Molecular Dynamics Simulation of Heat Transport through Solid

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Molecular dynamics simulation on heat transport through solidliquid interface during argon droplet evaporation on heated substrates Jiajia Yu, Rui Tang, You-Rong Li, Li Zhang, and Chunmei Wu Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b04047 • Publication Date (Web): 17 Jan 2019 Downloaded from http://pubs.acs.org on January 18, 2019

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Molecular dynamics simulation on heat transport through solid-liquid interface during argon droplet evaporation on heated substrates Jia-Jia Yu *, Rui Tang, You-Rong Li, Li Zhang, Chun-Mei Wu

Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, School of Energy and Power Engineering, Chongqing University, Shazheng Street, Shapingba District, Chongqing 400044, China

*Corresponding Author E-mail: [email protected]

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ABSTRACT: This paper presented a series of molecular dynamics simulations on the evaporating process of the argon droplet on heated substrates and the energy transport mechanism through solid-liquid interface. Results indicate that the mass-density through liquid-vapor interface decreases sharply when the evaporation is in the steady state. Meanwhile, there is an adsorption layer in the way of clusters at the solid-liquid interface, which has a higher mass-density than the droplet inside. Furthermore, the wetting property of the solid substrate is related with the system initial temperature and the solid-liquid potential energy parameter. The contact angle decreases with the increase of initial temperature and solid-liquid potential energy parameter. During the accelerated evaporation process, small part of energy transports into the liquid inside in perpendicular direction to the solid-liquid interface and most of the energy is transported along parallel direction to the solid-liquid interface in the adsorption layer to the three phase contact line. The heat transfer process from the solid substrate to the droplet inside is hindered by the Kapitza resistance at the solid-liquid interface, no matter the solid substrate is hydrophilic or hydrophobic. Meanwhile, the Kapitza resistance gradually increases with the increase of initial temperature, and decreases with the increase of solid-liquid energy parameter.


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INTRODUCTION The droplet evaporation is a common natural phenomenon and attracts more and more attentions because of many applications in technology and biology, such as inkjet printing 1, DNA/RNA arrangement 2, medical diagnostics 3, the manufacturing of novel optical and electronic materials 4, etc. Many experimental and theoretical works have been performed over the past several decades in order to understand the mechanisms of droplet evaporation. It was found that the evaporation process of a pure sessile droplet is usually divided three stages 5. They are that the contact radius is constant meanwhile the contact angle reduces, the contact angle is constant while the contact radius reduces, and both the contact radius and the contact angle reduce until the droplet disappears finally. The evaporating process is so complicated that the simulation mode is usually simplified to three categories, which are constant contact angle mode, constant contact area mode and the mixed mode. When the droplet wets the solid surface, there is a contact angle in the region of the three phase contact line, which can be calculated through the Young equation and Dhir

9

6-8.

Shi

affirmed that the contact angle decreases with the increase of the system

temperature and the potential well parameter for the solid-liquid interaction. Therefore, the contact angle can be changed through the adjustment of the temperature and the potential well parameter in molecular dynamics simulations with the purpose to change the wetting property of solid-liquid interface

10-12.

On the other hand, the wetting

property has an indispensable influence on the evaporation process of a sessile droplet. Erbil et al. 13 studied the evaporation of water droplets placed on smooth solid substrates, and found that the evaporation rate is related to the original contact radius for constant contact radius mode. Furthermore, the evaporation rate decreases linearly with time when the contact angle is less than 90o, whereas it is nonlinear when the contact angle is larger than 90o. Shin et al. 14 also found that the evaporating time of a sessile droplet is related to the contact angle. Meanwhile, Sobac and Brutin

15

reported that the

evaporation process of the droplets deposited on the substrates with different wetting properties is completely different, no matter the droplets are water or some other simple organic molecular droplets. Moreover, the evaporation time of water is prolonged


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around 58% when the contact angle is increased from 63o to 135o. Recently, the local evaporation flux distribution and the energy transport in the region of three-phase contact line of a sessile droplet has been of great interest. Deegan et al. 16 found that the evaporation rate at the area of three-phase contact line is larger than that at other area of the droplet surface. In addition, the non-uniform evaporation results in the outward flow 17-18. Ibrahem et al. 19 also showed that the local heat flux at the area of three-phase contact line is about 6 times larger than the mean input heat flux at the substrate. Teshigawara and Onuki

20

studied the droplet evaporation at

hydrophilic substrates through molecular dynamics simulation, and found that the evaporation rate at the area of three-phase contact line is twice of the total evaporation rate. Hence, the investigation on the evaporation process in the vicinity of three-phase contact line is meaningful to understand the evaporation mechanism at the microscopic scale. Zhang et al. 21 studied the influence of wetting property on the local heat flux and the local mass flux during the evaporation process of nanodroplets on heated substrates and found that the local heat flux from the substrate to the droplet for hydrophilic substrates is much larger than that for hydrophobic substrates. However, the local mass flux for hydrophilic and hydrophobic substrates follows the same regulation. Meanwhile, Xie et al.

22

performed molecular dynamics simulations on evaporation

mass flux distribution of the droplet on a hydrophilic or hydrophobic flat surface at three evaporation modes, including the diffusion dominant mode, the substrate heating mode and the environment heating mode. The results indicated that the evaporation at hydrophilic substrates is more effective than that at hydrophobic substrates, because the droplet is thinner and the contact area is larger at the hydrophilic substrate than at the hydrophobic substrate. When a droplet is heated on a solid substrate, the liquid evaporates gradually into its own vapor, the heat flux from the solid substrate to the bulk liquid through the solidliquid interface is usually assumed to be continuous 23. However, there is an adsorbed phase between the solid and the bulk liquid phases, which gives rise to the possibility of a thermal or Kapitza resistance at the solid-liquid interface

24-27.

The heat flux is

transported along both perpendicular and parallel directions to the solid-liquid interface.


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Ghasemi and Ward 28 studied the cooling of Au(111) substrate by an evaporating water droplet, and found that only a small portion of the thermal energy is transported along perpendicular direction to the solid-liquid interface into the bulk liquid because of a large Kapitza thermal resistance at the solid-liquid interface. A much larger fraction up to 87% is transported along parallel direction to the solid-liquid interface to the threephase line where thermocapillary convection distributes this energy along the liquidvapor interface to be consumed by the evaporation process. This paper presented a series of molecular dynamics simulations on the evaporation process of an argon droplet on heated substrates. The aim focused on energy transport through the solid-liquid interface by analyzing the proportion of local heat flux along the perpendicular and parallel directions to the solid-liquid interface. THEORETICAL MODEL AND SIMULATION METHOD Figure 1(a) shows a typical snapshot of the initial simulation box, which consists of a cubic argon liquid droplet, a solid substrate and a solid wall. Both the liquid and the solid substrate are Lennard-Jones atoms for simplification. The particle numbers of the liquid droplet and solid substrate are 9842 and 43200, respectively. The velocities of both liquid and solid substrate particles all obey the Gaussian distribution. In addition, the liquid particles are initially distributed with a density close to the liquid density with a FCC lattice. The structure of solid particle is FCC. (100)-oriented solid substrates is used here. The mass of each solid particle is 63.55 (Cu particle). The size of the simulation box is 70.48×70.48×70.48, where  is the collision diameter and

=0.3405 nm. Noted that there is a solid wall to be set underneath the solid substrate. The particle number of the solid wall is 14400. The velocity and the force of wall particles are zero to prevent the particles to be adsorbed at the bottom of the solid substrate. Periodic boundary condition is applied in all the directions. The Verlet velocity function is chosen to update the velocity and coordinate of all the particles constantly. The time interval t is 5fs 21. The cutoff distance rc is 1.2 nm. In order to avoid the sizeeffect, several tests are conducted for different sizes of system, and the chosen one can


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make sure that the influence of the size-effect could be negligible.

Figure 1. Typical snapshot of the initial simulation box (a) and fitted curve of liquid-vapor interface at T 0 * =2.61 and ε sl * =0.5 (b) at meridian plane.

There are three interactions in the system, including the interaction between liquid and liquid particles, the interaction between solid and liquid particles, and the interaction between solid and solid particles. All the interactions are set as the 12-6 Lennard-Jones potential,   12   6  U  rij   4       r    rij   ij   

(1)

where, ε is the potential well, σ is the collision diameter, and rij is the distance between particles i and j. The function is truncated by the cat-off radius rc=3.5σ. Specifically, σl=3.405×10-10 m and εl=0.35 kJ/mol are applied for the interaction between liquid and liquid particles, σs=2.34×10-10 m and εs=3.5 kJ/mol for the interaction between solid and solid particles

29-30.

The parameters for the liquid-solid interaction obey the

Lorentz-Berthelot rule 31. Thus, the collision diameter for the liquid-solid interaction σsl is set as 2.873×10-10 m, and the dimensionless parameters of potential well, which is defined as εsl*=εsl/εl, varies from 0.2 to 0.7 to study the influence of potential well parameter on the evaporation process. By applying , (mσ2/ε)1/2, ε/k, ε and ε/3 as reference values for length, time, temperature, energy and pressure, we can obtain a set of dimensionless parameters as


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follows

 X ,Y , Z  

 x, y , z  , 

t* 

t

 m 2 /  

1/2

, T* 

T e p , E *  , P*   / kB   / 3

(2)

where , ε and m are collision diameter, potential well and mass of argon particle, respectively. x, y, z are coordinates in Cartesian coordinates. t, T, e and p are the simulation time, temperature, energy and pressure. At the beginning of simulations, there is only the cubic droplet and solid substrate with a vacuum atmosphere, as shown in Fig. 1(a). The NVE ensemble is applied to the whole system, and the Berendsen thermostat is chosen to control the system temperature (T 0 * =2.61), that is, the NVT ensemble is applied to the whole system. After certain time of simulation, some of the liquid particles depart from the droplet into the vapor phase because of the pressure difference. Fig. S1 showed the variations of the pressure and the number of argon particles in vapor phase with simulation time at T 0 * =2.61 and ε sl * =0.5 (T 0 * and ε sl * are dimensionless initial system temperature and potential well between solid and liquid particles). It can be found that the number N of the particles in the vapor phase gradually increases until the pressure of vapor phase reaches a constant value, which means the droplet gradually evaporates to a steady state. At that time, the system parameters, including pressure, temperature, potential energy, contact angle and the contact radius of droplet, are all steady. When the simulation time t * runs up to 1.98×10 4 , the Berendsen thermostat for the whole system is canceled, the temperature of the solid substrate T s * is increased to 4.75 by an additional Berendsen thermostat. Only three layers of the solid substrate are temperature-controlled. The evaporation of droplet is accelerated. More and more liquid particles depart from the droplet into the vapor phase until the droplet absolutely disappears. In this case, most of the liquid particles are in the vapor phase. However, there is still a liquid film to be right adsorbed at the solid-liquid interface. RESULTS AND DISCUSSION Relaxation evaporation process. Figure 1(b) gave the snapshot of the whole system in the steady state at T 0 * =2.61 and ε sl * =0.5. It can be found that the droplet seems like


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a part of sphere at the steady state. The average mass-density is taken by assuming a rotational symmetry around the center axis. Meanwhile, a contour curve is fitted by setting the plots of 50% mass-density of the droplet as the position of the solid-liquid interface. Thus, the liquid-vapor interface curve (shown in Fig. 1(b)) is just as, X 2   Z  31.48   20.17 2  Z  27.45  2

(3)

where dimensionless radius of interfacial curve is 20.17, the center of curve for the interfacial curve is (0, -31.48). On the basis of the curvature of droplet fitted curve above, the contact angle is determined by means of the following standard mathematical formula,

tan 

ab 1  ab

(4)

where θ is the contact angle and a and b are slopes of the curvature at the two intersections at the solid-liquid interface, respectively

32.

Thus, the contact angle is

θ=65.37o at T 0 * =2.61 and ε sl * =0.5. When the system is in the steady state, the mass-density distribution along the radial direction is calculated by dividing the droplet along the radial direction with a dimensionless thickness of 1.17. Fig. 2(a) presents the dimensionless mass-density (     3 / m ) distribution of argon particles along the radial direction. Shells with the dimensionless thickness of 1.17 is applied to determine the sampling regions. In addition, the radiuses of these shells, r*, increase orderly during the sampling process. The largest radius of the shell is the dimensionless radius of droplet r0*, which is 20.17. Obviously, the mass-density decreases sharply at the liquid-vapor interface and increases at the solid-liquid interface, which is in good agreement with Huang’s result 33.

Therefore, the mass-density distribution of argon particles presents the largest value

at about r*≈4.1, as shown in Fig. 2(a). The region of liquid-vapor interface is between two dotted lines showed in Fig. 2(a), and the thickness can be calculated by the following formula 32, * =

 2  r *  r0*   1 * 1  l   *g    l*   *g  tanh   2 2 d lv*  


(5)

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where, l* and g* are respectively the dimensionless mass-densities of droplet inside and the vapor phase. In this case, the dimensionless mass-densities of droplet inside and the vapor phase are 0.78 and 0.0008, respectively. dlv* is the dimensionless thickness of liquid-vapor interface 15, and is calculated to be 2.12, 2.29, 2.58, 2.79 by Eq. (5) when the initial system temperature is 2.14, 2.37, 2.61, 2.85, respectively. That means, the thickness increases with the increase of initial system temperature. The regulation is the same with that on a flat interface 34. In addition, the adsorbed layer at the solid-liquid interface affects the evaporation process 35. Slicing the droplet with the dimensionless distance of 1.47 in perpendicular direction (Z-axis) is used to determine the massdensity distribution. Fig. 2(b) gives the mass-density distribution of liquid particles near the solid-liquid interface at T 0 * =2.61 and ε sl * =0.5. It is clear that the mass-density of the adsorption layer is much larger than that in the droplet inside.

(a)

1.2



0.8 

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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0.4

0.0 5

10

15

*

r

20

25


30

35

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(b)

1.20 1.05 

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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0.90 0.75 -27

-24

-21 Z

-18

-15

Figure 2. Mass-density distribution of argon particles along the radial direction (a) and near the solid-liquid interface (b) at T 0 * =2.61 and ε sl * =0.5.

The initial temperature of the system and the potential energy parameter between solid and liquid particles have important effects on the evaporation process of sessile droplets, as related to contact angle from shown in Fig. S2. In addition, Fig. S3 gives the snapshots of different simulation box for different solid-liquid potential parameters at T 0 * =2.61 when the simulation time t * was 1.98×10 4 . It is easily seen that the contact angle gradually decreases with the increase of initial system temperature and the solidliquid energy parameter, which is in good agreement with the result of Shi and Dhir 9. Compared with the results in Ref. 36, the variation of the contact angle with the solidliquid energy parameter is in the same tendency at T 0 * =2.61, while the maximum relative deviation of the contact angle is about 25%, as shown in Fig. S2. The accelerated evaporation process. After the system was in the steady state, the dimensionless temperature of solid substrate T s * was heated up to 4.75 with an additional Berendsen thermostat when the simulation time t * was 1.98×10 4 . Fig. 3 presents the variations of the contact angle, the contact radius and the droplet height with simulation time when the dimensionless initial system temperature T 0 * is 2.61 and the dimensionless wall potential is 0.5. It can be found that the height of droplet gradually decreases and finally approaches to zero. However, there are obviously three stages for the variations of the contact angle and the contact radius during the heated


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evaporation process, as reported in Ref. 5. The adsorption layer on the solid wall has a significant influence on the evaporation process of sessile droplets. Therefore, the heat transfer in the adsorption layer was analyzed separately in this section. The dimensionless thickness of the adsorption layer is set as 1.5

21.

The dimensionless local heat flux (J*=J/( 3)) at the solid-liquid

interface can be calculated by the following formula 37,

J* 

1  * *  e v - S* v* *  i i  i i  V  i i 

(6)

where, ei* is the per-atom energy, including potential energy and kinetic energy. Si* in the second term of the right is the per-atom stress tensor, vi* is the velocity tensor. The tensor multiplies vi* as a 3×3 matrix-vector multiply to yield a vector, the dimensionless local heat flux is the product of kB (Boltzmann number) and the value of local heat flux. This equation was deduced step by step by Fan et al. 38 based on the definition of heat flux and energy, which is only used to calculate the heat flux for systems with two-body potentials.

(1)

10

(2)

(3)

5 0

2.0

2.5

3.0 t*×10-4

3.5

50 

40 30



15

60

*

*

20

70

h

18 16 14 12 10 8 6 4 2 0

25

R

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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20 10 0

4.0

Figure 3. The variations of droplet contact angle (circle), contact radius (triangle) and the height of droplet (square) with simulation time at T s * =4.75, T 0 * =2.61 and ε sl * =0.5.

Figure 4(c) shows distributions of local heat flux in the adsorption layer at the solidliquid interface when T s * =4.75, T 0 * =2.61, ε sl * =0.5 and t*=2.05×104. J*n is the normal


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component of local heat flux at the perpendicular direction to the solid-liquid interface, and J* is the tangent component of local heat flux at the parallel direction to the solidliquid interface. It was clearly seen that the tangent component of local heat flux is much larger than the normal component, which is in accordance with experimental and theoretical results of Duan et al.

39-41.

The tangent and normal components of

dimensionless local heat flux are respectively 29.32 and 7.53. The former one is as 3.89 times as the later one. Because of the existence of Kapitza resistance at the solid-liquid interface, the heat flux transport from the substrate to the droplet along the normal direction is hindered, and most of the heat flux is transported along the parallel direction to the solid-liquid interface to the three phase contact line. Thus, the Kapitza resistance was further calculated through RK*  T * Q*

(7)

where Q* (Q*=Q/) is the dimensionless total heat flux transferred from the substrate from the droplet inside, which is 39.01 for the case above. Meanwhile, T* is the dimensionless temperature jump at the solid-liquid interface. Temperature is a reflection of kinetic energy, thus, T* is calculated to be 3.16, the dimensionless Kapitza resistance is 0.0810.

60

132 126

(a)

55 *

J 120

50

*

Jn

(b) *

J *

Jn

J

*

*

45 J

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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12 8

4

4 0

8

-40 -30 -20 -10

0 X

10

20

30

40

0

-40 -30 -20 -10


0 X

10

20

30

40

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40

30

35 30

25

(c) *

*

J *

*

Jn

15

Jn

*

20

20

J

(d)

J

*

25 J

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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15

10

10

5

5 0 -40

-30

-20

-10

0 X

10

20

30

40

0 -40

-30

-20

-10

0 X

10

20

30

40

Figure 4. Distributions of local heat flux in the adsorption layer at the solid-liquid interface for different initial temperature at εsl*=0.5, T s * =4.75 and t*=2.05×104. (a) T0*=2.14; (b) T0*=2.37; (c) T0*=2.61; (d) T0*=2.85.

The initial temperature of the system has also an important influence on the accelerated evaporation process of the droplets. Fig. 5(a) shows the variation of drop height with simulation time at different initial temperatures when the solid-liquid energy parameter εsl* is 0.5 and the dimensionless substrate temperature T s * is 4.75. The results showed that the drop height gradually decreases until the drop completely disappears. The droplet evaporation time decreases with the increase of the initial temperature of the system. Figure 4 presents distributions of local heat flux in the adsorption layer at the solidliquid interface for different initial system temperatures when T s * =4.75, sl=0.5 and t*=2.05×104. Meanwhile, Table 1 gives statistical data of heat transfer in the adsorption layer at the solid-liquid interface. The substrate is hydrophilic for all chosen initial system temperatures. The tangent component of local heat flux is much larger than the normal component of local heat flux for all situations. When the solid substrate is hydrophilic, the heat transfer from the solid substrate to the droplet inside is hindered by the Kapitza resistance at the solid-liquid interface. Furthermore, with the increase of the initial temperature, the dimensionless value of total heat flux Q* from the solid substrate to the droplet gradually decreases, the temperature jump T* at the solid-liquid interface gradually decreases, and the Kapitza resistance gradually increases. These results are in accordance with the experimental research of Ward 28.


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25

20 (a)

*

T0=2.37 T0=2.61

15

*

T0=2.85

*sl=0.3

*sl=0.5

*sl=0.4

*sl=0.6

15 h*

10

(b)

20

*

h*

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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*sl=0.7

10

5

5

0

0 2

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 t*×10-4

3

4

5 6 t*×10-4

7

8

9

Figure 5. Variation of droplet height with simulation time for different initial temperatures at εsl*=0.5 and T s * =4.75 (a) and for different solid-liquid energy parameters at T0*=2.61 and T s * =4.75 (b).

Table 1. Statistical data of heat transfer in the adsorption layer at the solid-liquid interface for different initial system temperature at T s * =4.75, εsl*=0.5 and t*=2.05×104. (φ=J*/J*n)

T0*



J*n

J*



Q*

T*

Rk*

2.14

87.87

1.54

64.16

41.66

70.11

3.41

0.0486

2.37

71.63

3.86

52.51

13.60

59.72

3.26

0.0546

2.61

65.65

7.53

28.35

3.76

39.01

3.16

0.0810

2.85

50.64

9.54

25.31

2.65

35.86

2.97

0.1217

Figure 5(b) shows the variation of droplet height with simulation time for different solid-liquid potential energy parameters at T0*=2.61 and T s * =4.75. Obviously, the drop height gradually decreases until the drop completely disappears. On the one hand, the contact area of the droplet with the substrate increases with the increase of solid-liquid energy parameters. Therefore, the evaporation time of droplets decreases. That is, during the accelerated evaporation process, the heat transfer from the substrate to the droplet inside becomes fast when the solid-liquid energy parameter increases. Figure 6 shows distributions of local heat flux in the adsorption layer at the solidliquid interface for different solid-liquid potential energy parameters at T s * =4.75, T 0 * =2.61 and t*=2.05×104. It can be clearly seen that when the other simulation conditions remain unchanged, the tangent component of local heat flux is much larger


Page 15 of 22

than the normal component of local heat flux for all situations. That means, the heat transfer from the solid substrate to the droplet inside is hindered by the Kapitza resistance, no matter the substrate is hydrophilic or hydrophobic. Zhang et al. 21 studied the evaporation process of droplets on heated substrates through molecular dynamics simulations. The result shows that the above conclusions exist for hydrophilic substrates, but it is not clear for the situation of hydrophobic substrates. Furthermore, Xie et al. 22 also investigated the evaporation process of droplets on heated substrates through molecular dynamics simulations. The results show that heat transfer along parallel direction to the solid-liquid interface is more effective than that along perpendicular direction to the solid-liquid interface, no matter the substrate is hydrophilic or hydrophobic. 8

*

Jn

*

(a)

J

*

Jn

10

4

J

*

J

*

*

J

(b)

6

5

2 0 -40

-30

-20

-10

10

20

30

0 -40

40

*

Jn

*

(c)

0 X

J

40 30

20

20

*

30

J

*

40

J

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10 0 -40

-30

-20

(d)

-10

0 X

10

20

30

40

*

Jn

*

J

10

-30

-20

-10

0 X

10

20

30

40

0

-40 -30 -20 -10

0 X

10

20

30

40

Figure 6. Distributions of local heat flux in the adsorption layer at the solid-liquid interface for different solid-liquid potential energy parameters at T s * =4.75, T 0 * =2.61 and t*=2.05×104. (a) εsl*=0.2; (b) εsl*=0.4; (c) εsl*=0.6; (d) εsl*=0.7.

Table 2 shows the statistical data of heat transfer in the adsorption layer at the solid-


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liquid interface for different solid-liquid potential parameters at T s * =4.75, T 0 * =2.61 and t*=2.05×104. For all conditions, the heat flux from the solid substrate to the droplet increases with the increase of the solid-liquid energy parameter. When εsl* is 0.2, the substrate is hydrophobic. When εsl* is 0.4, the contact angle approaches to 90°. When εsl* is larger than 0.5, the surface of the substrate is hydrophilic. For hydrophilic substrates, both tangent and normal components of local heat flux all increase gradually with the potential energy parameter. At the same time, with the increase of solid-liquid energy parameter, the total heat flux from the solid substrate to the droplet gradually increases, the temperature jump at the solid-liquid interface gradually decreases, and the Kapitza resistance gradually decreases, which are in accordance with the results of Shenogina 34. Furthermore, the contact angle of solid-liquid interface decrease with the increase of solid-liquid energy parameter in Table 2, the adsorption force at the solidliquid interface is related to contact angle 42. Meanwhile, he Kapitza resistance is related to the adsorption force at the solid-liquid interface

28,

thus, the solid-liquid energy

parameter directly affects the Kapitza resistance.

Table 2. The statistical data of heat transfer in the adsorption layer at the solid-liquid interface for different solid-liquid potential energy parameters at T s * =4.75, T 0 * =2.61 and t*=2.05×104.

ε sl*



J*n

J*

φ

Q*

T*

Rk*

0.2

129.03

3.34

6.13

1.84

10.55

2.93

0.2778

0.3

116.54

2.46

11.87

4.83

15.63

2.75

0.1759

0.4

85.21

6.67

12.99

3.90

27.63

3.19

0.1155

0.5

65.65

7.53

28.35

3.76

39.01

3.16

0.0810

0.6

53.76

12.09

34.79

2.88

50.73

2.96

0.0583

0.7

35.73

21.84

39.43

1.81

63.47

2.74

0.0432

CONCLUSIONS A series of molecular dynamics simulations on the evaporation of the argon droplet on heated substrates were performed. The following conclusions can be drawn from the


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results presented in this paper. (1) During the relaxation evaporation process, when the system is in a steady evaporation state, there is an adsorption layer in the way of clusters with a higher massdensity than the droplet inside at the solid-liquid interface. The mass-density decreases sharply through the liquid-vapor interface. Moreover, when the system is in the accelerated evaporation process, there are clearly three stages for hydrophilic substrates. (2) During the accelerated evaporation process, because of the Kapitza resistance at the solid-liquid interface, small part of energy transports into the liquid inside along perpendicular direction to the solid-liquid interface and most of the energy is transported along parallel direction to the solid-liquid interface in the adsorption layer to the three phase contact line. (3) When the system is in the steady state, the contact angle decreases with the increase of initial temperature and solid-liquid potential energy parameter. That means the wetting properties of solid substrate is related with the two factors. Furthermore, during the accelerated evaporation process, the heat transfer from solid substrate to the droplet inside is hindered by the Kapitza resistance at the solid-liquid interface, no matter the substrate is hydrophilic or hydrophobic. Meanwhile, with the increase of initial temperature, the total heat from solid substrate to the droplet gradually decreases, the temperature jump decreases, and the Kapitza resistance gradually increases. At the same time, with the increase of solid-liquid energy parameter, the total heat from solid substrate to the droplet gradually increases, the temperature jump and the Kapitza resistance gradually decrease.

SUPPORTING INFORMATION Supporting information list: variations of the number of argon particles in vapor phase and the pressure with simulation time (Figure S1); Variations of the contact angle with initial system temperature and solid-liquid energy parameter (Figure S2); Snapshots of different simulation box for different solid-liquid potential parameters (Figure S3).


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENT This work is supported by National Natural Science Foundation of China (Grant No. 11532015), Chongqing University Postgraduates' Innovation Project (Grant No: CYS18041) and the Fundamental Research Funds for the Central Universities (No. 2018CDXYDL0001).

REFERENCES (1) de Gans B. J.; Schubert U. S. Inkjet printing of well-defined polymer dots and arrays. Langmuir 2004, 20 (18), 7789-7793. (2) Dugas V.; Broutin J.; Souteyrand E. Droplet evaporation study applied to DNA chip manufacturing. Langmuir 2005, 21 (20), 9130-9136. (3) Wong T. S.; Chen T. H.; Shen X. Y.; Ho C. M. Nanochromatography driven by the coffee ring effect. Anal. Chem. 2011, 83 (6), 1871-1873. (4) Norris D. J.; Arlinghaus E. G.; Meng L. L.; Heiny R.; Scriven L. E. Opaline photonic crystals: How does self - assembly work. Adv. Mater. 2004, 16 (16), 1393-1399. (5) Semenov S.; Starov V. M.; Velarde M. G.; Rubio R. G. Droplets evaporation: Problems and solutions. Eur. Phys. J.-Spec. Top. 2011, 197 (1), 265-278. (6) Gennes P. G. D.; Brochard-Wyart F.; Quéré D. Capillarity and wetting phenomena. Springer, 2004. (7) Chattoraj D. K.; Birdi K. S. Adsorption and the Gibbs surface excess. Plenum Press, New York, 1984. (8) Sikkenk J. H.; Indekeu J. O.; Vanleeuwen J. M. J.; Vossnack E. O. Moleculardynamics simulation of wetting and drying at solid-fluid interfaces. Phys. Rev. Lett. 1987, 59 (1), 98-101.


Page 18 of 22

Page 19 of 22 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

(9) Shi B.; Dhir V. K. Molecular dynamics simulation of the contact angle of liquids on solid surfaces. J. Chem. Phys. 2009, 130 (3), 034705. (10) Vo T. Q.; Kim B. H. Transport phenomena of water in molecular fluidic channels. Sci Rep 2016, 6, 33881. (11) Vo T. Q.; Barisik M.; Kim B. H. Near-surface viscosity effects on capillary rise of water in nanotubes. Phys. Rev. E 2015, 92 (5), 053009. (12) Ramos-Alvarado B.; Kumar S.; Peterson G. P. Wettability transparency and the quasiuniversal relationship between hydrodynamic slip and contact angle. Appl. Phys. Lett. 2016, 108 (7), 074105. (13) Erbil H. Y., McHale G., Newton M. I. Drop evaporation on solid surfaces: Constant contact angle mode. Langmuir 2002, 18 (7), 2636-2641. (14) Shin D. H.; Lee S. H.; Jung J. Y.; Yoo J. Y. Evaporating characteristics of sessile droplet on hydrophobic and hydrophilic surfaces. Microelectron. Eng. 2009, 86 (4-6), 1350-1353. (15) Sobac B.; Brutin D. Triple-line behavior and wettability controlled by nanocoated substrates: Influence on sessile drop evaporation. Langmuir 2011, 27 (24), 1499915007. (16) Deegan R. D.; Bakajin O.; Dupont T. F.; Huber G.; Nagel S. B.; Written T. A. Capillary flow as the cause of ring stains from dried liquid drops. Nature 1997, 389 (6653), 827-829. (17) Deegan R. D. Pattern formation in drying drops. Phys. Rev. E 2000, 61 (1), 475485. (18) Deegan R. D.; Bakajin O.; Dupont T. F.; Huber G.; Nagel S. R.; Witten T. A. Contact line deposits in an evaporating drop. Phys. Rev. E 2000, 62 (1), 756-765. (19) Ibrahem K.; Abd Rabbo M. F.; Gambaryan-Roisman T.; Stephan P. Experimental investigation of evaporative heat transfer characteristics at the 3-phase contact line. Exp. Therm. Fluid Sci. 2010, 34 (8), 1036-1041. (20) Teshigawara R.; Onuki A. Droplet evaporation in one-component fluids: Dynamic van der Waals theory. EPL 2008, 84 (3), 36003. (21) Zhang J. G.; Leroy F.; Müller-Plathe F. Evaporation of nanodroplets on heated


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

substrates: A molecular dynamics simulation study. Langmuir 2013, 29 (31), 97709782. (22) Xie C. Y.; Liu G. Z.; Wang M. R. Evaporation flux distribution of drops on a hydrophilic or hydrophobic flat surface by molecular simulations. Langmuir 2016, 32 (32), 8255-8264. (23) Xu X. F.; Luo J. B.; Guo D. Criterion for reversal of thermal Marangoni flow in drying drops. Langmuir 2010, 26 (3), 1918-1922. (24) Ward C. A.; Wu J. Y. Effect of adsorption on the surface tensions of solid - fluid interfaces. J. Phys. Chem. B 2007, 111 (14), 3685-3694. (25) Ramos-Alvarado B.; Kumar S.; Peterson G. P. Solid–liquid thermal transport and its relationship with wettability and the interfacial liquid structure. J. Phys. Chem. Lett 2016, 7 (17), 3497-3501. (26) Barisik M.; Beskok A. Temperature dependence of thermal resistance at the water/silicon interface. Int. J. Therm. Sci. 2014, 77, 47-54. (27) Vo T. Q.; Kim B. H. Interface thermal resistance between liquid water and various metallic surfaces. Int. J. Precis. Eng. Manuf. 2015, 16 (7), 1341-1346. (28) Ghasemi H.; Ward C. A. Mechanism of sessile water droplet evaporation: Kapitza resistance at the solid - liquid interface. J. Phys. Chem. C 2011, 115 (43), 21311-21319. (29) Golubkov P. A.; Wu J. C.; Ren P. Y. A transferable coarse-grained model for hydrogen-bonding liquids. Phys. Chem. Chem. Phys. 2008, 10 (15), 2050-2057. (30) Zhu S. B.; Philpott M. R. Interaction of water with metal surfaces. J. Chem. Phys. 1994, 100 (9), 6961-6968. (31) Allen M. P.; Tildesley D. J.; Banavar J. R. Computer simulation of liquids, Oxford University Press, 1987. (32) Dutta R. C.; Khan S.; Singh J. K. Wetting transition of water on graphite and boron-nitride surfaces: A molecular dynamics study. Fluid Phase Equilib. 2011, 302 (1-2), 310-315. (33) Sun Y. J.; Huang T.; Zhao J. F.; Chen Y. Evaporation of a nanodroplet on a rough substrate. Front. Phys. 2017, 12 (5), 126401. (34) Wu Y.W.; Pan C. Molecular dynamics simulation of thin film evaporation of


Page 20 of 22

Page 21 of 22 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

Lennard-Jones liquid. Nanoscale Microscale Thermophys. Eng. 2006, 10 (2), 157-170. (35) Hens A.; Biswas G.; De S. Evaporation of water droplets on Pt-surface in presence of external electric field - A molecular dynamics study. J. Chem. Phys. 2015, 143 (9) 094702. (36) Becker S.; Urbassek H. M.; Horsch M.; Hasse H. Contact angle of sessile drops in Lennard-Jones systems. Langmuir 2014, 30 (45), 13606-13614. (37) Caro M.; Beland L. K.; Samolyuk G. D.; Stoller R. E.L Caro A. Lattice thermal conductivity of multi-component alloys. J. Alloys Compd. 2015, 648, 408-413. (38) Fan Z. Y.; Pereira L. F. C.; Wang H. Q.; Zheng J. C.; Donadio D.; Harju A. Force and heat current formulas for many-body potentials in molecular dynamics simulation with applications to thermal conductivity calculations. Phys. Rev. B 2015, 92 (9), 094301. (39) Feng D. Local evaporation flux affected by thermocapillary convection transition at an evaporating droplet. J. Phys. D-Appl. Phys. 2009, 42 (10) 102004. (40) Feng D.; Ward C. A. Investigation of local evaporation flux and vapor-phase pressure at an evaporative droplet interface. Langmuir 2009, 25 (13), 7424-7431. (41) Shenogina N.; Godawat R.; Keblinski P.; Garde S. How wetting and adhesion affect thermal conductance of a range of hydrophobic to hydrophilic aqueous interfaces. Phys. Rev. Lett. 2009, 102 (15), 156101. (42) Marchand A.; Weijs J. H.; Snoeijer J. H.; Andreotti B. Why is surface tension a force parallel to the interface? Am. J. Phys. 2011, 79 (10), 999-1008.


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Table of Contents Graphic


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Molecular Dynamics Simulation of Heat Transport through Solid

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