently bonded atoms. U angle is the three-body angu-

ar bond potential from the angular vibrational motion between a

riple of covalently bonded atoms.

The non-bonded potential terms, U columb and U LJ , describe the

otentials that involve interactions between pairs of atoms other

han covalently bonded atoms. U columb is the Coulomb potential

nd describes the electrostatic interaction energy. The Lennard-

ones potential, U LJ , describes interactions between two atoms that

rise from a balance between repulsive and attractive forces. The

2-6 Lennard-Jones potential used in this paper is expressed as

T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352 3

Fig. 1. Coordinate system and computational domain for the simulation of a water droplet on a surface with the dual structure: (a) initial state, (b) equilibrium state, and

(c) after external force is applied.

e

U

ɛ

a

e

c

ε

σ

i

b

e

s

o

t

q. (2) .

LJ = 4 ε i j

[ (σi j

r i j

)12

−(

σi j

r i j

)6 ]

(2)

ij and σ ij are the LJ energy and length parameters, respectively,

nd r ij is the distance between a pair of atoms i and j . The LJ en-

rgy and length parameters are obtained by the Lorentz-Berthelot

ombination in equation (3) and (4) .

i j =

√

ε ii × ε j j (3)

i j =

σii + σ j j

2

(4)

Fig. 1 shows the coordinate system and computational domain

n the initial state, the equilibrium state, and after the external

ody force is applied. The simulation was performed in two differ-

nt steps. In the first step, a cube of water was set on a surface, as

hown in Fig. 1 (a), and then the simulation was conducted with-

ut any external force. After this step, the water droplet reaches

he static equilibrium state, as shown in Fig. 1 (b). In the second

4 T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352

Fig. 2. Geometry information for the dual and single structure: (a) top view (single structures), (b) side view (single structures), (c) top view (dual structures), and (d) side

view (dual structures).

2

s

r

t

d

d

w

S

i

w

t

a

t

o

p

o

i

+

a

d

F

ɛ

l

l

T

i

w

f

a

o

stage, constant external force is applied to the water droplet, which

changes its shape on the surface, as shown in Fig. 1 (c).

A canonical ensemble (NVT ensemble) was used during the

molecular dynamics simulation with a constant number of atoms

(N), fixed volume (V), and fixed temperature (T). Periodic bound-

ary conditions were applied in the x, y and z directions. As

shown in Fig. 1 (a), the dimension of the modeled surface used is

L x × L z = 320 A × 120 A, which is large enough to avoid any merg-

ing of the droplet at the periodic boundaries. The temperature was

fixed at 298.15 K, and the number of water molecules was 3921.

The water molecules were modeled with the TIP3P model, which

describes the behaviors of water molecules well in the standard

state of 1 atm and 298.15 K ( Price and Brooks, 2004 ).

The values of ɛ ww

and σ ww

between water molecules in the LJ

potentials of the TIP3P model are 0.1521 kcal/mol and 0.3536 nm.

For the sake of simplification in the modeling of the minor bumps

of the dual structure, the surface structure was selected as a sim-

ple cubic structure with a lattice distance of 2.12 A. The LJ length

parameter of the solid atoms σ s was set as 0.28 nm from the char-

acteristic length of the solid. In order to change the intrinsic hy-

drophobicity of the surface, the characteristic energy of the solid

atoms ɛ s was varied from 0.1 kcal/mol to 0.3 kcal/mol.

Fig. 2 shows the geometry information used for the single and

dual structures. As shown in Fig. 2 (a) and (b), the single structure

has only major rectangular pillars. In the case of the dual struc-

ture, minor cubic bumps are attached to the top and sides of the

major pillars and are represented with dark and bright gray colors

in Fig. 2 (c) and (d). The width of the pillars P and the interpillar

gap between pillars G are both fixed at 12.72 A. The height of pil-

lars H was varied from 8.48 to 25.44 A. The length of each minor

cubic bump was fixed at 4.24 A.

The velocity Verlet algorithm is used to integrate Newton’s

equation of motion. The time step for the simulation was set to

.0 fs. As explained above, the simulation was conducted in two

tages. It takes about 2,50 0,0 0 0 iterations to reach a static equilib-

ium state in the first stage, and then the contact angle between

he solid surface and water droplet is measured from a normalized

ensity field of the droplet to investigate the static behaviors. The

istance between a normalized density of 0.2 and 0.8 is the same

ith the thickness of the liquid-vapor interface of water droplet.

o, it can be considered as the liquid-vapor interface. As a result,

n this study, the water droplet periphery is defined as the line

ith a normalized density of 0.5 which is the centerline between

hat of 0.2 and 0.8 ( Hong et al., 2009 ). The contact angle is defined

s the angle between a tangential vector that starts from the con-

act point with the solid surface and a projected vector on the top

f the structures from a normal vector that starts from the same

oint, as shown in Fig. 3 (a). The contact angle was time-averaged

ver the last 2 ns of molecular dynamics simulations. As shown

n Fig. 3 (b), the contact angles were calculated at 4 points ( + x , - x ,

z and –z ), and their values were averaged to evaluate the contact

ngle.

In the second stage, a constant force F is applied in the x -

irection:

= exp (C ε s / σs ) (5)

s represents the characteristic energy of the solid surface. The LJ

ength parameter of the solid atoms σ s is used as the characteristic

ength of the solid surface. The values of C are shown in Table 1 .

he interactions between molecules are affected by the character-

stic energy ɛ s and characteristic length σ s . The external body force

as determined using Eq. (5) to consider the effects of these sur-

ace characteristics. The basic force was set with two surface char-

cteristics and the value of C was varied to control the magnitude

f forces as used by Jung et al. ( Jung et al., 2012 ).

T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352 5

Fig. 3. Density profile of a water droplet and measurement of the contact angles: (a) side view, (b) top view

Table 1

Three different forces applied to the water

droplet

C ( F = exp (C ε s / R min ) ) Force [kcal/mol A]

40 0.056264

60 0.013346

80 0.003166

Fig. 4. Dynamic advancing and receding of the contact angle

t

e

t

e

J

θ

w

3

w

a

i

s

t

s

e

t

k

s

t

i

I

a

t

i

t

a

T

H

o

e

t

n

s

o

A

p

u

a

3

g

e

w

d

g

S

F

a

e

t

c

f

w

l

To evaluate the dynamic behavior of the water droplet, the con-

act angle hysteresis was calculated, which is defined as the differ-

nce between the advancing contact angle θ adv and receding con-

act angle θ rec , as shown in Fig. 4 . θ adv and θ rec are expressed as

xponential functions of time according to the suggestion given by

ung et al. ( Jung et al., 2012 ):

adv or rec = exp (A × log t + B ) (6)

here A and B are constants, and t is the time in nanoseconds.

. Results and discussion

For the sake of simplicity and readability, subscript notions

ere used to distinguish different cases. As defined in Table 2 , E

nd H represent the normalized characteristic energy and normal-

zed height, respectively, which characterize the geometry of the

urface. F represents the magnitude of the force applied to the wa-

er droplet. The types of the structure is represented by N (non-

tructured smooth), S (single structure), and D (dual structure). For

xample, DE 1 H 1 F 1 means the case corresponding to the dual struc-

ure with the height of 8.48 A at the characteristic energy of 0.1

cal/mol when the applied force of 0.0031 kcal/mol A.

Table 2

Subscript notations for the normalized charac

force applied to the water droplet

Subscripts Characteristic energy (E) Pill

0 - Sm

1 0.1 kcal/mol 8.4

2 0.2 kcal/mol 16.

3 0.3 kcal/mol 25.

Fig. 5 shows an image of water droplets on the non-structured

mooth surfaces ( NE 1 H 0 F 0 , NE 2 H 0 F 0 , and NE 3 H 0 F 0 ). For NE 1 H 0 F 0 ,

he contact angle is 110.3 ±5.6 °, which is larger than 90 °, as shown

n Fig. 5 (a). Therefore, the surface at E 1 is intrinsically hydrophobic.

n Fig. 5 (b), the water droplet formed a hemisphere with a contact

ngle of 91.4 ±3.8 ° on a smooth surface at E 2 . The surface is neu-

ral or partially hydrophobic in this case. At E 3 , the contact angle

s 70.4 ±5.2 , which shows intrinsically hydrophilic surface charac-

eristics, as shown in Fig. 5 (c).

Fig. 6 shows the contact angles on smooth flat surfaces as

function of 1/ r d , where r d is the radius of the water droplet.

he obtained contact angles were compared with previous results.

ong et al. ( Hong et al., 2009 ) considered characteristic energies

f 0.29 to 0.56 kcal/mol and used 6845 water molecules. Werder

t al. ( Werder et al., 2003 ) carried out simulations for characteris-

ic surface energies of 0.1881 to 0.4389 kcal/mol with a constant

umber of water molecules (40 0 0). Ko et al. ( Ko et al., 2015 ) con-

idered characteristic energies of 0.1 to 1.0 kcal/mol. The number

f water molecules was 3921, which is the same as in this study.

s shown in Fig. 6 , our computational results generally represent

revious results well when considering the differences in the sim-

lations conditions, such as the boundary conditions, atom array,

nd number of water molecules used.

.1. Static wetting behavior

The static wetting behaviors of droplets on surfaces with sin-

le and dual structures were examined in order to reach the

quilibrium state. Fig. 7 shows images of droplets on the surface

ith single and dual structures at E 1 . As shown in Fig. 7 (a), the

roplet for SE 1 H 1 F 0 is in the Wenzel state and has a contact an-

le of 116.3 ±3.6 °. As H increases to H 2 and H 3 , the droplets for

E 1 H 2 F 0 and SE 1 H 3 F 0 change to the Cassie-Baxter state as shown in

igs. 7 (b) and 7(c), resulting in higher contact angles of 127.4 ±4.3 °nd 131.7 ±3.1 °, respectively. The characteristic energy E 1 is not

nough to attract water molecules on the top of the pillars to

he gaps between the pillars. Thus, the single structure for E 1 auses the surface to be more hydrophobic than the smooth sur-

ace, which has a contact angle of 110.3 ±5.6 °. On the other hand,

ith the dual structure, the water molecules on the top of pil-

ars cannot penetrate into the gaps between pillars because the

teristic energy, normalized height, and

ar height (H) Force (F)

ooth flat surface Static state

8 A 0.0031 kcal/mol A

96 A 0.0134 kcal/mol A

44 A 0.0562 kcal/mol A

6 T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352

Fig. 5. Water droplets on a smooth flat surface: (a) NE 1 H 0 F 0 , (b) NE 2 H 0 F 0 , and (c) NE 3 H 0 F 0

Fig. 6. Contact angle on a smooth flat surface obtained from the present study and

previous studies as a function of 1/ r d .

t

r

l

a

D

o

e

e

d

r

s

8

h

t

d

a

t

t

d

a

a

a

i

p

a

a

9

s

t

d

d

3

s

minor bumps on the major pillars prevent it. As a result, the

droplets for DE 1 H 1 F 0 , DE 1 H 2 F 0 , and DE 1 H 3 F 0 are in the hydropho-

bic (Cassie-Baxter) state on the dual surface as shown in Figs. 7 (d),

7(e) and 7(f), and the contact angles are 120.6 ±4.3 , 122.6 ±1.5 ,

and 127.0 ±2.3 , respectively. Similar to the single structure, the

dual structure results in a more hydrophobic state than that of a

smooth surface.

Fig. 8 shows the static shapes of droplets that formed on the

surfaces with single and dual structures in the static equilibrium

state at E 2 . As the characteristic energy increases from E 1 to E 2 ,

the attraction between the surface and water droplet increases so

that water molecules can penetrate the gaps between the pillars.

As a result, the droplets for SE 2 H 1 F 0 , SE 2 H 2 F 0 , and SE 2 H 3 F 0 are

in the Wenzel state as shown in Figs. 8 (a), 8(b) and 8(c). Those

droplets have the static contact angles of 89.3 ±6.3 , 88.5 ±5.5 , and

87.7 ±5.1 , respectively, showing partially hydrophilic characteris-

ics. In Fig. 8 (d), the droplet for DE 2 H 1 F 0 is also in the Wenzel state,

esulting in a static contact angle of 92.2 ±6.2 , which is a little

arger than that for SE 2 H 1 F 0 , which is 89.3 ±6.3 . However, Figs. 8 (e)

nd 8(f) show different static states of droplets for DE 2 H 2 F 0 and

E 2 H 3 F 0 . As H increases from H 1 to H 2 to H 3 , the water molecules

n surfaces with dual structures for DE 2 H 2 F 0 and DE 2 H 3 F 0 cannot

asily penetrate into the gaps between pillars due to the combined

ffect of the minor bumps and the pillar height. As a result, the

roplets for DE 2 H 2 F 0 and DE 2 H 3 F 0 are in the Cassie-Baxter state,

esulting in static contact angles of 106.4 ±5.3 and 110.6 ±4.3 , re-

pectively. These angles are larger than the values of 88.5 ±5.5 and

7.7 ±5.1 for SE 2 H 2 F 0 and SE 2 H 3 F 0 , respectively, due to the larger

ydrophobicity of the dual structure compared to the single struc-

ure.

Fig. 9 shows images of droplets on the surface with single and

ual structures at E 3 in the static equilibrium state. As the char-

cteristic energy increases further to E 3 , the water molecules on

he single structure penetrate into the gaps between pillars due

o the presence of the strong characteristic energy E 3 . Thus, the

roplets for SE 3 H 1 F 0 , SE 3 H 2 F 0 , and SE 3 H 3 F 0 are in the Wenzel state

s shown in Figs. 9 (a), 9(b) and 9(c). The resulting static contact

ngles for SE 3 H 1 F 0 , SE 3 H 2 F 0 , and SE 3 H 3 F 0 are 40.5 ±3.7 , 43.5 ±2.3 ,

nd 47.5 ±2.1 , respectively, showing hydrophilic surface character-

stics. Similar to the droplets on the single structure, the droplets

enetrated into the gaps between pillars due to the strong char-

cteristic energy. As a result, the droplets for DE 3 H 1 F 0 , DE 3 H 2 F 0 ,

nd DE 3 H 3 F 0 are also in the Wenzel state as shown in Figs. 9 (d),

(e) and 9(f). DE 3 H 1 F 0 , DE 3 H 2 F 0 , and DE 3 H 3 F 0 have the hydrophilic

tatic contact angles of 50.5 ±4.9 , 75.8 ±4.5 , and 79.9 ±5.2 , respec-

ively. Thus, when E = 3, the static contact angles are larger for the

ual structure than the single structure because of the higher hy-

rophobicity of the dual structure.

.2. Dynamic shape of water droplets

The water droplet changes its shape when it moves along the

urface in the presence of an applied constant force. The dy-

T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352 7

Fig. 7. Water droplets on the surfaces with single and dual structures in the static state at the characteristic energy of 0.1 kcal/mol: (a) SE 1 H 1 F 0 , (b) SE 1 H 2 F 0 , (c) SE 1 H 3 F 0 , (d)

DE 1 H 1 F 0 , (e) DE 1 H 2 F 0 , and (f) DE 1 H 3 F 0

Fig. 8. Water droplets on the surfaces with single and dual structures in the static state at the characteristic energy of 0.2 kcal/mol: (a) SE 2 H 1 F 0 , (b) SE 2 H 2 F 0 , and (c) SE 2 H 3 F 0 ,

(d) DE 2 H 1 F 0 , (e) DE 2 H 2 F 0 , and (f) DE 2 H 3 F 0

Fig. 9. Water droplets on the surfaces with single and dual structures in the static state at the characteristic energy of 0.3 kcal/mol: (a) SE 3 H 1 F 0 , (b) SE 3 H 2 F 0 , and (c) SE 3 H 3 F 0 ,

(d) DE 3 H 1 F 0 , (e) DE 3 H 2 F 0 , and (f) DE 3 H 3 F 0

8 T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352

Fig. 10. Four groups of dynamic shape of the water droplet: (a) Hemisphere, (b) Tear drop, (c) Wetted stream, and (d) Non-wetted stream.

c

f

i

s

v

a

g

d

a

t

t

a

g

namic shape of the water droplet can be classified into four differ-

ent groups: hemisphere, teardrop, wetted stream, and non-wetted

stream shapes, as shown in Fig. 10 . Fig. 11 shows the advancing

and receding contact angles of the moving water droplet as a func-

tion of time. The rectangles and solid lines are the advancing con-

tact angle and its exponential fitting curve, while the triangles and

dashed line are the receding contact angles and its exponential fit-

ting curve, respectively.

The first group is the case where the dynamic shape of the

droplet on single and dual structures shows a hemispherical form.

Fig. 10 (a) shows an example of the first group for the case of

SE 1 H 1 F 1 . When the droplet moves along the surface with force ap-

plied to the water molecules, the change in the dynamic shape of

the droplet is not large, and the droplet maintains its hemispheri-

al shape, which is similar to the hemispherical shape on the sur-

ace at the static equilibrium state. In this first group, the advanc-

ng and receding contact angles are similar, as shown in Fig. 11 (a),

o that the contact angle hysteresis, θadv − θrec , has a small

alue.

In the second group, the dynamic shape of the droplet shows

teardrop form. Fig. 10 (b) shows an example of the second

roup that corresponds to the case of SE 1 H 1 F 2 . In this group, the

roplet changes its dynamic form from a hemispherical shape to

teardrop shape as it moves along the surface in the presence of

he applied force. This occurs because of the combined effects of

he applied force and the surface characteristic energy. The contact

ngle hysteresis, θadv − θrec , in this group is larger than that in the

roup 1, as shown in Fig. 11 (b).

T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352 9

Fig. 11. Advancing and receding contact angles of the moving water droplet corresponding the time: (a) SE 1 H 1 F 0 , (b) SE 1 H 2 F 0 , and (c) SE 1 H 3 F 0

s

t

c

s

d

f

d

d

A

c

c

g

i

g

a

i

w

t

t

d

p

t

t

t

d

t

w

d

s

r

�

t

�

w

t

o

3

o

s

r

d

d

Fig. 12. Map of water droplet shape on surfaces with single and dual structures at

the characteristic energy of 0.1 kcal/mol.

s

a

d

h

t

t

H

s

c

I

s

t

s

I

s

o

d

t

t

s

In the third group, the dynamic shape of the droplet shows a

tream form in the wetted state. Fig. 10 (c) shows an example of

he third group that corresponds to the case of SE 1 H 1 F 3 . In this

ase, the droplet is normally in the hydrophilic state in its initial

tatic equilibrium state. When the external force is applied, the

roplet is continuously stretched in the direction of the applied

orce along the surface because of the resistance acting on the

roplet. The resistance is caused by the interaction between the

roplet and surface atoms and results in the wetted stream shape.

s shown in Fig. 11 (c), the contact angle cannot be measured be-

ause the droplet is transformed into a stream. Thus, the advancing

ontact angle gradually increases while the receding contact an-

le decreases. As a result, the contact angle hysteresis, θadv − θrec

n this group becomes much larger than that in the group 1 and

roup 2.

In the fourth group, the dynamic shape of the droplet shows

stream form in the non-wetted state. The shape in this group

s similar to that of the third group. However, in this group, the

ater molecules do not permeate into the gaps between the struc-

ures. The case of DE 1 H 1 F 1 is shown in Fig. 10 (d) as an example of

he fourth group. Similar to the group 3, the dynamic shape of the

roplet is also continuously stretched in the direction of the ap-

lied force and is transformed into the stream form. The trend of

he advancing and receding dynamic contact angles is also similar

o that of the group 3, as shown in Fig. 11 (c). However, in con-

rast to the group 3, the droplet in the group 4 starts in a hy-

rophobic state in its initial static equilibrium state. Consequently,

he dynamic shape of the droplet in the group 4 shows a non-

etted stream form, which only occurs on the surface with the

ual structure. Since the dynamic shape and contact angle hystere-

is of the fourth group are similar to those of the third group, the

ate of water molecules penetrating into the gaps between pillars,

, was measured to estimate the results for different groups quan-

itatively:

=

N penet

N tot (7)

here N penet and N tot represent the number of water molecules

hat penetrate into the gaps between pillars and the total number

f water molecules, respectively.

.2.1. ɛ s = 0.1 kcal/mol

Fig. 12 shows a map of the different groups of dynamic shapes

f the droplets that formed on the surfaces with single and dual

tructures at E 1 . The empty and filled symbols in Fig. 12 rep-

esent the single and dual structures, respectively. The square,

iamond, inverted triangle, and triangle symbols represent the

ynamic shapes of the droplets (hemisphere, tear drop, wetted

tream, and non-wetted stream corresponding to groups 1, 2, 3,

nd 4, respectively).

As shown in Fig. 12 , when F 1 is applied to the droplet at E 1 , the

ynamic shape of droplets obtained with single and dual structures

ave the same hemispherical form, regardless of the pillar height.

As F increases to F 2 , the dynamic shape depends on the surface

ype as well as the pillar height. In the case of the single struc-

ure with F 2 , the dynamic shape shows a tear drop form at H 1 .

owever, as H increases to H 2 and H 3 , the droplet on the single

tructure transforms into the hemisphere form because of the in-

rease in the surface hydrophobicity with increasing pillar height.

n the case of the dual structure, the dynamic shape of the droplet

hows a tear drop form regardless of the pillar height because of

he geometric characteristics of the structure.

Finally, when F 3 is applied to the droplet at E 1 , the dynamic

hape also depends on the surface type as well as the pillar height.

n this condition, the dynamic shape obtained with the single

tructure has the wetted stream shape at H 1 . Similar to the cases

f F 2 , the surface hydrophobicity increases as H increases. Thus, the

roplet on the single structure at H 2 and H 3 changes from the wet-

ed stream to the hemisphere form. In the case of the dual struc-

ure with F 3 at E 1 , however, the dynamic shape is the non-wetted

tream form, regardless of the pillar height. The minor bumps dis-

10 T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352

Fig. 13. Contact angle hysteresis, θadv − θrec , and rate of water molecules pene-

trating into the gaps between pillars, �, according to the pillar height at ɛ s = 0.1

turb the penetration of the droplet into the gaps between pillars,

keeping the droplet in the hydrophobic state. At the same time,

they become obstacles to the movement of the droplet in the di-

rection of the applied force. Consequently, the droplet on the dual

structure is stretched in the direction of the applied force along

the surface and forms a non-wetted stream. However, the droplet

on the single structure forms a hemisphere or wetted stream de-

pending on the pillar height.

Fig. 13 shows the contact angle hysteresis ( θadv − θrec ) and the

rate of water molecules penetrating into the gaps between pillars

( �) at E 1 . The black and blue symbols represent θadv − θrec and

�, respectively. The rectangular and triangle symbols represent the

single and dual structures, respectively.

Fig. 13 (a) shows θadv − θrec and � according to the pillar height

when F 1 is applied to the water molecules at E 1 . The rate of wa-

ter molecules penetrating into the gaps between pillars, �, is less

than 5% for all cases except SE 1 H 1 F 1 , meaning that a small num-

ber of water molecules penetrates into the gaps between pillars

in the Cassie-Baxter state except for SE 1 H 1 F 1 . However, in the case

of SE 1 H 1 F 1 , � is relatively high at 10.1% because of the low pillar

height, which results in easy penetration of the droplet into the

gaps. Thus, the droplet for SE 1 H 1 F 1 shows the Wenzel state with a

hemispherical form. All the values of θadv − θrec under F 1 at E 1 for

heights of H 1 , H 2 , and H 3 are less than 10 , meaning that the dy-

namic shapes of water molecules on the single and dual structures

have a hemispherical form, which corresponds to the first group,

as shown in Fig. 10 .

Fig. 13 (b) shows θadv − θrec and � according to the pillar height

under F 2 at E 1 . For the single structure, θadv − θrec are 64.3 , 14.0 ,

and 10.7 for H 1 , H 2 , and H 3 , respectively. In the cases of H 2 and

H 3 under F 2 at E 1 , the dynamic shape of the droplets on the sin-

gle structure shows a hemispherical form, similar to the cases of

H 2 and H 3 under F 1 at E 1 . This corresponds to group 1 and results

in small values of �, which is less than 5%. However, in the case

of H 1 under F 2 at E 1 , the increase in force results in the tear drop

shape for SE 1 H 1 F 2 on the single structure, which corresponds to

the group 2. This is different from the case of H 1 under F 1 , which

is categorized into the first group with the hemispherical shape,

resulting in a � value of 12.4 %. However, because of the increase

from F 1 to F 2 , the dynamic shape on the dual surface in the cases

of H 1 , H 2 , and H 3 show the tear drop form, which corresponds to

the group 2. This contrasts with the results under F 1 at E 1 , which

is categorized in the group 1 with a hemispherical shape. Thus,

� for H 1 , H 2 , and H 3 under F 2 at E 1 are 2.3%, 2.0%, and 1.9%, re-

spectively because of the increasing hydrophobicity with increasing

pillar height. The values of � for the dual structure are less than

those for the single structure because of the larger hydrophobicity

of the dual structure. As a result of the variation of � according

to the pillar height under F 2 , the values of θadv − θrec for the dual

structure are 31.7 , 29.0 , and 27.9 for H 1 , H 2 , and H 3 , respectively.

The values of θadv − θrec for the dual structure are larger than those

for the single structure, meaning that the droplet shapes on the

dual surface were much closer to the tear drop form. Due to the

increasing hydrophobicity, the droplet slightly transforms from a

fully tear drop form to a partial tear drop form as H increases,

which is close to the hemisphere with decreasing θadv − θrec .

Fig. 13 (c) shows the values of θadv − θrec and � according to

the pillar height under F 3 at E 1 . The dynamic shape on the single

structure for H 1 under F 3 at E 1 ( SE 1 H 1 F 3 ) has the wetted stream

form, which can be categorized into the third group, as shown in

Fig. 11 (c). However, as H increases to H 2 and H 3 under F 3 ( SE 1 H 2 F 3and SE 1 H 2 F 3 ), the droplets change to the hemispherical form be-

cause of the increasing hydrophobicity. Thus, � for SE 1 H 1 F 3 is

19.8%, while � for SE 1 H 2 F 3 and SE 1 H 2 F 3 is 0.5% and 0.4%, respec-

tively, because of the increasing hydrophobicity with increasing

pillar height. The value of θadv − θrec for SE 1 H 1 F 3 is 111.2 , while

kcal/mol under (a) F 1 , (b) F 2 , and (c) F 3

T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352 11

Fig. 14. Map of water droplet shape on the surfaces with single and dual structures

at the characteristic energy of 0.2 kcal/mol.

t

c

e

p

I

T

e

v

8

3

s

3

E

h

g

o

s

o

s

t

s

T

f

s

F

w

a

w

m

t

b

a

t

a

t

t

F

Fig. 15. Contact angle hysteresis, θa v d − θrec , and rate of water molecules pene-

trating into the gaps between pillars, �, according to the pillar height at ɛ s = 0.2

hose for SE 1 H 2 F 3 and SE 1 H 2 F 3 are 19.6 and 20.0 , respectively, be-

ause the shape changes with the pillar height in this case. How-

ver, the droplets for DE 1 H 1 F 3 , DE 1 H 2 F 3 , and DE 1 H 2 F 3 could not

enetrate into the gaps between pillars due to the minor bumps.

nstead, they are stretched in the direction of the applied force F 3 .

his results in the non-wetted stream shape, which can be cat-

gorized into the fourth group, as shown in Fig. 11 (d). Thus, the

alues of θadv − θrec for DE 1 H 1 F 3 , DE 1 H 2 F 3 , and DE 1 H 2 F 3 are 91.6 ,

6.0 , and 80.1 , while � for DE 1 H 1 F 3 , DE 1 H 2 F 3 , and DE 1 H 2 F 3 are

.2%, 1.7%, and 1.1%, respectively. These values are less than 4%, as

hown in Fig. 13 (c).

.2.2. ɛ s = 0.2 kcal/mol

Fig. 14 shows a map for different groups of dynamic shapes at

2 . When F 1 is applied to the droplet under E 2 , all the droplets

ave the same tear drop shapes, which correspond to the second

roup. As the applied force increases to F 2 from F 1 , all the droplets

n the single structure for H 1 , H 2 , and H 3 show the wetted stream

hape, which corresponds to the group 3. In addition, the droplet

n the dual structure for H 1 under F 2 at E 2 also has a wetted

tream shape. However, as H increases to H 2 and H 3 in the case of

he dual structure, the droplet transforms from the wetted stream

hape to the tear drop shape, which corresponds to the group 2.

his occurs because of the increased surface hydrophobicity.

As F increases further to F 3 , the droplets on the single structure

or H 1 , H 2 , and H 3 show the wetted stream shapes, which corre-

pond to the group 3. This is similar to the cases corresponding to

2 at E 2 . Also, the droplets on the dual structure at H 1 show the

etted stream form. However, the droplets on the dual structure

t H 2 and H 3 under F 3 at E 2 show the non-wetted stream shapes,

hich correspond to the group 4. This occurs because the water

olecules on the dual structure cannot penetrate into the gaps be-

ween pillars due to the combined effect of the presence of the

umps on the pillars and the increase in the applied force.

Fig. 15 shows θadv − θrec and � according to the pillar height

t E 3 . Fig. 15 (a) shows the results when F 1 is applied to the wa-

er molecules at E 2 . θadv − θrec for SE 2 H 1 F 1 , SE 2 H 2 F 1 , and SE 2 H 3 F 1 re 37.9 , 50.3 , and 53.8 , meaning that the dynamic shape with

he single structure for all pillar heights considered with F 1 is in

he tear drop form corresponding to the group 2, as shown in

ig. 11 . The values of � for SE H F , SE H F , and SE H F are

2 1 1 2 2 1 2 3 1 kcal/mol under (a) F 1 , (b) F 2 , and (c) F 3

12 T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352

Fig. 16. Map of water droplet shape on the surfaces with single and dual structures

at the characteristic energy of 0.3 kcal/mol.

E

s

t

θ

t

t

c

t

p

f

d

a

4

t

f

t

w

t

t

a

p

m

t

h

c

t

t

f

s

p

b

c

t

t

t

20.1%, 59.7%, and 75.7%, respectively, which are larger than 20%.

This shows that many water molecules penetrate into the gaps be-

tween pillars for all pillar heights considered with F 1 for the single

structure. As the pillar height increases with the single structure in

this case, θadv − θrec and � increase due to the increase in the sur-

face hydrophilicity. The values of θadv − θrec for DE 2 H 1 F 1 , DE 2 H 2 F 1 ,

and DE 2 H 3 F 1 are 62.1 , 39.8 , and 27.2 , meaning that the dynamic

shape on the dual surface for H 1 , H 2 , and H 3 with F 1 is the tear

drop form corresponding to the group 2. � for the dual structure

with H 1 and F 1 is 34.6%. As H increases from H 1 to H 2 and H 3 , �

decreases to 13.4% and 8.2%, respectively. θadv − θrec and � strongly

depend on the shape of the droplets in the static equilibrium state.

In the static equilibrium state, the droplets for DE 2 H 1 F 0 were in

the Wenzel state similar to SE 2 H 1 F 0 , while the droplets for DE 2 H 2 F 0 and DE 2 H 3 F 0 were in the Cassie-Baxter state, and the static contact

angles increase with increasing pillar height, unlike SE 2 H 2 F 0 and

SE 2 H 3 F 0 . Thus, as the pillar height increases with the dual struc-

ture at F 1 and E 2 , θadv − θrec and � decrease due to the increase in

the surface hydrophobicity, unlike on the surface with the single

structure.

Fig. 15 (b) shows θadv − θrec and � corresponding to the pillar

height under F 2 at E 2 . In this case, the dynamic shape and the

values of θadv − θrec and � also strongly depend on the shape of

droplets in the static equilibrium state. The droplet on the surface

with the single structure is in the Wenzel state at E 2 . Thus, in the

dynamic state with F 2 , the droplet on the single structure has large

θadv − θrec values of 85.2 , 82.9 , and 71.5 and large � values of

39.3%, 97.5%, and 99.4% for SE 2 H 1 F 2 , SE 2 H 2 F 2 , and SE 2 H 3 F 2 , respec-

tively. As a result, the dynamic shape on the single structure for

H 1 , H 2 , and H 3 with F 2 is a wetted stream form corresponding to

the group 3 with large values of θadv − θrec and �. Similar to sin-

gle structures, DE 2 H 1 F 2 , which shows the Wenzel state in the static

equilibrium state, has a wetted stream form of droplet categorized

into the group 3. The θadv − θrec and � are 98.6 and 39.5%, respec-

tively. In contrast to the case of H 1 , for DE 2 H 2 F 2 and DE 2 H 3 F 2 , the

values of θadv − θrec are 72.1 and 69.0 , respectively, and the values

for � are 23.6% and 21.6%, respectively. Thus, the dynamic shape of

droplet on the dual surface for H 2 and H 3 with F 2 is a non-wetted

stream form of the droplet corresponding to the group 4. There-

fore, with F 2 at E 2 , � is much smaller for the dual structure than

the single structure. This shows that the surfaces with the dual

structure have more hydrophobic characteristics than those with

single structures.

Fig. 15 (c) shows θadv − θrec and � corresponding to the pillar

height under F 3 at E 2 . With the strong applied force F 3 , all the

droplets on single and dual structures are stretched in the direc-

tion of the applied force and transformed into a wetted or non-

wetted stream, resulting in large θadv − θrec . Thus, θadv − θrec for

SE 2 H 1 F 3 , SE 2 H 2 F 3 , and SE 2 H 3 F 3 are 101.8 , 85.0 , and 73.9 , respec-

tively, while the values of θadv − θrec for DE 2 H 1 F 3 , DE 2 H 2 F 3 , and

DE 2 H 3 F 3 are 108.2 , 104.0 , and 102.1 , respectively. However, �

in the dynamic state strongly depends on the shape of droplets

in the static equilibrium state. The droplets for SE 2 H 1 F 3 , SE 2 H 2 F 3 ,

SE 2 H 3 F 3 , and DE 2 H 1 F 3 are in the Wenzel state in the static equilib-

rium state and have relatively large � values of 45.2%, 99.1%, 99.9%,

and 36.8%, respectively. This means that their dynamic shapes are

the wetted stream form corresponding to the group 3. However,

because the droplets for DE 2 H 2 F 3 and DE 2 H 3 F 3 are in the Cassie-

Baxter state in the static equilibrium state, their dynamic shapes

are the non-wetted stream form corresponding to the group 4. As

a result, � for DE 2 H 2 F 3 and DE 2 H 3 F 3 are smaller than 30% (21.4%

and 19.5%, respectively).

3.2.3. ɛ s = 0.3 kcal/mol

Fig. 16 shows a map of the dynamic shape at E 3 . When F 1 ,

F , and F are applied to the droplet at H , H , and H under

2 3 1 2 3

3 , the dynamic shapes of all the droplets are the same wetted

tream form, which corresponds to the group 3. This is due to

he strong characteristic energy E 3 . As a result, for all droplets,

adv − θrec are over 100 , and � are almost 100% because most of

he water molecules penetrate into the gaps between pillars due

o the strong surface characteristic energy. Thus, when the surface

haracteristic energy is as large as E 3 , the dynamic behaviors of

he droplets do not depend on the type of surface roughness, ap-

lied force, or pillar height. They depend on only the strong sur-

ace characteristic energy, resulting in a wetted stream form of the

roplet corresponding to the group 3 for different applied forces

nd pillar heights.

. Conclusions

Molecular dynamics simulations were carried out to investigate

he static and dynamic wetting behaviors of water droplets on sur-

aces with single and dual structures for different surface charac-

eristic energies, pillar heights, and applied forces. The dynamic

etting behavior of the droplets can be classified as hemisphere,

eardrop, wetted stream, and a non-wetted stream forms, based on

heir dynamic shape. As the applied force increases, the droplets

re stretched more in the direction of the applied force.

When the surface is intrinsically hydrophobic at E 1 , at the low

illar height H 1 , the contact angle hysteresis and the rates of water

olecules penetrating into the gaps between pillars are smaller for

he dual structures than the single ones. However, when the pillar

eight is high at H 2 and H 3 , the dual structures result in higher

ontact angle hysteresis but small rates of water molecules pene-

rating into the gaps between pillars (close to 0%), which is similar

o that for the single structures.

When the surface is partially hydrophilic at E 2 and the applied

orce is weak at F 1 , the contact angle hysteresis for the single

tructures increase while that for dual structures decrease as the

illar height increases. However, the contact angle hysteresis for

oth single and dual structures decrease as the pillar height in-

reases at F 2 and F 3 . The rate of water molecules penetrating into

he gaps for the single structure increases as the pillar height while

he rate decreases as the pillar height increases for the dual struc-

ures due to the disturbance effect of the minor bumps.

T.W. Kwon, K.H. Lee and Y.M. Seo et al. / International Journal of Multiphase Flow 129 (2020) 103352 13

b

f

t

h

b

t

h

e

s

s

w

w

c

D

c

i

C

s

-

v

v

A

o

2

R

B

C

C

H

H

J

K

K

K

L

L

M

M

O

O

P

R

S

W

W

W

W

Y

Y

Y

Y

When the surface is intrinsically hydrophilic at E 3 , the dynamic

ehavior of the droplets on the structures shows the wetted stream

orm with contact angle hysteresis over 100 , and the rates of wa-

er molecules penetrating into the gaps are close to 100%.

The dual structures cannot make the hydrophilic surface more

ydrophobic but can make the partially hydrophilic or hydropho-

ic surfaces more hydrophobic. The dynamic shape of the wa-

er droplets on the surface with the dual structures shows the

ydrophobic form, giving small rates of water molecules pen-

trating into the gaps between pillars. In conclusion, the dual

tructures make the surface more hydrophobic in the dynamic

tate, as well as in the static state. The surface with the

eak surface characteristic energy, the high pillar height, the

eak external force and dual structures show more hydrophobic

ondition.

eclaration of Competing Interest

The authors declare that they have no known competing finan-

ial interests or personal relationships that could have appeared to

nfluence that work reported in this paper.

RediT authorship contribution statement

Tae Woo Kwon: Conceptualization, Writing - original draft, Vi-

ualization. Kwang Ho Lee: Investigation. Young Min Seo: Writing

review & editing. Joonkyung Jang: Methodology, Writing - re-

iew & editing. Man Yeong Ha: Writing - review & editing, Super-

ision.

cknowledgement

This work was supported by the National Research Foundation

f Korea (NRF) grant funded by the Korea government (MSIT) (No.

019R1A5A808320111 ).

eferences

arthlott, W., Neinhuis, C., 1997. Purity of the sacred lotus, or escape from contam-ination in biological surfaces. Planta 202, 1–8. doi: 10.10 07/s0 04250 050 096 .

assie, A.B.D., Baxter, S., 1944. Wettability of porous surfaces. Trans. Faraday Soc. 40,546–551. doi: 10.1039/TF94 4 40 0 0546 .

hai, J., Liu, S., Yang, X., 2009. Molecular dynamics simulation of wetting on mod-

ified amorphous silica surface. Appl. Surf. Sci. 255, 9078–9084. doi: 10.1016/j.apsusc.2009.06.109 .

irvi, J.T., Pakkanee, T.A., 2008. Nanodroplet impact and sliding on structured poly-mer surfaces. Surf. Sci. 602, 1810–1818. doi: 10.1016/j.susc.2008.03.020 .

ong, S.D., Ha, M.Y., Balachandar, S., 2009. Static and dynamic contact angles ofwater droplet on a solid surface using molecular dynamics simulation. Journal

of Colloid and Interface Science 339 (1), 187–195. doi: 10.1016/j.jcis.2009.07.048 .

ung, W.J., Ha, M.Y., Yoon, H.S., Ambrosia, M., 2012. Dynamic behavior of waterdroplets on solid surfaces with pillar type nanostructures. Langmuir 28 (12),

5360–5371. doi: 10.1021/la205106v . o, J.A., Ambrosia, M., Ha, M.Y., 2015. A study of the wetted characteristics of a

nano-sized water droplet on heterogeneous striped surfaces. Computer & Fluids112, 19–34. doi: 10.1016/j.compfluid.2015.02.005 .

oishi, T., Yasuoka, K., Fujikawa, S., Zeng, X.C., 2011. Measurement of contact an-gle hysteresis for droplets on nanopillared surface and in the Cassie and Wen-

zel states: A molecular dynamics simulation study. ACSNANO 5 (9), 6 834–6 842.

doi: 10.1021/nn2005393 . won, T.W., Jang, J., Ambrosia, M.S., Ha, M.Y., 2018. Molecular Dynamics Study on

the Hydrophobicity of a Surface Patterned with a Hierarchical Nanotextures. Col.Surf. A 559, 209–217. doi: 10.1016/j.colsurfa.2018.09.056 .

i, S., Page, K., Sathasivam, S., Heale, F., He, G., Lu, Y., Lai, Y., Chen, G., Carmalt, C.J.,Parkin, I.P., 2018. Efficiently texturing hierarchical superhydrophobic fluoride-

free translucent films by AACVD with excellent durability and self-cleaning abil-

ity. J. Mater. Chem. A 6, 17633. doi: 10.1039/c8ta05402a . undgren, M., Allan, N.L., Cosgove, T., 2007. Modeling of wetted: a study of nanowet-

ted at rough and heterogeneous surfaces. Langmuir 23, 1187–1194. doi: 10.1021/la060712o .

artines, E., Seunarine, K., Morgan, H., Gadegaard, N., Wilkinson, C.D.W.,Riehle, M.O., 2005. Superhydrophobicity and superhydrophilicity of regular

nanopatterns. Nano Letter 5 (10), 2097–2103. doi: 10.1021/nl051435t .

iwa, M., Nakajima, A., Fujishima, A., Hashimoto, K., Watanabe, T., 20 0 0. Effects ofthe Surface Roughness on Sliding An-gles of Water Droplets on Superhydropho-

bic Surfaces. Langmuir 16, 5754–5760. doi: 10.1021/la991660o . ner, D., McCarthy, J., 20 0 0. Ultrahydrophobic surfaces. Effects of topography length

scales on wettability. Langmuir 16, 7777–7782. doi: 10.1021/la0 0 0598o . u, J., Perot, B., Rothstein, J.P., 2004. Laminar drag reduction in microchannels using

ultrahydrophobic surfaces. Physics of Fluids 16, 4635. doi: 10.1063/1.1812011 .

rice, D.J., Brooks, C.L., 2004. A modified TIP3P water potential for simulation withEwald summation. J. Chem. Phys. 121 (20), 10096. doi: 10.1063/1.1808117 .

ahmawan, Y., Moon, M., Kim, K., Lee, K., Suh, K., 2010. Wrinkled, Dual-Scale Struc-tures of Diamond-Like Carbon (DLC) for Superhydrophobicity. Langmuir 26 (1),

4 84–4 91. doi: 10.1021/la902129k . ong, J.H., Sakai, M., Yoshida, N., Suzuki, S., Kameshima, Y., Nakajima, A., 2006. Dy-

namic hydrophobicity of water droplets on the line-patterned hydrophobic sur-

faces. Surf. Sci. 600, 2711–2717. doi: 10.1016/j.susc.2006.04.044 . ang, N., Lu, Y., Xiong, D., Carmalt, C.J., Parkin, I.P., 2016. Designing durable and

flexible superhydrophobic coatings and its application in oil purification. J.Mater. Chem. A 4, 4107. doi: 10.1039/c6ta00170j .

atson, G.S., Cribb, B.W., Watson, J.A., 2011. Contrasting Micro/Nano Architecture onTermite Wings: Two Divergent Strategies for Optimising Success of Colonisation

Flights. PLoS ONE 6, 1–10. doi: 10.1371/journal.pone.0024368 .

enzel, R.N., 1936. Resistance of solid surfaces to wetting by water. Ind. Eng. Chem28, 988–994. doi: 10.1021/ie50320a024 .

erder, T., Walther, J.H., Jaffe, R.L., Halicioglu, T., Koumoutsakos, P., 2003. Onthe water carbon interaction for use in molecular dynamics simulations of

graphite and carbon nanotubes. J. Phys. Chem. B 107 (6), 1345–1352. doi: 10.1021/jp0268112 .

ong, X., Zhang, L.T., 2009. Nanoscale Wetting on Groove-Patterned Surfaces. Lang-muir 25, 5045–5053. doi: 10.1021/la804025h .

oo, M.J., Ambrosia, M.S., Kwon, T.W., Jang, J., Ha, M.Y., 2018. Wetting characteristics

of a water droplet on solid surfaces with various pillar surface fractions un-der different conditions. Journal of Mechanical Science and Technology 32 (4),

1593–1600. doi: 10.1007/s12206- 018- 0314- 6 . oshimitsu, Z., Nakajima, A., Watanabe, T., Hashimoto, K., 2002. Effects of Surface

Structure on the Hydrophobicity and Sliding Behavior of Water Droplets. Lang-muir 18, 5818–5822. doi: 10.1021/la020088p .

oung, T., 1805. An Essay on the Cohesion of Fluids. Philos. Trans. R. Soc. London

95, 65–87. doi: 10.1098/rspl.180 0.0 095 .