Molecular Dynamics Simulations on Coalescence and Non

Subscriber access provided by NEW YORK UNIV

Article

Molecular Dynamics Simulations on Coalescence and Non-coalescence of Conducting Droplets Bing-Bing Wang, Xiao-Dong Wang, Wei-Mon Yan, and Tian-Hu Wang Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b01574 • Publication Date (Web): 18 Jun 2015 Downloaded from http://pubs.acs.org on June 22, 2015

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

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

Page 1 of 19

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

Langmuir

Molecular Dynamics Simulations on Coalescence and Non-coalescence of Conducting Droplets Bing-Bing Wang 1,2, Xiao-Dong Wang 1,2*, Wei-Mon Yan 3**, Tian-Hu Wang4 1.

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China; 2.

Beijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy, North China Electric Power University, Beijing 102206, China;

3.

Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 106, Taiwan;

4.

School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China.

Abstract When an electric field with various strengths is applied to two adjacent conducting droplets, the droplets maybe completely coalesce, partially coalesce, or bounce off one another. To reveal atom-scale mechanism of coalescence or non-coalescence, dynamic behaviors of two conducting nanodroplets at a homogeneous electric field are studied via molecular dynamics simulations in this work. The results show that there is a critical field strength and a critical cone angle above which the two droplets partially coalesce or bounce off. Charge transfer between the two droplets is observed when the droplets are brought into contact. The partial coalescence and the bounce-off of the two droplets at strong field strengths are found to be due to the high charge transfer rate which leads to the breakup of the coalescing droplet at different locations.

1 ACS Paragon Plus Environment

Langmuir

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

*Corresponding Author: Xiao-Dong Wang, Tel. and Fax: +86-10-62321277, E-mail: [email protected]

**Corresponding Author: Wei-Mon Yan, Tel. and Fax: +886-939259149, E-mail: [email protected]


Page 2 of 19

Page 3 of 19

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

Langmuir

1. Introduction Electro-coalescence is a well-known means for separation of water-in-oil emulsions, in which the coalescence rate of conducting droplets is remarkably enhanced by applying an external electric field [1]. However, coalescence does not take place for the two conducting droplets when the electric field strength is strong enough and the droplets repel one another after moving within a gap (bouncing behavior) in which the electrical discharge presumably occurs [2]. By using high-speed video, the formation of a short-lived liquid bridge is observed between the bouncing droplets [3-13]. The bouncing behavior is speculated that the charge transfer occurs between the droplets through the bridge, and there exists a critical electric field strength (Ec) above which the two conducting droplets do not completely coalesce [3]. The bridge radius increases gradually until the droplets entirely coalesce when the electric field strength is below Ec. However, when the electric field strength is above Ec, the bridge radius increases at the initial stage and then decreases during the bounce process [4]. At a relatively strong electric field, partial coalescence of the two droplets may also take place [5-10], in which one or many daughter droplets are ejected before the two droplets fully coalesce. Furthermore, the size of the daughter droplet varies with the external electric field strength and the ionic conductivity [5]. When the two droplets approach, the electrostatic force deforms the leading edge of each droplet into conical structure in the direction of the electric field [6]. The coalescence behavior depends on the cone angle, and there also exists a critical cone angle (θc) above which the two droplets fail to completely coalesce [6]. The adjacent droplets will entirely coalesce at weak electric field strengths (below Ec), partially coalesce at intermediate electric field strengths (above Ec), and bounce off one another at


Langmuir

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

sufficiently strong electric field strengths (above Ec). The charge transfer between the two droplets is speculated to be the reason of the non-coalescence behaviors which contain the partial coalescence and bounce. However, up to now the details of the charge transfer between the two droplets have remained obscure. Consequently, the microscopic mechanisms of non-coalescence behaviors are not very clear. Molecular dynamics (MD) simulations have an excellent track record of following the motion of each molecule and ion through the basic laws of the classical mechanics. This method has proven to be a powerful tool for microscopic analysis of the nanodroplet dynamics behaviors once an appropriate interatomic potential is specified. Until now, MD method has been adopted for investigating the coalescence of pure water nanodroplets [14-16] and metal nanodroplets [17, 18] in the absence of the electric field. In the present study, MD simulations are used to examine coalescence and non-coalescence of two conducting nanodroplets at various electric field strengths. The time evolutions of the charge transfer process for partial coalescence or bounce of the two conducting droplets are presented in details and the mechanisms are explained from the microscopic viewpoints.

2. Simulation Model and Method Similar to the experimental cases [4, 6, 7, 11, 13], dynamic behaviors of a pair of conducting droplets are examined via MD method in this work. The initial simulation system for two conducting nanodroplets with dissolved 0.44 M KCl (3360 water molecules and 30 KCl molecules in each nanodroplet) in the nitrogen gas (800 nitrogen molecules) is shown schematically in Fig. 1. The two droplets and nitrogen gas are placed in a box (600×240×240 Å3), and periodic boundary


Page 4 of 19

Page 5 of 19

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

Langmuir

condition is applied to three directions of the box. The radius of the initial droplets is 30 Å which corresponds to the pure water density of 1 g cm-3, and the initial gap thickness between the two droplets is 80 Å.

Figure 1. Model of initial simulation system: A pair of conducting nanodroplets with dissolved KCl being surrounded by the nitrogen gas and applied by a homogeneous electric field along negative x direction.

In the present study, the SPC/E water model [19] is chosen because it adequately captures the properties of liquid water in MD simulations [20], nitrogen molecules and ions are modeled as L-J and charged L-J particles, respectively. The intermolecular interactions of these particles consist of Coulombic and Lennard-Jones 12-6 potentials

U ij =

qi q j rij

 σ ij + 4ε ij   rij 

12

  σ ij  −    rij

  

6

   

(1)

The interaction and simulation parameters are available in our previous simulations [21-23]. The particle-particle particle-mesh (PPPM) method [24] with a real space cutoﬀ of 10 Ǻ, a splitting parameter of 0.207 Ǻ-1, a grid of 144×72×72 mesh points and a fifth-order interpolation is used to calculate the electrostatic potential. It is found that a run of 500 ps can ensure that the two droplets and the surrounding gas are in equilibrium at the temperature of 298 K. During this period, the mass 5 ACS Paragon Plus Environment

Langmuir

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

centers of the two droplets are fixed at their initial positions. After the preparation of equilibrium system, the temperature of surrounding gas is maintained at 298 K by rescaling the velocities of the nitrogen molecules, and a homogeneous electric field along the negative x direction is applied to the system for studying coalescence and non-coalescence of the two conducting droplets. When the electric field is applied to the system, an additional force Fe,i=qieE is imposed on each particle, where e=1.602176462×10-19 C is the electric charge carried by a single proton. The value of qi is 0 for N atom, -0.8476 for O atom, 0.4238 for H atom, 1 for Na ion, and -1 for Cl ion [21-23]. In our simulations, the values of field strength, E, are firstly assumed to be 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, and 1.2 V nm-1. The simulations show that coalescence occurs at E≤0.5 V nm-1, while non-coalescence occurs at E≥0.6 V nm-1. In order to determine the critical field strength, the values are subsequently changed from 0.51 to 0.59 V nm-1 with an increase of 0.1 V nm-1.

3. Comparison with Experiment The experimental observations for coalescence or non-coalescence behavior of two conducting droplets under the action of electric field are used to validate the present MD code. In the previous experimental investigations, oil/water system is generally used [3-6]; however, it is extremely time-consuming for MD to simulate such system. Recently, Ristenpart et al. [3] investigated the coalescence and non-coalescence behaviors in various liquid systems (vinegar in olive oil, deionized water with polystyrene particles in silicone oil, ethanol in mineral oil, multiple droplets of l M KCl in crude oil, and deionized water in air). Their results showed that the coalescence and non-coalescence can occur for any liquid/liquid or gas/liquid system and there exists a critical field strength above which the non-coelescence will occur. The non-coelescence for all the systems


Page 6 of 19

Page 7 of 19

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

Langmuir

studied was attibuted to the same reason that the meniscus bridge between the bouncing droplets is unstable with respect to capillary pressure when it forms in an electric field exceeding the critical field strength [3]. Since the non-coalescence behavior is of an universal nature and its inherent mechanism is regarded to be the same [3], the nitrogen/water system is adopted in the present MD simulations for saving computational cost. The experimental images for coalescence or non-coalescence of two conducting droplets were reported in the open literature only for liquid/liquid system. Consequently, the present simulations are compared with the result of oil/water system studied by Guo and He [4] as shown in Fig. 2. The comparison shows a good agreement for dynamic droplets behaviors between simulations and experiments, i.e. complete coalescence at lower field strength while non-coalescence and bouncing at high field strength. It should be noted that in the present simulations, the order of magnitude of the applied electric field strength and the time-scale required for coalescence or non-coalescence deviate from the experiments. The deviation maybe comes from the following two reasons. First, the present simulations adopt nanoscale droplets due to the limitation of MD computational ability. Second, the oil/water system used in the experiments is modelled by the nitrogen/water system. In addition, the resistance force on the water droplets exerted by the nitrogen atmosphere is far less than that by the oil, leading to that the two droplets are elongated more significantly along the elecric field direction at high field strength, as shown in Fig. 2(b2) at t=96 ps. Nonetheless, the present MD simulations reproduce the phenomena observed in the macroscopic experiments, and hence useful information can be extracted from MD simulations to reveal the mechanism on coalescence or non-coalescence of two conducting droplets at the atom scale.


Langmuir

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

Figure 2. Experimental results of droplet dynamic behaviors at (a1) E=167 and (b1) 200 V mm-1; MD results of droplet dynamic behaviors at (a2) E=0.4 and (b2) 0.80 V nm-1.

4. Results and Discussion 4.1 Statistical Relevance of Simulations Observations To examine the statistical relevance of simulated results, three different initial states of the system are used at all the electric field strengths of interest. Although a run of 500 ps can ensure enough good equilibrium, simulations are still performed in 500, 600, and 700 ps during the preparation of equilibrium system. Thus, the three equilibrium systems have almost the same macroscopic properties, while the position and velocity for each particle (water molecules, nitrogen molecules, and ions) differ significantly for the three systems. Subsequently, a same electric field is applied to the three systems, and the dynamic behaviors of the systems are compared to verify the statistical relevance. The coalescence behavior and gap thickness of the two conducting droplets for the three systems at the field strength of 0.4 V nm-1 are shown in Fig. 3. It can be seen that the time required for bringing the two droplets into contact differs slightly (457, 463, and 458 ps) due to different initial position and velocity for each particle in the three systems.


Page 8 of 19

Page 9 of 19

However, dynamic behaviors of the droplets are very similar (Fig. 3(a)) and the variation of gap thickness with time is almost the same (Fig. 3(b)). Furthermore, the critical field strength between coalescence and non-coalescence is also examined and the same value is obtained for the three systems. 90

equil: 500 ps equil: 600 ps equil: 700 ps

80 70 60

L1-2 (Å)

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

Langmuir

50 40 30 20 10 0

(b) 0

50

100 150 200 250 300 350 400 450 500

t (ps)

Figure 3. Time evolutions of (a) dynamic behaviors of the droplets and (b) gap thickness between the two droplets at the field strength of 0.4 V nm-1 (equilibrated time 500, 600 and 700 ps).

4.2 Dynamic Behaviors of Droplets at Various Electric Fields Dynamic behaviors of a pair of conducting droplets subjected to various electric field strengths are captured in series of plots shown in Fig. 4. The instant when the two droplets just contact with each other is defined as t=0 ps. For the lowest electric field strength E=0.4 V nm-1 (Fig. 4(a)), the two droplets slowly approach, then contact with each other, and finally coalesce into a spherical droplet. With increasing the electric field strength to E=0.53 V nm-1 (Fig. 4(b)), the droplets approach more quickly, as compared with that of E=0.4 V nm-1. Besides, the conical structures of the two droplets are developed and the cone angle is about 34.80° at t=0 ps. Finally, the droplets completely coalesce into an ellipsoid droplet, and the droplet maintains this shape thereafter. The time required from the initial equilibrium states to complete coalescence decreases with the increase


Langmuir

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

in the electric field strength, indicating that the coalescence rate increases with the external electric field strength.

Figure 4. Dynamic behaviors of a pair of conducting nanodroplets subjected to various electric field strengths of (a) 0.4, (b) 0.53, (c) 0.54, (d) 0.8 and (e) 1.2 V nm-1.

For the electric field strengths greater than E=0.53 V nm-1, the two droplets approach and contact with each other more quickly. A coalescing droplet would be formed and is then elongated to spindle shape along the electric field direction, which is qualitatively similar to the experiment observation [11]. Finally, the breakup of the coalescing droplet takes place and the separated parts surprisingly move toward opposite directions along the electric field. Besides, it is clear by comparing Figs. 4(c), 4(d) and 4(e) that the time required for the breakup of the coalescing droplet decreases with the increase in the electric field strength. Noted in Fig. 4(c) (E=0.54 V nm-1), at the left part of droplet 1 the breakup presents while the right part of droplet 1 coalesces with droplet 2. This phenomenon stands for the occurrence of the partial coalescence. Therefore, the critical electric strength is determined as Ec=0.53 V nm-1 in the present simulations with the corresponding critical cone angle of 34.80° which is in good agreement with the experiment measurements [6]. Moreover, dynamic behaviors of the two droplets with the initial gap of 40 Å or 120 Å are also examined in the separate simulation runs, and the results for two specific field strengths of 0.53 and 0.54 V nm-1 are shown in Fig. 5. It can be seen that the time required for bringing the two separated 10 ACS Paragon Plus Environment

Page 10 of 19

Page 11 of 19

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

Langmuir

droplets into contact is found to be less for the initial gap of 40 Å. However, comparisons of Figs. 5(a) and 5(c) as well as Figs. 5(b) and 5(d) show that, after the two droplets are brought into contact, the dynamic behaviors are very similar when the same field strength is applied to the system. Complete coalescence of the two droplets occurs at the field strength of 0.53 V nm-1, while non-coalescence occurs at the field strength of 0.54 V nm-1, indicating that the critical value is also Ec=0.53 V nm-1 for the initial gaps of 40 and 120 Å. In addition, the critical cone angle for the two initial gaps is found to be 34.80°, which is also the same as that for the initial gap of 80 Å. The present comparisons demonstrate that at least in a specific range of the initial gap (e.g. 40-120 Å for the present simulations), the critical field strength and cone angle are independent of the initial gap.

Figure 5. Coalescence and non-coalescence of two conducting droplets with initial gaps of (a and b) 40 Å and (c and d) 120 Å.

The velocity variations of the two droplets for the initial gaps of 40, 80, and 120 Ǻ at E=0.53 V nm-1 are shown in Fig. 6. It can be seen that when the two droplets are brought into contact, the average velocity of the two droplets is 0.040 nm ps-1 for the initial gap of 40 Ǻ, 0.042 nm ps-1 for the initial gap of 80 Ǻ, and 0.044 nm ps-1 for the initial gap of 120 Ǻ. Although the average velocity at contact depends on the initial gap, their difference is relatively small, which is the reason for the non-dependence of the critical field strength and cone angle on the initial distance. 11 ACS Paragon Plus Environment

Langmuir

0.06

-1

V (nm ps )

-1

0.02 0.01 0.00 -0.01 -0.02 -0.04 -0.05 -0.06

0

10

0.03

0.02

0.02

0.01 0.00 -0.01 -0.02 -0.03

V droplet2

-0.05

30

V droplet1 V droplet2

-0.04

40

t (ps)

50

60

70

80

-0.06

0

50

100

(c) L1-2=120 Å

0.04

0.03

V droplet1 20

0.05

(b) L1-2=80 Å

0.04

0.03

-0.03

0.06

0.05

(a) L1-2=40 Å

0.04

-1

0.05

V (nm ps )

0.06

V (nm ps )

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

Page 12 of 19

0.01 0.00 -0.01 -0.02

V droplet1 V droplet2

-0.03 -0.04 -0.05

150

200

250

300

t (ps)

-0.06

0

100

200

300

400

500

600

700

t (ps)

Figure 6. The velocity variations of the two droplets before contact.

Noticed in Fig. 4(d) (E=0.8 V nm-1) that the breakup location of the coalescing droplet is closer to the interface of the two droplets than that of E=0.54 V nm-1. The size of bouncing daughter droplet is relatively larger, which agrees with the experiment results [5]. When the electric field strength is raised to E=1.2 V nm-1, the coalescing droplet breaks up at the interface of the two droplets. Thus, the bouncing behavior occurs. As can be seen in Figs. 4(c) (t=185 ps) and 4(e) (t=-3 ps), several ions evaporate and detach from the droplet (ion evaporation) because the ions are accelerated by the strong electrostatic force, and some water molecules in the droplet move together with the evaporated ions due to the hydration effect [21-23]. The ion evaporation has been used in the technique of electrospray ionization for producing intact ions [25]. Furthermore, when the equilibrated time is changed to 600 or 700 ps, the two droplets also completely coalesce at Ec=0.53 V nm-1, partially coalesce at E=0.54 V nm-1, and bounce off each other at E=1.2 V nm-1, which verifies the statistical relevance of the simulated results again. In processes of complete coalescence, partial coalescence, or bounce of two conducting droplets, the two droplets would approach and then contact and form a conical structure. As shown in Fig. 4, with the increase in the electric field strength, the time required from the initial equilibrium state to the droplets contact decreases, and the cone angle increases. The potential energy between the two droplets based on Eq. (1) and the gap thickness are presented in Fig. 7. At 12 ACS Paragon Plus Environment

Page 13 of 19

initial equilibrium state, the potential energy between the two droplets is -38 kJ mol-1, and the gap thickness is 79.05 Å for all simulations. The magnitude of the potential energy between the two droplets gradually increases with time and the gap of the two droplets slowly decreases at E=0.4 V nm-1. The droplets deformation and ions distribution at t=-45 ps for the two droplets at E=0.8 V nm-1 are also presented in the subplot of Fig. 7(a). It is disclosed that the droplets deformation is more serious and the more ions with the opposite charges distribute at the leading edge of each droplet, as compared with those with low electric field strengths. As a result of attraction between the opposite charges, the time rate of the potential energy between the two droplets increases with the electric field strength (Fig. 7(a)) and the two droplets approach more quickly at high electric field strengths (Fig. 7(b)). After the two droplets are brought into contact (t>0 ps), the magnitude of potential energy remarkably increases, as shown in Fig. 7(a), and the two droplets coalesce quickly. 1

90

(a)

80

0

79.05

-0.038

-2

-1

0.4 V nm -1 0.53 V nm -1 0.54 V nm

(b)

70 60

-1

L1-2 (Å)

-1

0.8 V nm -1 1.2 V nm -1

E=0.8 V nm

3

-1

E1-2×10 (kJ mol )

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

Langmuir

-3

-1

50 40

0.4 V nm -1 0.53 V nm -1 0.54 V nm

-1

0.8 V nm -1 1.2 V nm

30 20

-4 10 -5 -480 -420 -360 -300 -240 -180 -120

-60

0

0 -480 -420 -360 -300 -240 -180 -120

60

t (ps)

-60

0

60

t (ps)

Figure 7. Time evolutions of (a) potential energy and (b) gap thickness between two conducting nanodroplets.

4.3 Mechanisms of Droplets Non-coalescence The mechanisms of partial coalescence and bounce of the two droplets are associated with charge transfer by ionic conduction [3, 5]. To validate this speculation, dynamic behaviors of pure


Langmuir

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

water nanodroplets at E=0.4 and 0.8 V nm-1 are presented in Fig. 8. The pure water droplets approach, contact and finally completely coalesce into a spherical droplet at the low field strength of 0.4 V nm-1. For the high field strength of 0.8 V nm-1 in Fig. 8(b), the coalescing droplet is elongated to be a spindle shape along the electric field direction and it also does not break up all along. As mentioned in Fig. 4, the coalescing droplet would also be elongated to be a spindle shape at E>Ec. Although the interaction between water molecules in the spindle droplet is found to be very weak in our previous work [22], the comparison of Figs. 4(c) and 8(b) demonstrates that the deformation is not the primary reason for the partial coalescence and bounce of the two conducting droplets. Consequently, the non-coalescence of the droplets should be attributed to the addition of ions in the droplets.

Figure 8. Dynamic behaviors of a pair of pure water nanodroplets subjected to field strengths of 0.4 and 0.8 V nm-1.

The distributions and velocities in the x-direction of K+ and Cl- in the conducting droplets at E=0.53 (t=500 ps), 0.54 (t=251 ps) and 1.2 V nm-1 (t=43 ps) are respectively shown in Fig. 9. Here, negative ion velocity stands for the ion motion in the negative x direction. Figure 9 shows that not all the K+ and Cl- distribute at the two edges of the coalescing droplet due to the ion association 14 ACS Paragon Plus Environment

Page 14 of 19

Page 15 of 19

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

Langmuir

between K+ and Cl- [23]. At E=0.53 V nm-1, the distributions of ions are clustered when the two droplets completely coalesce. As the electric field strength is raised to E=0.54 V nm-1, the ions dispersedly distribute in the coalescing droplet and the average magnitude of the ion velocity is greater than that of E=0.53 V nm-1. Besides, some Cl- in droplet 1 have transferred to droplet 2, and some K+ in droplet 2 have also transferred to droplet 1, which implies that the charge transfer takes place because of the electrostatic force after the two droplets are brought into contact. More importantly in Fig. 9(b), the more K+ (more net charges) gather at the left part of droplet 1 at t=251 ps. Under the action of electrostatic force (Fe), the ions at the left part with negative x direction velocity will overcome the constraints and move toward the negative x direction, which leads to the occurrence of the partial coalescence.

Figure 9. Distributions and velocities in the x-direction of K+ and Cl- in the conducting nanodroplets at the electric field strengths of 0.53 (t=500 ps), 0.54 (t=251 ps) and 1.2 V nm-1 (t=43 ps).

Noticed in Fig. 9(c) when the electric field strength is increased to a higher value of E=1.2 V nm-1, both K+ and Cl- are accelerated to the higher velocities in a very short duration. In addition, as shown in Fig. 7(a), the more ions with the opposite charge distribute at the leading edge of each droplet before the two droplets are brought into contact when the electric field strength is stronger. Thus, once the two droplets are brought into contact with each other, the more ions will transport 15 ACS Paragon Plus Environment

Langmuir

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

between the two droplets as compared with the low field strengths. As a result, the number of K+ is remarkably more than that of Cl- in droplet 1; however, the opposite trend occurs in droplet 2. Furthermore, little ions of K+ or Cl- gather at the end part of the coalescing droplet at this moment. Consequently, droplets 1 and 2 with enough opposite charges move in the opposite directions under the action of electrostatic force and the breakup of coalescing droplet takes place at the interface, as found in Fig. 4(e). The droplets bounce off each other. Therefore, charge transfer between the droplets through the liquid bridge is the fundamental mechanism on that the droplets bounce off each other at high electric field. This confirms the previous experimental speculation [3].

5. Conclusions In summary, the critical electric field strength (Ec) and cone angle (θc) for coalescence and non-coalescence of the two conducting nanodroplets are obtained. Two droplets approach, then contact with each other, and finally completely coalesce when the electric field strength is lower than Ec. The coalescence rate of the two droplets increases with the external electric field strength. However, the two droplets would partially coalesce at the electric field strength above Ec and bounce off at higher electric field strength. Furthermore, charge transfer between the two droplets after the droplets contact is directly presented and explained in details. The charge transfer rate increases with the increase in the electric field strength, which causes the partial coalescence and bounce of the two conducting nanodroplets at high electric field strengths.

Acknowledgments This study was partially supported by The National Science Fund for Distinguished Young


Page 16 of 19

Page 17 of 19

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

Langmuir

Scholars of China, the 111 Project (No. B12034), and the Fundamental Research Funds for the Central Universities (No. 13ZX13).

References [1] Eow, J. S.; Ghadiri, M.; Sharif, A. O.; William, T. J. Electrostatic Enhancement of Coalescence of Water Droplets in Oil: A Review of The Current. Chem. Eng. J. 2001, 84, 173-192. [2] Allan, R. S.; Mason, S. G. J. Particle Motions in Sheared Suspensions XIV. Coalescence of Liquid Droplet in Electric and Shear Fields. Colloid Sci. 1962, 17, 383-408. [3] Ristenpart, W. D.; Bird, J. C.; Belmonte, A.; Dollar, F.; Stone, H. A. Non-Coalescence of Oppositely Charged Drops. Nature (London) 2009, 461, 377-380. [4] Guo, C. H.; He, L. M. Coalescence Behaviour of Two Large Water-Drops in Viscous Oil under A DC Electric Field Understanding. J. Electrostatics 2014, 72, 470-476. [5] Hamlin, B. S.; Creasey, J. C.; Ristenpart, W. D. Electrically Tunable Partial Coalescence of Oppositely Charged Drops. Phys. Rev. Lett. 2012, 109, 094501. [6] Bird, J. C.; Ristenpart, W. D.; Belmonte, A.; Stone, H. A. Critical Angle for Electrically Driven Coalescence of Two Conical Droplets. Phys. Rev. Lett. 2009, 103, 164502. [7] Torza, S.; Mason, S. G. Coalescence of Two Immiscible Liquid Drops. Science 1969, 163, 813-814. [8] Aryafar, H.; Kavehpour, H. P. Electrocoalescence: Effects of DC Electric Fields on Coalescence of Drops at Planar Interfaces. Langmuir. 2009, 25, 12460-12465. [9] Mousavichoubeh, M.; Shariaty-Niassar, M.; Ghadiri, M. The Effect of Interfacial Tension on Secondary Drop Formation in Electro-Coalescence of Water Droplets in Oil. Chem. Eng. Sci.

2011, 66, 5330-5337. [10] Mousavichoubeh, M.; Ghadiri, M.; Shariaty-Niassar, M. Electro-Coalescence of an Aqueous Droplet at an Oil-Water Interface. Chem. Eng. Process. 2011, 50, 338-344. [11] Thiam, A. R.; Bremond, N.; Bibette, J. Breaking of an Emulsion under an AC Electric Field. Phys. Rev. Lett. 2009, 102, 188304. [12] Chen, G.; Tan, P.; Chen, S. Y.; Huang, J. P.; Wen, W. J.; Xu, L. Coalescence of Pickering Emulsion Droplets Induced by an Electric Field. Phys. Rev. Lett. 2013, 110, 064502. [13] Bararnia, H.; Ganji, D. D. Experimental Investigation of Water Droplets’ Behavior in Dielectric Medium: The Effect of an Applied DC Electric Field. Mech. Sci. 2013, 4, 333-344. [14] Zhao, L.; Choi, P. Molecular Dynamics Simulation of the Coalescence of Nanometer-Sized 17 ACS Paragon Plus Environment

Langmuir

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

Page 18 of 19

Water Droplets in N-Heptane. J. Chem. Phys. 2004, 120, 1935-1942. [15] Liao, M. L.; Ju, S. P.; Yang, S. H. Coalescence Behavior of Water Nanoclusters: Temperature and Size Effects. J. Chem. Phys. C 2007, 111, 6927-6932. [16] Rekvig, L.; Frenkel, D. Molecular Simulations of Droplet Coalescence in Oil/Water/surfactant Systems. J. Chem. Phys. 2007, 127, 134701. [17] Hendy,

S.;

Brown,

A.;

Hyslop,

M.

Coalescence

of

Nanoscale

Metal Clusters:

Molecular-Dynamics Study. Phys. Rev. B 2003, 68, 241403(R). [18] Pothier, J. C.; Lewis, L. J. Molecular-Dynamics Study of the Viscous to Inertial Crossover in Nanodroplet Coalescence. Phys. Rev. B 2012, 85, 115447. [19] Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269-6271. [20] Varilly, P.; Chandler, D. J. J. Water Evaporation: A Transition Path Sampling Study. Phys. Chem. B 2013, 117, 1419-1428. [21] Wang, B. B.; Wang, X. D.; Wang, T. H. Microscopic Mechanism for the Effect of Adding Salt on Electrospinning by Molecular Dynamics Simulations. Appl. Phys. Lett. 2014, 105, 121906. [22] Wang, B. B.; Wang, X. D.; Duan, Y. Y.; Chen, M. Molecular Dynamics Simulation on Evaporation of Water and Aqueous Droplets in the Presence of Electric Field. Int. J. Heat Mass Transfer 2014, 73, 533-541. [23] Wang, B. B.; Wang, X. D.; Wang, T. H. Size Control Mechanism for Bio-Nanoparticle Fabricated by Electrospray Deposition. Drying Tech. 2015, 33, 406-413. [24] Beckers, J. V. L.; Lowe, C.P.; De Leeuw, S. W. An iterative PPPM method for simulating coulombic systems on distributed memory parallel computers. Mol. Simulat. 1998, 20, 369-383. [25] Fenn, J. B.; Mann, M.; Meng, C. K.; Wong, S. F.; Whitehouse, C. M. Electrospray Ionization for Mass Spectrometry of Large Biomolecules. Science 1989, 246, 64-71.


Page 19 of 19

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

Langmuir

Graphic for the "Table of Contents"


Molecular Dynamics Simulations on Coalescence and Non

Recommend Documents