Wetting and Spreading Behaviors of Nanodroplets: The Interplay

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Wetting and Spreading Behaviors of Nanodroplets: The Interplay Among Substrate Hydrophobicity, Roughness and Surfactants Zhi Li, Kai Liao, Feiyang Liao, Qianxiang Xiao, Fei Jiang, Xianren Zhang, Bei Liu, Changyu Sun, and Guangjin Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b04299 • Publication Date (Web): 06 Jul 2016 Downloaded from http://pubs.acs.org on July 9, 2016

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The Journal of Physical Chemistry

Wetting and Spreading Behaviors of Nanodroplets: The Interplay Among Substrate Hydrophobicity, Roughness and Surfactants Zhi Li,†,¶ Kai Liao,‡,¶ Feiyang Liao,† Qianxiang Xiao,§ Fei Jiang,† Xianren Zhang,*,§ Bei Liu,*,† Changyu Sun, † and Guangjin Chen† †

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249,

China. ‡

MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing

102249, China. §

State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical

Technology, Beijing 100029, China.

ABSTRACT: Molecular dynamics simulations were employed here to explore the molecular mechanism for wetting and spreading behaviors of droplets on smooth and textured substrates, in either the absence or presence of surfactants. In particular, we focus on the interplay among substrate hydrophobicity, roughness, and the addition of surfactants. Our simulation results indicate that substrate roughness exerts different effects on the contact angle of nanodroplets, depending on the substrate chemistry. While the presence of surfactants always changes the droplet contact angle via reducing both the vapor-liquid and liquid-solid interfacial tensions, which is independent of the substrate chemistry and roughness. In addition, our calculation

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results show that the addition of surfactants may lead to the wetting transition of nanodroplets on hydrophobic textured surfaces, or induce the appearance of precursor film for droplet spreading on hydrophilic textured surfaces. On the spreading dynamics, we also discuss how the introduction of roughness change motion mode of contact line and how the initial distribution of surfactants affect droplet spreading.

KEYWORDS: nanodroplet, spreading behavior, roughness, surfactant


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1. INTRODUCTION In the field of oil exploitation, waterflooding is usually used to enhance oil recovery after the primary production period.1 In fractured reservoirs, the wettability of reservoir rock have great impact on the efficiency of oil recovery during waterflooding. Reservoir wettability can cover a broad range of wettability conditions that are from very strongly water wet to very strongly oil wet.2 In strongly water-wet rock, the water injection process is efficient. But most of the fractured carbonate reservoirs are oil-wet or mixed-wet, and the waterflooding oil recoveries are very low. One effective way of addressing the above problem is to modify the wettability of rock surfaces using surfactants.3 By far, numerous researches have been carried out to study the effect of surfactant on the wettability of solid surface.4-12 Among these researches, Hill13 found that complete spreading of water on hydrophobic surfaces can even be achieved with the presence of surfactants such as polyethylene. Kim et al.14 employed molecular dynamics simulations to probe the surfactantmediated spreading of a Lennard-Jones liquid droplet on a solid surface and found that the spreading speed is strongly influenced by the attraction of the hydrophobic surfactant tail to the solid surface. Zhdanov et al.15 carried out experimental investigations on the spreading of small drops of aqueous SDS solutions over dry thin porous substrates and observe the phenomenon of contact angle hysteresis. These previous studies could be summarized to two major aspects: The first one is to evaluate the oil displacement performance of different kinds of surfactants by observing the dynamic wetting process of surfactant-containing aqueous drop on substrate. The second one is to select different core materials and analyze the impact of roughness and heterogeneity on the wetting behaviors of droplets in presence of surfactants. However, there are many factors influencing the wetting condition of reservoir rock including the solid components,


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morphology of the surface mineral, the addition of surface active material, et al. Thus it is necessary to uncover the synergetic mechanism of numerous factors upon wettability of solid. In this work, molecular dynamics simulations were carried out to investigate the mechanism of synergistic interaction among substrate chemical property, roughness, and surfactants. The mechanisms of wetting alternation under the influence of many factors were revealed by simulating the dynamic process of wetting contact angle. The conclusions we get are expected to give a guidance on the surfactant flooding technology and serve as the supplement for experiment research.

2. MODEL AND SIMULATION DETAILS Coarse-grained molecular models were adopted in this work to improve the efficiency of molecular simulations. The droplet studied in this work consists of 10000 solvent molecules and each was represented as a chain-like molecule with 4 particles that are connected by springs. The surfactant is composed of 8 particles with four hydrophilic particles (head group) and four hydrophobic particles (tail groups), which are also connected by springs. Here hydrophobicity or hydrophilicity refers to the poor or good solubility of a particle in the solvent, originating from the relatively favorable or unfavorable interaction between the particle and the solvent. The substrates were constituted by fixing solid particles on a FCC (face-centered cubic) lattice with lattice parameter of 1.65 σ. The number of FCC lattice is 100×16×5 in XYZ directions for smooth surface. The rough surface consists of 100×16×2 FCC lattice as the base area, on which pillars were placed to represent roughness (see Figure 1).


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Figure 1. The schematic representation of the building block of the rough surface.

The non-bonded interactions in this work were described by LJ potential

U ij  4Cij εij [(

σ ij 12 σ ij 6 ) ( ) ] rij rij

(1)

where ε is the energy scale and σ is the length parameter, which were treated as energy and length units throughout our simulations. rij is the distance between particles. Cij is a constant which is used to adjust the attractive strength between particles. The interaction parameters for different particle pairs, including solid-solid (SS), solid-head (SH), solid-tail (ST), liquid-liquid (LL), liquid-head (LH), liquid-tail (LT), head-head (HH), head-tail (HT) and tail-tail (TT), are listed in Table 1.


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Table 1. Pair interaction parameters Cij used in this work. S, H, T, and L stand for substrate, head, tail, and solvent monomers, respectively. Cij

S

L

H

T

S

1.00

0.45 ~ 0.85

0.85

0.85

0.90

1.00

0.50

0.10

0.10

L H T

0.10

The particles of solvent molecule as well as surfactants were bounded together by the finite extensible nonlinear elastic (FENE) potential

1 V FENE   KR02ln[1  (r / R0 ) 2 ] 2

(2)

where R0 is the maximum extent of the bond and was set to 1.5 σ here. K is a spring constant and was set to 30 ε/σ2. 16 The simulation box was set to 165 σ × 26.4 σ × 100 σ and the length along the Y direction is much smaller than that along the X and Z direction. This quasi-two dimensional model was adopted here for simplification to determine the droplet contact angle and spreading dynamics. For the initial configuration of pure nanodroplet, the cylindrical droplet with a radius of 15 σ was placed near the solid surface. For surfactant-containing nanodroplet model, 112 surfactants were added inside the cylindrical nanodroplet model. Firstly, energy minimization was employed and then a molecular dynamics simulation in NVT (constant number of particles, volume, and temperature) ensemble was carried out with the


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molecular dynamics program Lammps (Large-scale Atomic/Molecular Massively Parallel Simulator).17 Periodic boundary conditions were employed in three dimensions and the substrate was kept fixed. Since the size of the simulation box in Z direction (100 σ) is much larger than the droplet size (~40 σ), using periodic boundary condition in Z direction does not affect the simulation results. The average non-dimensional temperature T*=kBT/ε was set to 0.80 with reference to Kim’s work14 and kept constant throughout the whole simulation. Here kB is the Boltzmann constant. The LJ potential cutoff radius rc= 2.5 σ. The velocity Verlet algorithm with a time step of 5 fs was used to integrate the equations of motion. The Nosé-Hoover thermostat with a time constant of 0.5 ps was used to control the fluid temperature.18

3. RESULTS AND DISCUSSION 3.1 Contact angle and spreading behaviors of pure nanodroplets. We initially started our work with the spreading of a pure nanodroplet as a reference. It is known that the interaction between liquid and solid substrate plays a vital role in the characteristics of droplet spreading. We changed the value of CSL from 0.45 to 0.85 that corresponds to changing substrate chemistry from hydrophobic to hydrophilic and obtained the equilibrium contact angle of the nanodroplet on smooth surface. In this work, contact angle was calculated by using a curve fitting method. We first determined the vapor-liquid interface of a droplet from the obtained density distribution via averaging over a number of configurations over a time of 0.5 ns, and then calculated the droplet contact angle via a circle fitting of the vapor-liquid interface from which the interface meets the substrate. From Figure 2 we can see that there exists a nearly linear relationship between contact angle and CSL, which is consistent with the previous simulation results.19-21 For CSL > 0.6, the equilibrium contact angle θ is smaller than 90º, which shows the hydrophilic


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properties. For CSL < 0.6, the equilibrium contact angle θ is larger than 90º, which shows the hydrophobic features. Therefore, in our studies we selected CSL=0.45, CSL=0.6, and CSL=0.85 as examples to explore the effect of surfactant in promoting the spreading of droplets on substrates with different material chemistry, respectively. The equilibrium configurations of pure liquid droplets on these smooth surfaces are given in Figure 3. Figure 3a shows the initial configurations of nanodroplet. Figures 3b, 3c, and 3d show the equilibrium wetting state of droplets on smooth surface with different hydrophobicity. 180

Smooth surface Rough surface Smooth surface & surfactants

160 Contact Angle 

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140 120 100 80 60 40 0.4

0.5

0.6

0.7

0.8

0.9

CSL

Figure 2. The effect of the liquid-solid (CSL) interaction strength on the contact angle of the droplets.

Figure 3. Initial configurations of nanodroplets (a) and equilibrium wetting state at t=30 ns (right) on smooth surfaces with different interactions between solvent and solid particles: (b) CSL=0.45, (c) CSL=0.6, and (d) CSL=0.85.


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In order to investigate the effect of surface roughness on the wetting behavior of pure nanodroplets, we carried out the corresponding simulation study on rough surfaces. The Initial model (Figure 4a) and equilibrium configurations (Figures 4b, 4c, and 4d) are shown below. From Figure 4 we can see for CSL=0.45 (Figure 4b) the droplet is in the Cassie−Baxter state, sitting on the top surface of pillared substrate. While for CSL=0.6 and CSL=0.85 (Figures 4c and 4d), solvent penetrated into the space between pillars and thus the nanodroplet is in the Wenzel state instead. Like the results shown in Figure 2, Figure 4 again indicates that roughness decreases the contact angle for droplets on hydrophilic substrate and increases the contact angle on hydrophobic substrate, which is consistent with the Wenzel relation.

Figure 4. Initial configurations of nanodroplets (a) and equilibrium wetting state at t=30 ns on textured surfaces with different interactions between nanodroplets and surface: (b) CSL=0.45, (c) CSL=0.6, and (d) CSL=0.85.

3.2 Spreading behavior of surfactants-containing nanodroplets. Except for pure droplet, we investigated the influence of surfactants on the droplet spreading behavior. The spreading processes of surfactants-containing droplets on smooth surface with hydrophobicity (Figures 5a, 5b, 5c, and 5d) and hydrophilicity (Figures 5e and 5f) are shown below. From Figure 5 we can see on smooth surface, surfactants facilitate the spreading of a partially wetting droplet and decrease the equilibrium contact angle. Surfactants inside the droplets gradually spread to the vapor-liquid and liquid-solid interfaces and reduce the vapor-liquid and liquid-solid interfacial


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tension, as found before.11, 14, 15 An inhomogeneous distribution of surfactants over the vaporliquid interface which drive the Marangoni convection could also enhance the droplet spreading.

Figure 5. Typical spreading process of a droplet with linear surfactants (a, c, e) and time sequence for the surfactants on smooth surface (b, d, f): (a and b) CSL=0.45, (c and d) CSL=0.6, and (e and f) CSL=0.85. The white particles are solvent, the blue particles are the hydrophobic particles, the magenta particles are the hydrophilic particles, and yellow particles represent the lattice of the substrate.


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Then we turn our attention to the wetting behavior of surfactant-containing nanodroplets on rough substrate with pillars. The spreading processes of surfactants-containing droplets on rough surface with hydrophobicity (Figures 6a, 6b, 6c, and 6d) and hydrophilicity (Figures 6e and 6f) are shown below. As shown in Figure 6a and 6b, for hydrophobic substrate with CSL=0.45, droplet with surfactants experienced a wetting transition, i.e. from Cassie-Baxter state to partial Wenzel state, then to Wenzel state. The wetting transition is advanced by impregnating surfactants and solvent molecules into the grooves gradually. In the early stage of spreading, the surfactants existed in liquid bulk phase and the weak liquid-solid interaction led to the droplet sitting on the pillars, which is similar to the pure nanodroplet (see Figure 4b). With the surfactants gradually moving to the vapor-liquid and solid-liquid interface, the tails-solid interaction induced the adsorption of surfactants on the space between the pillars, and the strong head-solvent attraction pulled the solvent molecules permeating into the gaps. For CSL=0.85, the contact angle of surfactants-water droplets nearly equals to the pure liquid droplet’s contact angle on textured surface (Figures 6e and 6f). Although surfactants facilitated droplet spreading by reducing the liquid-solid interfacial tension, they entered the grooves and decreased the surface roughness which had been testified to promote spreading in hydrophilic substrate. Eventually there is no obvious contact angle change for the surfactants−containing nanodroplets. At the same time, we found a thin liquid film called precursor film located in the front of macroscopic contact line, which had not been observed in the spreading of pure nanodroplet. This means that surfactants could also facilitate the appearance of precursor film for droplet spreading on textured hydrophilic surface.


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Figure 6. Typical spreading process of a droplet with linear surfactants (a, c, e) and time sequence for the surfactants on textured surface (b, d, f): (a and b) CSL=0.45, (c and d) CSL=0.6, and (e and f) CSL=0.85. The white particles are solvent, the blue particles are the hydrophobic particles, the magenta particles are the hydrophilic particles, and yellow particles represent the lattice of the substrate.

We also computed the change of contact angle and contact line diameter of surfactantscontaining droplets as a function of time on smooth and textured surface. For the surfactantscontaining droplets on hydrophobic textured surface (Figure 7a), the spreading process shows


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strong fluctuation and three sections of the curves can be clearly identified. Detailed inspection on the spreading process indicates that, firstly, the change of contact angle is caused by the transition of wetting state of the nanodroplet. This is also confirmed by the time evolution of contact line diameter (Figure 7b), from which it is found that the contact line length almost remains constant in the process of spreading. The three sections of curves represent in fact sequential wetting transitions, i.e., from Cassie-Baxter state, to partial Wenzel state, and finally to Wenzel state, respectively. Comparing with the droplet on smooth surface, the contact angle of surfactants-containing droplets decreases much more slowly and reaches a smaller value on textured hydrophilic substrate (Figure 8a). In the spreading process, the pinning effect caused by the protrusions on substrate slows down the wetting rate, but both the grooves and the presence of surfactants would decrease the equilibrium contact angle. The step-like curve in Figure 8a and 8b reveals the stick-slip motion of moving contact line:22 the pillars hinder droplet from moving forward and keep the contact line pinned within a short time. With accumulating solvent molecules nearby the contact line, the droplet would overcome the pinning force, cross the barrier, and continue spreading.


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150

(a)

65

Smooth surface Rough surface

130 120

55 50 45 40

110 100


(b)

60

Diameter d ()

140 Contact Angle  ()

35 0

10

20

30

40

50

0

10

20

30

40

50

Time (ns)

Time (ns)

Figure 7. (a) Contact angle and (b) contact line diameter as a function of time for the spreading of a droplet with surfactant on smooth and rough substrate: CSL=0.45.

120

140

(a)



(b)

120

Diameter d ()


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

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80 60

100 80

40 60 20

0

10

20

30

40

50

0

10

20

Time (ns)

30

40

50

Time (ns)

Figure 8. (a) Contact angle and (b) contact line diameter as a function of time for the spreading of a droplet with surfactant on smooth and rough substrate: CSL=0.85.

3.3 Effect of initial configuration. To explore whether initial configuration affects the spreading behavior of droplets and the distribution of surfactants, we also constructed a different initial surfactants-containing droplet model. In this model, a cylindrical surfactant-containing nanodroplet was firstly placed in air and equilibrated for 30 ns for the surfactants to reach vapor-


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liquid interface. The pre-equilibrated droplet was then translated to the vicinity of the solid surface, as shown in Figure 9. From Figure 9 we can see that for most of surfactants in the preequilibrated initial configuration, the hydrophobic tails stretched out to the vapor-liquid interface and the hydrophilic heads pointed toward the solvent phase. The spreading process of preequilibrated surfactants-containing droplet on smooth surface with hydrophobicity (Figures 10a, 10b, 10c, and 10d) and hydrophilicity (Figures 10e and 10f) are shown below.

Figure 9. Two different initial models of surfactants-containing droplets. The white particles are solvent, the blue particles are the hydrophobic particles, the magenta particles are the hydrophilic particles, and yellow particles represent the lattice of the substrate.


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Figure 10. Typical spreading process of pre-equilibrated surfactant-containing nanodroplet (a, c, e) and time sequence for the surfactants on smooth surface (b, d, f): (a and b) CSL=0.45, (c and d) CSL=0.6, and (e and f) CSL=0.85. The white particles are solvent, the blue particles are the hydrophobic particles, the magenta particles are the hydrophilic particles, and yellow particles represent the lattice of the substrate.

Figure 11 compares the contact angle changes for droplets on smooth substrate when they spread from different initial configurations. From the comparison of Figure 10 and Figure 11 we can deduce that initial configuration only affects the spreading dynamics, such as the


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spreading process of droplet on hydrophobic solid surface, but has little impact on the final equilibrium states (the contact angle). Its effect on spreading dynamics is ascribed to the different rate of surfactants approaching the vapor-liquid and liquid-solid interfaces that strongly changes the local vapor-liquid and liquid-solid interfacial tensions. From Figure 11a, we can see that it takes less time for the pre-equilibrated droplet to reach equilibrium than no-equilibrated droplets. For CSL=0.45, the pre-equilibrated droplet fell down to contact the solid surface more quickly due to the faster rearrangement of surfactants on the liquid-solid interface. In addition, for pre-equilibrated droplet, the liquid-solid interfacial tension reduced more rapidly at the beginning of the spreading process. The rapid decrease of liquidsolid interfacial tension and the strong tail-solid interaction are supposed to promote the spreading behavior, 11 resulting in a more rapid decline of contact angle. For CSL=0.85, no obvious changes of spreading rate were observed, as shown in Figure 11b. This means initial configuration has little impact on the equilibrium state as well as the spreading dynamics. For no-equilibrated droplets, surfactants stay in the bulk phase at the beginning of the period. With the time goes on, surfactants gradually move to the gas-liquid and liquid-solid interface and reduce interfacial tension which is thought to facilitate the spreading of droplets. Thus the spreading process of no-equilibrated droplets can be divided into two stages: In stage I, surfactants mainly stay in the bulk phase and the spreading behavior mainly depend on the attraction between water molecules and substrate. Thus we think that liquid-solid interaction governes the droplets’ spreading in stage I. In stage II, surfactants moved to the liquid-solid and gas-liquid interface, and the adsorption of tail onto the substrate becomes particularly important in the follow-up spreading. Thus, tail-solid interaction has the leading role in spreading at this stage. In this work, as CSL =CST=CSH=0.85, no apparent differences of spreading rate occur using


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these two initial models on hydrophilic surface. 130

140

No pre-equilibrium Pre-equilibrium

120

110

100

(b)



(a) Contact Angle  ()

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

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100 80 60 40

0

10

20 30 Time (ns)

40

50

0

10

20

30

40

50

Time (ns)

Figure 11. Contact angle as a function of time for the spreading of two different initial droplets with surfactant on smooth substrate: (a) CSL=0.45 and (b) CSL=0.85.

Except for smooth surfaces, we then explored the effect of initial configuration on the droplet spreading dynamics on textured surface, as shown in Figure 12 and Figure 13. We also show the spreading processes of surfactants-containing droplets on rough surface with hydrophobicity (Figures 12a, 12b, 12c, and 12d) and hydrophilicity (Figures 12e and 12f). From Figure 12 we can see for CSL=0.45 (Figure 12a and 12b), the pre-equilibrated droplet remains in Wenzel state without observing the transformation of wetting states throughout the whole process. The kinetic contact angle curve of pre-equilibrated droplet in Figure 13a which shows ladder-like shape without strong fluctuation also certifies no transition of wetting state. That is the hydrophobic groups which extended to the vapor phase immediately adsorbed on the spaces between pillars when the pre-equilibrated droplet came into contact with the substrate. The strong attraction between solvent and hydrophilic groups as well as the rapid reduction of solid-liquid interfacial tension led to the infiltration of solvent molecules. For CSL=0.85 (Figure 13b), again there is no


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obvious changes of spreading dynamics for the two different initial configurations because of the equal value of solvent-substrate attraction and tail-substrate attraction. Thus we can get that the different distribution of surfactants in initial configuration may influence the spreading velocity as well as the wetting state in the process of wetting.

Figure 12. Typical spreading process of pre-equilibrated surfactants-water droplet (a, c, e) and time sequence for the surfactants on textured surface (b, d, f): (a and b) CSL=0.45, (c and d) CSL=0.6, and (e and f) CSL=0.85. The white particles are solvent, the blue particles are the hydrophobic particles, the magenta particles are the hydrophilic particles, and yellow particles represent the lattice of the substrate.


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140

100


(a)

Contact Angle  ()

130

125

120

(b)


80


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0

10

20

30

40

50

60

40

20

0

10

20

Time (ns)

30

40

50

Time (ns)

Figure 13. Contact angle as a function of time for the spreading of two different initial droplets with surfactant on textured substrate: (a) CSL=0.45 and (b) CSL=0.85.

4. CONCLUSIONS In this work, molecular dynamics simulations were carried out to study the molecular mechanism for wetting and spreading of nanodroplets on textured surfaces, in the absence/presence of surfactants

respectively.

Especially,

we

investigated

the

interplay

among

substrate

hydrophobicity, roughness, and the addition of surfactants on the wetting and spreading behaviors of droplets. Our simulation results indicate that substrate microstructure exerts different effects on the contact angle of nanodroplets, depending on the substrate chemistry. The introduction of substrate roughness tends to increase the contact angle for hydrophobic surfaces, but decrease the contact angle for hydrophilic surfaces. In contrast, the presence of surfactants always changes the droplet contact angle via decreasing both the vapor-liquid and liquid-solid interfacial tensions, which is independent of the substrate chemistry and roughness. In general, surfactants have more significant effects in determining the equilibrium state of droplets on hydrophobic substrates.


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Interestingly, our calculation results demonstrate that the addition of surfactants might lead to the transition of wetting state for the nanodroplets on hydrophobic textured surfaces, e.g. from the Cassie-Baxter to Wenzel states. While for nanodroplets on hydrophilic textured surfaces, the presence of surfactants may facilitate the appearance of precursor film for droplet spreading. On the spreading dynamics, our simulations show that the introduction of roughness tend to induce the pinning effect on the contact line, changing its motion mode from a continuous motion to stick-slip motion. We also considered the effect of initial distribution of surfactants on the spreading dynamics and found that the differences of initial configurations can influence the spreading dynamics especially for droplets on hydrophobic surfaces, but have little impact on the equilibrium states.

AUTHOR INFORMATION Corresponding Author *

E-mail: [email protected] (X. Z.); [email protected] (B. L.).

*

Tel.: +86-13718383567(X. Z.); +86-10-89733252 (B. L.).

Author Contributions ¶

Z. L. and K. L. contributed equally to this work.

Notes The authors declare no competing financial interest.


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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Nos. 21276007, 91434204, 21522609) and the Research Fund of China University of Petroleum, Beijing (2462015YQ0308).

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Wetting and Spreading Behaviors of Nanodroplets: The Interplay

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