Nanoscale Study of Bubble Nucleation on a Cavity Substrate Using

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Nanoscale study of bubble nucleation on a cavity substrate using molecular dynamics simulation Yujie Chen, Jingfa Li, Bo Yu, Dongliang Sun, Yu Zou, and Dongxu Han Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b03044 • Publication Date (Web): 06 Nov 2018 Downloaded from http://pubs.acs.org on November 8, 2018

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Nanoscale study of bubble nucleation on a cavity substrate using molecular dynamics simulation Yujie Chen1, Jingfa Li2, Bo Yu2*, Dongliang Sun2, Yu Zou2, Dongxu Han2 1

National Engineering Laboratory for Pipeline Safety/MOE Key Laboratory of Petroleum

Engineering/Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum, Beijing 102249, China 2

School of Mechanical Engineering, Beijing Key Laboratory of Pipeline Critical Technology and

Equipment for Deepwater Oil & Gas Development, Beijing Institute of Petrochemical Technology, Beijing, 102617, China

Abstract: In this paper, the molecular dynamics simulation method is utilized to investigate the phase transition behavior of an argon film placed on cavity substrates with different wettability conditions. The simple L-J liquid is heated by the metal platinum substrate with different temperatures, and a complete process of bubble nucleation is successfully visualized on the cavity substrate at a temperature of 150 K and 160 K. Moreover, the bubble nucleation behavior shows a dependence on cavity wettability. A layer of liquid atom is attracted to the strong-hydrophilic cavity and obtains more energy to nucleate first. In contrast, the liquid atom suffers a large repulsive force from the metal atom in the hydrophobic cavity, thus an original small bubble nucleus stably stays inside before the incipient boiling time. With increasing heating time, the original bubble nucleus grows up from the hydrophobic cavity. This bubble nucleation behavior on a hydrophobic cavity is in agreement with macro theory, which states that a cavity provides an original nucleus for bubble formation and growth. Besides, cavity wettability plays a crucial role in the incipient boiling temperature of an argon film. The incipient boiling temperature increases with the weakening of the cavity hydrophobicity, and this trend is in accordance with macro experiments, which show that liquid is easier to boil on a more hydrophobic substrate.

Keywords: Bubble nucleation; Cavity substrate; Wettability; Incipient boiling temperature; Molecular dynamics simulation *Corresponding author: Bo Yu, Tel: +86-10-81292805, E-mail: [email protected]

Introduction Nucleate boiling heat transfer has a broader application background in engineering, such as electronic cooling, power generation, refrigeration, and cryogenics [1,2]. The relevant studies have 1

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been performed in recent decades [3-8]. Following these pioneering efforts, especially with the development of microelectronic technology, the investigation into heat transfer of nucleate boiling on the microscale has attracted considerable attention recently [9-18]. However, traditional macroresearch methods are inapplicable to the study of microcosmic bubble nucleation behavior on a solid substrate, which receives considerable attention for engineering applications [9]. Therefore, achieving a better understanding of the physical process of nucleate boiling on the microscale is vital and urgent. Molecular dynamics simulation is a powerful approach for describing nanoscale bubble nucleation behavior, and many studies have been conducted in recent years [10]. Nagayama et al. [11] studied the bubble nucleation behavior in a nanochannel based on the molecular dynamics method. It was found that bubble nucleation behavior was significantly different on a smooth substrate with varying wettability. Homogeneous nucleation and heterogeneous nucleation respectively appeared on hydrophilic and hydrophobic substrates. Moreover, the inapplicability of the Young-Laplace equation in nanoscale was verified. Maruyama et al. [12] expanded the nanochannel, and the heterogeneous nucleation processes successfully were visualized under different surface wettability conditions. Yamamoto et al. [13] investigated the initial stage of bubble nucleation on smooth substrates with nonuniform superheat and surface wettability, respectively. Under these two conditions, the bubble nucleus successfully generated in the vicinity of the substrate, and the inception time of nucleation was found to be related to the surface wettability and superheat. Hens et al. [14] investigated evaporation and boiling phenomena on a smooth surface. It was found that the bubble nucleus did not easily form on a non-wetting substrate but was easy to nucleate on a hydrophilic substrate with a high degree of superheat. Inaoka et al. [15] constructed a large simulation box to investigate pool boiling, and a pool boiling curve was presented. Moreover, the curve trend is consistent with that observed in experiment for pool boiling. Chen et al. [16] studied homogeneous and heterogeneous nucleation in NPT and NPzzT ensembles. The results demonstrated that there was no stable homogeneous bubble nucleus in both ensembles, and the phenomena were different from literature results in NVE or NVT ensembles [11, 17]. She et al. [17] analyzed the bubble nucleation process on a substrate with a triangular cavity, which enhanced the formation of the bubble nucleus. The top surface was kept weak-hydrophilic, and the wettability of the bottom substrate was changed in different simulation cases. The results showed that the hydrophilic bottom substrate had a better performance for bubble nucleation, and no bubble nucleus formed on a strong-hydrophobic substrate. Liu et al. [18] studied the process of bubble nucleation on a rough hydrophobic substrate, and the thermodynamic integration method was applied to quantitatively evaluate the change of free energy in the phase transition process. The above studies provide significant insight for bubble nucleation on a substrate with different conditions, and the effects of substrate wettability on bubble nucleation have been thoroughly 2


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discussed. However, the effects of cavity substrate on bubble nucleation are lacking. On the macroscale, Foust [19] and Bankoff [20] have developed a hypothesis that the cavity in a solid substrate is likely to be a breeding place for bubble nucleation due to the presence of residual gas, and this gas will grow up to be a bubble when the substrate temperature is increased. Based on this theory, a rough surface with grooves has been constructed to enhance the heat transfer efficiency in many macroscopical pool boiling experiments [6, 7]. On the microscale, the surface is rough as well. Therefore, a crucial challenge for the study of nucleate boiling study is a better understanding of the microcosmic bubble nucleation behavior on a cavity substrate. However, unfortunately, such relevant study is still far from maturity, and more efforts are needed. In this paper, a molecular dynamics method is applied to study the phase transition of an argon film on cavity substrates under different wettability and temperature conditions. The paper is organized as follows: in the first part, the simulation system and method are introduced. In the second part, the phase transition behavior of argon film on a strong-hydrophilic cavity substrate at different temperatures is explored. In the third part, the cavity wettability of strong hydrophilicity is replaced with strong hydrophobicity and its effects on bubble nucleation are illustrated. In the fourth part, based on the results of strong-hydrophilic and strong-hydrophobic cavity, the moderate-hydrophobic and weak-hydrophobic cavities are constructed to figure out the relationship between cavity wettability and the incipient boiling temperature of the argon film. In the final part, the bubble nucleation behavior on cavity substrate is summarized.

Simulation system and method In this paper, the molecular dynamics method is utilized to investigate the phase transition behavior of an argon film placed on a cavity substrate. Figure 1 illustrates the initial configuration of the simulation system, which is a cubic box with size of 15.0 nm (x) × 7.7 nm (y) × 85.0 nm (z). Ten layers of platinum atoms are arranged at the bottom with an FCC (1 1 1) crystal lattice [22]. 28000 liquid argon atoms are placed on the platinum substrate with a density of 1.367 kg/cm³. The rest of the upper region is occupied by gaseous argon atoms. To figure out the effects of cavity wettability on bubble nucleation, different types of cavity substrates are constructed in the present study. As shown in Figure 2, the wettability is uniformly strong-hydrophilic in the first substrate, and the cavity region is replaced with hydrophobicity (strong, moderate and weak hydrophobicity) in the second substrate. In both types of substrates, the bottom three layers of platinum atoms are set as the heat source, the temperature of which is controlled by a Langevin thermostat. A spring force of -Kr is exerted to each platinum atom during the simulation process using a spring coefficient K of 46.8 N/m [12]. All platinum atoms are restricted to vibrate around their own original lattice position. In the molecular dynamics simulation of boiling on a platinum substrate, The Lennard-Jones 3


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(L-J) potential rather than the Embedded Atom Method (EAM) potential is usually adopted to describe the interatomic interaction between metal atoms. The reasons for this can be figured out as follows: first the heat transfer between platinum and argon atoms is the focus of the present study, and the L-J potential is well qualified for this work. Second, the simulation system includes 15664 platinum atoms, and the EAM potential requires more computing resources than the L-J potential. Besides, the argon atom is considered as the simple L-J atom. Therefore, the L-J potential is better choice for describing the interactions of both argon-argon and platinum-platinum in this paper.    Ar  Ar (r )  4 Ar  Ar [( Ar  Ar )12  ( Ar  Ar )6 ] r

Pt  Pt (r )  4 Pt  Pt [(

 Pt  Pt r

r

)12  (

 Pt  Pt r

)6 ]

(1) (2)

where  Ar  Ar and  Pt  Pt express the energy parameters for argon and platinum atoms,  Ar  Ar and  Pt  Pt express the length parameters for argon and platinum atoms. The details for these parameters

are listed in Table 1. The wettability of the metal surface is associated with the interaction between argon and platinum atoms, thus a new form of the L-J potential is presented to describe this interaction [23]. As shown in Eq. (3), this new potential is a combination of the potential models used by Din [24] and Barrat [25]. Pt  Ar (r )  4 Pt  Ar [(

 Pt  Ar r

)12   (

 Pt  Ar r

)6 ]

 Pt  Ar    Pt  Ar  Pt  Ar 

(3) (4)

 Pt   Ar

(5)

2

where  Pt  Ar and  Pt  Ar represent the energy parameter and length parameter between platinum and argon atoms, respectively. These values are calculated by Eq. (4) and Eq. (5) based on the Lorentz-Berthelot combining rule [26].  and  are used to adjust the solid-liquid interface wettability, and their values are presented in Table 2. The simulation can be conducted by the simulator, as long as the users input the parameters  and  . However, the additional parameters  and  in Eqs. (3) and (4) bring trouble to the implementation of simulation. Therefore, to better perform the molecular dynamics simulation study, the modified L-J potential needs to be further transformed into a general one. ' ' Pt  Ar (r )  4 Pt'  Ar [( Pt  Ar )12  ( Pt  Ar )6 ] r

r

 Pt'  Ar   Pt  Ar  2 4


(6) (7)

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

1

 Pt'  Ar   6 Pt  Ar

(8)

where  Pt'  Ar and  Pt'  Ar denote the new energy parameter and length parameter for the LennardJones potential, respectively. During the simulation process, the cut-off radius rc  3.5 Ar is set to save computation time, and the position and velocity of each atom are updated by a Velocity-Verlet algorithm [27] with a time step t  5 fs . 1 r (t  t )  r (t )  v (t )t  a(t )t 2 2 1 v (t  t )  v (t )  [a(t )  a(t  t )]t 2

(9) (10)

where r and v are respectively the position vector and velocity vector of the atoms. The heat flux q is an important parameter for evaluating the heat transfer efficiency. The substrate is the only energy source for argon, thus the heat flux absorbed by argon is estimated using Eq. (11) [13]. q

E&Ar

(11)

Asubstrate

where Asubstrate is the contact area of the liquid-solid interface and E&Ar is the exchanging energy for argon. The total energy of argon at each time step can be obtained by summing the per-atom kinetic energy and potential energy. The temperature value is a statistical result of the atomic kinetic energy based on a group of atoms, which can be calculated by Eq. (12). 1

2m

v2 

Ar i

i

3 NkT 2

(12)

where mAr  6.63  1026 kg is the argon atom mass, vi is the atom velocity, N is the total number of atoms in a group, and k  1.3806505  1023 J / K is the Boltzmann constant. A periodic boundary is applied to the x direction and y direction, while a reflecting wall is applied to the z direction, since argon atoms cannot penetrate through the metal substrate and return back to the simulation box after leaving the top boundary. The argon atoms will reflect from the top boundary without any loss of energy and momentum. In the present study, all simulation cases are performed using a Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [28], which is a popular open-source software for molecular dynamics simulation developed by the Sandia National Laboratory. The main simulation process includes two stages: preparation and nonequilibrium simulations. In the preparation stage, a 5


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2.5 ns simulation in the canonical ensemble NVT (N is atom number, V is volume, T is temperature) is conducted to achieve a steady system at 90 K. In the nonequilibrium simulation stage, the heatsource temperature is raised by the Langevin thermostat, additional 2.5 ns and 5 ns nonequilibrium simulations in the microcanonical ensemble NVE (N is atom number, V is volume, E is energy) are respectively conducted under uniform surface wettability and nonuniform surface wettability. In both stages, the simulation data are output every 100 time steps, and the atom trajectories are visualized by the open visualization tool OVITO [29].

Results and discussion The configuration of the simulation cases is arranged in Table 3, and these cases are performed based on the above simulation system and method. As shown in Figure 3, case 1 is chosen as a representative to illustrate the time evolution of temperature and total energy of the whole system in the preparation stage. It is clear that the simulation system achieves equilibrium in a 2.5 ns simulation. The nonequilibrium simulation results illustrating the effects of substrate temperature and solid-liquid interfacial wettability conditions on bubble nucleation behavior of the argon film are shown in the following parts. Effects of cavity substrate with uniform strong hydrophilicity on bubble nucleation under different superheats. The evaporation and explosive boiling phenomena of an argon film placed on a hydrophilic smooth substrate have been widely studied by many scholars [30]. For a hydrophilic cavity substrate, the phase transition behavior for an argon film may be different. To explore the difference, the simulation cases 1-7 with different substrate temperatures from 130 K to 190 K are explained in this subsection. The snapshots of cases 1-7 in the x-z plane at representative time steps are illustrated in Figure 4. For cases 1 and 2, only the evaporation phenomena are observed, and increasingly numerous argon atoms break away from the liquid region and enter into gas space during the whole simulation process. For case 3 and case 4, it is obvious that the bubble nuclei turn up on the cavity region, and the corresponding incipient nucleation time is approximately 4300 ps and 3050 ps, respectively. As time increases, the bubble nuclei continue growing and finally become a gas film. For cases 5-7, many slight bubble nuclei turn up on the cavity substrate at the same time; these bubble nuclei do not have chance to grow up before coalescing into a gas film. Clearly, the explosive boiling phenomena occur in cases 5-7. It can be concluded that the cavity substrate is different from the smooth substrate, and a complete process of bubble nucleation is visualized on the cavity, which plays a key role in nucleate boiling on the nanoscale. The boiling phenomenon happens when the argon temperature is higher than incipient nucleation temperature, and the bottom argon obtains more thermal energy to achieve a higher temperature 6


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within the same time. Therefore, the temperature of argon in the vicinity of the cavity as shown in Figure 5 is calculated to illustrate why only evaporation phenomenon happens on the cavity substrate at 130 K and 140K. The temperature trends of argon in cases 1-4 are illustrated in Figure 6. For cases 1 and 2, the temperature increases rapidly during the initial stage, and fluctuates around a value which is close to the substrate temperature after 3500 ps. The temperature trends indicate that the temperature of argon on the cavity region achieves an equilibrium after 3500 ps and can’t further increase. Additionally, according to the incipient nucleation time in cases 3 and 4, corresponding incipient nucleation temperatures of 145.8 K and 150.1 K are easily obtained from Figure 6(c) and Figure 6(d). The smaller temperature value of 145.8 K is treated as the approximate incipient nucleation temperature for the argon film placed on the strong-hydrophilic substrate in the present study. It is obvious that the temperature of argon on the cavity region at 130 K and 140K is smaller than the incipient nucleation temperature. Therefore, only evaporation phenomenon occurs when the substrate temperature is below 140 K. The bubble nucleation processes in cases 3 and 4 can be quantitatively described by the bubble nucleus diameter. It is noteworthy that the cavity traverses the substrate surface along the y direction, thus the bubble nucleus in Figure 4 is an approximate cylinder rather than a sphere. But this property will not affect the comparison results between cases 3 and 4, because the length of each bubble nucleus is the same. The three-dimensional uniform grids are taken to divide the liquid region into many cubes with a size of 2 Å × 2 Å × 2 Å. All cubes are checked in sequence, and the cube is treated as a part of the bubble nucleus if there are no argon atoms within the range of 1.2  Ar  Ar . As a result, the diameter is derived from the volume of the bubble nucleus. The growth trends for bubble nuclei in cases 3 and 4 are shown in Figure 7. In both cases, the bubble nucleus linearly grows with time, and the corresponding growth rates of 179.2 Å/ns and 187.2 Å/ns are obtained by the linear fitting method. It is obvious that case 4 possesses advantages in both the incipient nucleation time and growth rate because of the higher substrate superheat. The substrate superheat determines the phase transition phenomena of evaporation in cases 1 and 2. For cases 3-7, the reason for the phase transition behaviors can be explored from the temperature profiles of the argon. Along the x direction, a layer of argon film with a height of 3 nm clinging to the cavity substrate is evenly divided into ten slices to obtain the transverse temperature profile. In addition, along the z direction, the liquid region is evenly classified into nine slices with a height of 1.5 nm to obtain the longitudinal temperature profile. These two types of temperature profiles are shown in Figures 8 and 9, where the red dotted line represents the incipient nucleation temperature of 145.8 K for a strong-hydrophobic cavity substrate. When the argon temperature exceeds the red dotted line, the argon film is going to nucleate. For case 3 and case 4, the temperature of the cavity region rather than smooth regions exceeds the incipient nucleation temperature at approximately 4300 ps and 3000 ps, respectively, corresponding to the incipient nucleation time in 7


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Figure 4(c) and Figure 4(d). Moreover, the temperature of the bottom argon is higher than the upper argon and exceeds the incipient nucleation temperature in Figure 9. The thermal energy from the bottom argon cannot be transferred to the upper argon in time, and the heat accumulation happens in the bottom region. Therefore, the liquid argon on the cavity region obtain more energy to nucleate first. As time increases, the temperature of the argon on smooth regions increases and exceeds the incipient nucleation temperature after approximately 4700 ps and 3500 ps, respectively. This indicates that the bubble nucleus keeps growing and coalesces with the neighbors into a gas film because of the application of the periodic condition in the x and y directions. The heat flux absorbed by argon in cases 3-4 is illustrated in Figure 10(a). During the initial stage, the heat flux in case 4 is significantly higher than that in case 3, thus argon in case 4 obtains more energy to nucleate earlier and grow faster. With the increasing time, the heat flux decreases quickly with the increase of argon temperature, and the decreasing trend has become weaker before the incipient boiling time due to the decrease of the temperature difference between cavity surface and argon. Therefore, although the heat transfer efficiency is further reduced after bubble nucleation, there is no significant change in the trend of heat flux. Finally, the heat flux fluctuates around 0. For cases 5-7, the higher substrate temperature causes the temperature of the whole bottom region to exceed the incipient nucleation temperature in a short time. Therefore, many small bubble nuclei turn up on the cavity region and smooth region at the same time, and then rapidly coalesce into a gas film. As a result, explosive boiling occurs. The heat flux absorbed by argon in cases 5-7 is presented in Figure 10(b). The substrate with higher temperature supports more energy for the argon during the initial stage. Therefore, the higher the substrate temperature, the faster the explosive boiling occurs. In summary, the phase transition behavior on a cavity substrate is different from that found on a smooth substrate. A bubble nucleus generates on the cavity region when the substrate temperature is set to 150 K or 160 K, and an incipient nucleation temperature of 145.8 K is obtained for the stronghydrophilic substrate in this subsection. Effects of the strong-hydrophobic cavity on bubble nucleation under different superheats. The bubble nucleus successfully generates on the strong-hydrophilic cavity substrate. However, the interaction between the argon atom and platinum atom is sufficiently strong that a layer of argon atoms is attracted to the cavity. Therefore, no original gas nucleus exists on the strong-hydrophilic cavity, as shown in Figure 4. This bubble nucleation phenomenon is different from the macro theory, which states that the bubble grows from an original bubble nucleus. The liquid argon cannot completely wet a hydrophobic surface on the nanoscale [11], thus a nanosize bubble nucleus may stably exist on the hydrophobic cavity. Therefore, the cavity wettability is replaced with strong hydrophobicity to investigate the phase transition behavior for growth of the bubble nucleus from an 8


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original nucleus on the nanoscale, and the relevant simulation cases 8-14 are explained in this subsection. The heat transfer efficiency of hydrophobic surface is lower than hydrophilic surface [30], thus a longer simulation time of 5 ns is adopted in cases 8-14 to reduce the effect of the simulation time on the result. Figure 11 shows the snapshots of cases 8-14 in the x-z plane at representative time steps. Under different substrate temperatures, the phase transition behavior in cases 8-14 is similar to that observed in cases 1-7. A small number of argon atoms evaporate into the gas space when the substrate temperature is below 140 K. A clear process of bubble nucleation is visualized on the substrate with a temperature of 150 K and 160 K. In addition, a gas film rapidly forms on the substrate whose temperature is higher than 170 K. It is noteworthy that an original small bubble nucleus stably remains in the cavity no matter whether the bubble nucleus grows up or not. This phenomenon is entirely different from that on the strong-hydrophilic cavity substrate. The reason for this can be understood from Eq. (8) and Figure 12, which illustrates the relationship between L-J potential and atomic distance. If the distance between the platinum atom and argon atom is shorter than 21/6  -1/6 Pt  Ar , the argon atom will suffer a repulsive force from the platinum atom. The parameter  in Eq. (8) is set to be 0.1 and 1 for the strong-hydrophobic cavity and strong-hydrophilic cavity, respectively. Therefore, the length parameter of L-J potential between the platinum atom and argon atom for the strong-hydrophobic cavity is 1.47 times than that for the strong-hydrophilic cavity. The argon atom suffers a large repulsive force in the strong-hydrophobic cavity, and an original small bubble nucleus is formed inside the cavity. For case 8 and case 9, the argon film continues to evaporate during the entire simulation process. The corresponding temperature trends of argon on the cavity region are shown in Figure 13(a) and Figure 13(b). In both cases, the temperature achieves an equilibrium after approximately 5600 ps, thus the original bubble nucleus cannot grow up any further. For case 10 and case 11, the original bubble nuclei begin to grow up from the cavity after approximately 3700 ps and 3250 ps, and the corresponding incipient boiling temperatures of 133.7 K and 133.2 K are obtained from Figure 13(c) and Figure 13(d). The lower one is treated as the approximate incipient boiling temperature of the argon film placed on the strong-hydrophobic cavity in this paper. During the bubble growth process, the number of argon atoms becomes increasingly less in the cavity region. As a result, the temperature fluctuates acutely in Figure 13(c) and Figure 13(d) after the bubble nucleus growing up, because the temperature is a statistical result of the atomic kinetic energy. For cases 12-14, some bubble nuclei turn up on the smooth region, while in the meantime the original bubble nucleus on the cavity is growing up. These bubble nuclei coalesce into a gas film in a short time, leading to the explosive boiling. Notably, the original bubble nucleus cannot further grow up, although the temperature of the 9


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argon on the cavity region is higher than 133.2 K in case 9. The reason for this may be that the energy of the surrounding liquid argon is not enough to boil, and the phase transition is limited. Figure 14 shows the transverse temperature profiles of the argon film clinging to the cavity substrate in cases 10-14, where the red dotted line and black dotted line represent the incipient boiling temperature of the argon placed on strong-hydrophilic cavity and strong-hydrophobic cavity, respectively. For cases 10 and 11, the temperatures of the argon on the strong-hydrophobic cavity region are higher than the black dotted line while that on the strong-hydrophilic smooth region are lower than the red dotted line at approximately 3700 ps and 3200 ps respectively. The temperature of argon on the strong-hydrophobic cavity region is higher than the incipient temperature, and the original bubble nucleus grows up from the cavity. Then, the temperature of the argon on the smooth regions increases with time and exceeds the red dotted line at approximately 4600 ps and 3600 ps, respectively. As a result, a gas film forms on the cavity substrate. For cases 12-14, the temperature of the argon on the cavity region and smooth region respectively exceeds the black dotted line and the red dotted line almost at the same time. Therefore, many small bubble nuclei turn up on the whole cavity substrate at the same time and quickly coalesce into a gas film. In the vicinity of the uniform strong-hydrophilic substrate, the temperature of the argon on the central cavity region is higher than that on the smooth region in cases 1-7, as shown in Figure 8. However, the trend of the transverse temperature profile is opposite in cases 8-14, as shown in Figure 14. To further compare the difference, the liquid regions in cases 3 and 10 are uniformly divided into 100 subregions with a size of 15 Å (x) × 77 Å (y) × 13 Å (z), and the temperature contours are calculated by respectively summing the atom kinetic energy of each subregion. It is noteworthy that the number of argon atoms in the strong-hydrophobic cavity is so few that the argon atoms are counted to the nearest subregion, and the same treatment is applied for the strong-hydrophilic cavity to ensure a fair comparison between case 3 and case 10. Moreover, the snapshots of temperature contour are presented before 4000 ps to avoid the effect of bubble nucleation on temperature calculation. After obtaining the temperature of each subregion, a cubic interpolation method [31] is used to obtain more temperature data and smooth out the temperature contours. The argon temperature contours of case 3 and case 10 in the x-z plane at representative time steps are illustrated in Figures 15 and 16, respectively. In both cases, it can be observed that the temperature contours are uniform with a mean value of 90 K at the initial time step. Then, the bottom temperature increases rapidly, and the thermal energy of the bottom argon is transferred to the upper argon with time. It is remarkable that the evolution trends of temperature in the bottom region of liquid argon are totally different in these two cases. For case 3, the temperature of argon on the central region is higher than that on the smooth region because of larger heat transfer area in the cavity region. However, the temperature trend is opposite in case 10. The temperature of argon on the smooth region increases with time, but that on the central region is maintained at approximately 130 K. For the 10


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strong-hydrophobic cavity, the original bubble nucleus introduces a thermal resistance between the cavity surface and argon. Moreover, the heat transfer efficiency of the substrate in case 10 is obviously lower than case 3, as shown in Figure 17, and the difference between case 3 and case 10 is caused by the different wettability of the cavity region. Consequently, the argon on the strong-hydrophobic cavity region obtains less energy than that on the smooth region, thus the temperature contour in case 10 is different from that in case 3. In summary, a small bubble nucleus stably remains in the strong-hydrophobic cavity, and this phenomenon is different from that found in the strong-hydrophilic cavity. Moreover, the original bubble nucleus grows up from the cavity when the argon temperature is higher than 133.2 K, which is the approximate incipient boiling temperature of a liquid film placed on a strong-hydrophobic cavity substrate. Effects of hydrophobicity on the incipient boiling temperature of the argon film. The bubble nuclei successfully form and grow up on both strong-hydrophilic and strong-hydrophobic cavities, and the incipient boiling temperature of latter is lower. This rule is in agreement with macroscopic experiment, which illustrate that liquid is easy to boil on a more hydrophobic substrate [4]. Therefore, the strong-hydrophobic cavity is respectively replaced with weak-hydrophobic and moderatehydrophobic cavities for further research about the relationship between hydrophobicity and the incipient boiling temperature, and the corresponding simulation cases 15 and 16 are explained in this subsection. Snapshots of case 15 and case 16 in the x-z plane at representative time steps are shown in Figure 18. The original small bubble nuclei begin to grow up when the simulation time is longer than approximately 3700 ps and 3900 ps, corresponding to the incipient boiling temperatures of 136.9 K and 135.0 K in Figure 19(a) and Figure 19(b), respectively. From the bubble nucleation behavior in cases 3, 10, 15 and 16, a rule can be noticed that the incipient boiling temperature of the argon film increases with weakening of the cavity hydrophobicity. We believe that the incipient boiling temperature is affected by the interatomic interaction between the argon atom and platinum atom. For the strong-hydrophilic cavity, the argon atoms are attracted to the cavity substrate, and they need more energy to break the restraint of this strong interaction. However, the argon atoms suffer a large repulsive force in the strong-hydrophilic cavity; thus they are easy to get free and nucleate. In addition, the repulsive force is reduced with the weakening of the hydrophobicity, and higher temperature is required for the growth of original bubble nucleus. In summary, the incipient boiling temperature of the argon film is related to the cavity wettability condition, and increases with weakening of the cavity hydrophobicity.

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In this paper, the molecular dynamics method is used for the study of nucleate boiling on cavity substrate, and several different phase transition behaviors are observed under different substrate superheat and cavity wettability conditions. The conclusions are summarized as follows: (1) The bubble nucleus successfully generates on the strong-hydrophilic cavity substrate. Compared to the smooth regions, the cavity provides a larger heat transfer area, thus the argon on the cavity region obtains more energy to nucleate first. However, the position of bubble nucleation is not located on the substrate surface that is covered by argon atoms because of the strong interaction between platinum and argon atoms. In addition, an approximate incipient boiling temperature of 145.8 K for the argon film is obtained. When the substrate temperature is below the incipient boiling temperature, only the evaporation phenomenon occurs. When the substrate temperature is raised up to 150 K or 160 K, a complete bubble nucleation process is observed. If the substrate temperature is further increased to 170K, many bubble nuclei form and coalesce into a gas film in a short time. (2) The bubble nucleus successfully grows up from an original small one inside the stronghydrophobic cavity. The equilibrium distance between the platinum atom and argon atom is long enough that the argon atom suffers a repulsive force on the strong-hydrophobic cavity. Therefore, an original bubble nucleus stably exists on the cavity before the incipient boiling time. When the argon temperature in the cavity region exceeds 133.2 K, which is the approximate incipient boiling temperature of the argon film placed on a strong-hydrophilic substrate, the original small bubble nucleus begins to grow up from the cavity. This bubble nucleation behavior is in agreement with macro theory, which states that the cavity provides an original nucleus for the formation of a bubble. (3) The incipient boiling temperature of an argon film is related to cavity wettability. The incipient boiling temperature of the argon film on the hydrophobic cavity is lower than that on the hydrophilic cavity, and increases with weakening of the cavity hydrophobicity. This law is in accordance with macro experiments, which show that liquid is easy to boil on a more hydrophobic substrate.

Acknowledgment This work is supported by the National Natural Science Foundation of China (No.51636006, No.51606012, No.51706021), the Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges under Beijing Municipality (IDHT20170507), and the Program of Great Wall Scholar (No. CIT&TCD20180313).

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[2] Carey, V. P. Thermodynamic analysis of the intrinsic stability of superheated liquid in a micromechanical actuator with elastic walls. Nanoscale and Microscale Thermophysical Engineering, 2000, 4, 109-123. [3] Betz, A. R.; Jenkins, J.; Kim, C. C.; Attinger, D. Boiling heat transfer on superhydrophilic, superhydrophobic, and superbiphilic surfaces. International Journal of Heat and Mass Transfer, 2013, 57, 733-741. [4] Bourdon, B.; Bertrand, E.; Di, M. P.; Marengo, M.; Rioboo, R.; Coninck, J. D. Wettability influence on the onset temperature of pool boiling: experimental evidence onto ultra-smooth surfaces. Advances in Colloid & Interface Science, 2015, 221, 34. [5] Bourdon, B.; Marco, P. D.; Rioboo, R.; Marengo, M.; Coninck, J. D. Enhancing the onset of pool boiling by wettability modification on nanometrically smooth surfaces. International Communications in Heat & Mass Transfer, 2013, 45, 11-15. [6] Kong, X.; Zhang, Y. H.; Wei, J. J. Experimental study of pool boiling heat transfer on novel bistructured surfaces based on micro-pin-finned structure. Experimental Thermal and Fluid Science, 2018, 91, 9-19 [7] Das, S.; Saha, B.; Bhaumik, S. Experimental study of nucleate pool boiling heat transfer of water by surface functionalization with SiO2 nanostructure. Experimental Thermal and Fluid Science, 2017, 81, 454-465. [8] Jo, H.; Ahn, H. S.; Kang, S.; Kim, M. H. A study of nucleate boiling heat transfer on hydrophilic, hydrophobic and heterogeneous wetting surfaces. International Journal of Heat and Mass Transfer, 2011, 54, 5643-5652. [9] Rohsenow, W. M.; Hartnett, J. P.; Ganic, E. N. Handbook of Heat Transfer Fundamentals (Second Edition). McGraw-Hill, 1985, 242. [10]Maruyama, S. Molecular dynamics methods in microscale heat transfer, Adv. Numer. Heat Transfer 2002, 47, 189-226. [11]Nagayama, G.; Tsuruta, T.; Cheng, P. Molecular dynamics simulation on bubble formation in a nanochannel. International Journal of Heat & Mass Transfer, 2006, 49, 4437-4443. [12]Maruyama, S.; Kimura, T. A molecular dynamics simulation of bubble nucleation on solid surface. Nihon Kikai Gakkai Ronbunshu B Hen/Transactions of the Japan Society of Mechanical Engineers Part B, 1999, 65, 34613467. [13]Yamamoto, T.; Matsumoto, M. Initial stage of nucleate boiling: molecular dynamics investigation. Journal of Thermal Science & Technology, 2012, 7, 334-349. [14]Hens, A.; Agarwal, R.; Biswas, G. Nanoscale study of boiling and evaporation in a liquid Ar film on a Pt heater using molecular dynamics simulation. International Journal of Heat & Mass Transfer, 2014, 71, 303-312. [15]Inaoka, H.; Ito, N. Numerical simulation of pool boiling of a Lennard-Jones liquid. Physica A Statistical Mechanics & Its Applications, 2013, 392, 3863-3868. [16]Chen, M.; Chen, Y.; Yang, J.; Gao, Y.; Li, D. Molecular dynamics studies of homogeneous and heterogeneous thermal bubble nucleation. Journal of Heat Transfer, 2014, 136, 657-669. [17]She, X.; Shed, T. A.; Lindeman, B.; Yin, Y.; Zhang, X. Bubble formation on solid surface with a cavity based on molecular dynamics simulation. International Journal of Heat & Mass Transfer, 2016, 95, 278-287. [18]Liu, Y.; Zhang, X. Molecular dynamics simulation of nanobubble nucleation on rough surfaces. Journal of 13


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Figure Captions Figure 1 Initial configuration of the simulation system Figure 2 Configurations for the cavity substrates Figure 3 Time evolution for the system temperature and energy in the preparation stage Figure 4 Snapshots of phase transition processes on strong-hydrophilic cavity substrates at different temperatures Figure 5 Calculation domain for argon temperature in the cavity region Figure 6 Temperature trends for argon in the cavity region in cases 1-4 Figure 7 Growth trends for bubble nuclei in case 3 and case 4 Figure 8 Transverse temperature profiles for argon near the cavity substrate in cases 3-7 Figure 9 Longitudinal temperature profiles for argon along the z direction in cases Figure 10 Heat flux trends for a strong-hydrophilic cavity substrate with different temperatures Figure 11 Snapshots of phase transition processes on the strong-hydrophobic cavities at different temperatures Figure 12 Profile of the Lennard-Jones potential between the platinum atom and argon atom Figure 13 Temperature trends for argon in the cavity region in cases 8-11 Figure 14 Transverse temperature profiles for argon near the cavity substrate in cases 10-14 Figure 15 Temperature contours for the phase transition processes in case 3 Figure 16 Temperature contours for the phase transition processes in case 10 Figure 17 Heat flux trends in cases 3 and 10 Figure 18 Snapshots of the phase transition processes in case 15 and case 16 Figure 19 Temperature trends for argon in the cavity region in cases 15 and 16

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Figure 1 Initial configuration of the simulation system

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4000 ps

4100 ps

4200 ps

4300 ps

4400 ps

4500 ps

(b) moderate-hydrophobic cavity Figure 18 Snapshots of the phase transition processes in case 15 and case 16

36


Page 37 of 41


200

180

Temperature (K)


·

120 100


200

180

Temperature (K)

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


·

120

3700 ps 2800

3500

136.9 K 4200

3900 ps

100 4900

5600

6300

7000

2800


3500

135.0 K 4200

4900

5600

6300

7000


(a) weak-hydrophobic cavity (b) moderate-hydrophobic cavity Figure 19 Temperature trends for argon in the cavity region in cases 15 and 16

37


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 38 of 41

Table Captions Table 1 Lennard-Jones parameters for Ar-Ar, Pt-Pt Table 2 Different surface wettability based on

 and



Table 3 Configuration of substrates with different wettability conditions

38


Page 39 of 41 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

Table 1 Lennard-Jones parameters for Ar-Ar, Pt-Pt [21] Interaction type

 /eV

 /nm

Ar-Ar Pt-Pt

0.0104 0.52

0.34 0.2475

39


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 40 of 41

Table 2 Different surface wettability based on Surface wettability





Strong hydrophilicity Weak hydrophobicity Moderate hydrophobicity Strong hydrophobicity

1 0.14 0.14 0.14

1 0.5 0.3 0.1

40


 and

 [11] Contact angles (/ 。) 0 95 150 180

Page 41 of 41 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

Table 3 Configuration of substrates with different wettability conditions Cases

Substrate temperature

Substrate feature description

1

130 K

2

140 K

3

150 K

4

160 K

5

170 K

6

180 K

7

190 K

8

130 K

9

140 K

10

150 K

Cavity region is strong-

11

160 K

hydrophobic and the smooth

12

170 K

regions are strong-hydrophilic

13

180 K

14

190 K

The whole substrate is stronghydrophilic

Cavity region is weak15

150 K

hydrophobic and the smooth regions are strong-hydrophilic Cavity region is moderate-

16

150 K

hydrophobic and the smooth regions are strong-hydrophilic

41


Nanoscale Study of Bubble Nucleation on a Cavity Substrate Using

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