Effect of Nanostructure on Rapid Boiling of Water on a Hot Copper Plate: a Molecular Dynamics Study

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1 Effect of Nanostructure on Rapid Boiling of Water on a Hot Copper Plate: a Molecular Dynamics Study Ting Fu 1,2,3, Yijin Mao 3, Yong Tang 1 *,Yuwen Zhang 3 and Wei Yuan 1 1 Key Laboratory of Surface Functional Structure Manufacturing of Guangdong High Education Institutes, School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou , China 2 School of Machinery and Automation, Wuhan University of Science and Technology, Wuhan , China 3 Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65201, USA Abstract Molecular dynamic simulations (MDS) are performed to study the effects of nanostructure on rapid boiling of water that is suddenly heated by a hot copper plate. The results show that the nanostructure has significant effects on energy transfer from solid copper plate to liquid water and phase change process from liquid water to vapor. The liquid water on the solid surface rapidly boil after contacting with an extremely hot copper plate and consequently a cluster of liquid water moves upward during phase change. The temperature of the water film when it separates from solid surface and its final temperature when the system is at equilibrium strongly depend on the size of the nanostructure. These temperatures increase with increasing size of nanostructure. Furthermore, a non-vaporized molecular layer is formed on the surface of the copper plate even continuous heat flux is passing into water domain through the plate. Keywords: Rapid boiling; Nanostructure; Molecular dynamics Introduction The trends of miniaturization of devices demand more attentions on small spatial scale phenomenon, such as the temperature jump at a solid-fluid interface and the cohesive intermolecular forces between two different surfaces [1]. It is difficult to explain these phenomena using classical macroscopic theory, due to the breakdown of continuum assumption which is essential for continuum mechanics. Molecular dynamics simulation, on the other hand, which is able to describe the physical process from atomic level, is being an effective method to describe the liquid behavior near solid wall in the nanoscale. Boiling, which is considered as the process of phase change from liquid to vapor when temperature reach to its saturation temperature under certain pressure, has a wide range of application in industry [2-4]. To investigate the micro-scale mechanism of phase change, molecular dynamics is a good choice to study the behaviors of the phase change on metal solid surface, such as copper. Rapid boiling [5] is a special liquid-vapor phase change process that the liquid is superheated to a temperature that is much higher than the normal saturation temperature but lower than its thermodynamic critical temperature. In this process, the homogeneous vapor bubble nucleation takes place at an extremely high rate, which leads to the liquid near-surface region of the fluid being rejected rapidly [6]. To better understand the mechanism that explains the phenomena occurring at the locations close to solid wall is an attractive topic. Up to date, a literature survey shows that many related experimental works and numerical investigations are reported [7, 8]. Takamizawa et al. [9] heated water by a laser pulse and measured the average temperature during the rapid boiling, which revealed the macro and molecular level information about the vaporization. Kudryashov et al. [10] experimentally studied the rapid boiling of a thin water film on a silicon substrate using a * Corresponding author. ytang@scut.edu.cn 1

2 laser-heated method. They showed that using nanostructure on flat surface resulted in significant enhancement in heat transfer. However, experimental work to study physical phenomena during rapid boiling of liquid water on nanostructure surfaces is still one of the challenging subjects in nanoscale heat transfer [11]. Computer simulation is one of alternative methods to study the phase change during rapid boiling in nanoscale, which is difficult to observe experimentally due to the limits on length or time scales. Matsumoto et al. [12] studied the molecular diffusion on the contact line for the solid-liquid-vapor three phases. The results showed that there were a large number of molecules diffusing on the interfaces between solid and liquid, liquid, and vapor. Yi et al. [13] simulated the vaporization behavior of thin liquid argon on a platinum surface for two different heated temperatures using molecular dynamics. Shalabh et al. [14] focused on studying the phase change of liquid argon film on a flat solid surface. Seyf and Zhang [15] simulated the boiling of argon films over surfaces with and without spherical nanostructures using the MD method. Their results showed the liquid argon rapidly vaporized from the surface and formed several tiny liquid clusters when surface nanostructure is present, once the argon layers nearest the solid surface overheated. The geometry and size of nanostructures are two main factors affecting the behaviors of rapid boiling [11]. Experimental works may be suffering from its limitation in handling such small scale problem with current technologies. In other words, it is difficult to manufacture an atomic level structure by actual engineering technology. At the same time, most of the simulation studies about the boiling behavior are focused on heterogeneous phase transition of liquid on a flat solid surface [5, 16]. Few researchers paid attentions on the effect of square nanostructures on phase transition. Even among all similar works, most of the chosen liquid is argon [17-19] due to the fact that the intermolecular potential for argon is computationally easy to handle. Nevertheless the water is one of the most widely used working fluids in engineering system. A thorough understanding on the dynamic and thermal mechanisms about rapid boiling of liquid water on rough surface is definitely helpful for the trends of miniaturization of devices. In this paper, effect of nanostructure on rapid boiling of water on a hot copper surface will be studied via molecular dynamics simulation. Four equal sized nanoscale square structures are designed on a flat plate surface. The work reported in the present study aims at developing a methodology for investigating the thermal and dynamic mechanism of a thin water film on a flat surface due to the appearance of square nanostructures on the surface. Simulation method A simulation box with size of 7.22 nm(x) 7.22 nm(y) nm (z) is created. The height of simulation box is triple larger than the thickness of liquid, such that the liquid in the computational domain is fully developed. The solid copper atoms that serve as the wall material is placed at the bottom while liquid water is lying on it. The liquid molecules are modeled by a four-site water model (TIP4P) [20] that has a relatively better performance in describing system s dynamic and thermal property. The liquid water is built with face-centered cubic unit (FCC) that has a lattice constant of 4.9 Å corresponding to its density at temperature of 298 K under standard atmosphere pressure. The copper plate is also created with FCC type unit that has a lattice constant of 3.61 Å subject to its density of kg/m 3. In order to apply a more physically-sound thermostat, the entire copper plate is modeled with six layers. The two layers at bottom are fixed in order to prevent atoms from penetration. The middle two layers are considered to be phantom atoms [13] as the heat source. The top two layers are set as real copper atoms through which heat is transferred to the liquid water. The flat surface (surface type of I) is formed by this copper model. The nanostructures are formed by four equal-sized copper nano-squares on the top 2

3 of the flat surface. And the lengths are designed as Å (surface type of II), Å (surface type of III) and Å (surface type of IV), respectively, as shown in Fig. 1. The sizes of the nanostructures are equal to or less than the thickness of the liquid film. The total number of atoms is ranging from 13,264 to 18,912 due to different surface structure of the copper plate. Two different empirical potentials are used in this simulation. One is the well-known Lennard-Jones (L-J) potential. The other one is Lennard-Jones (L-J) with long-range Coulombic interaction which is able to provide acceptably accurate description in the interatomic interaction between water molecules. For the water molecules, the interatomic interaction between hydrogen atoms, oxygen atoms, hydrogen and oxygen is given by [5] a b k a b Cqa q i b j aib j 12 aib j 6 Uab 4 a [( ) ( ) ] ib (1) j r r r i j a b i j a b a b i j i j i j where kc is the electrostatic constant, raibj is the distance between two atoms, a and b denote two different atom types, and qi is the electric charge of site i. Subscripts i and j represent atoms of oxygen or hydrogen in one TIP4P water molecule. The long-range effect due to electrostatic potential is resolved by PPPM (particle-particle particle-mesh) approach [21] with an accuracy of In this simulation, only the pair potential between oxygen atoms is considered with a cutoff radius of 12 Å. And the SHAKE [22] algorithm is used to hold the rigidity of the water molecules. For the interaction between copper-oxygen atoms, the interatomic potential is given by the well-known Lenard-Jones potential: 12 6 U 4 [( ) ( ) ] (2) r r where ε is the depth of potential well, σ is the finite distance at which the interatomic potential is zero. It should be pointed out that the interactions between copper-hydrogen and hydrogen-hydrogen atoms are not considered [20]. And the interaction between copper-copper atoms is also not considered. Instead, artificial Cu-Cu harmonic bonds are created for the plate and nanostructures in order to introduce Cu-Cu interaction. It is imperative to use a reasonable spring constant k which is closely related to Young s modules. It could be estimated with formula below k Ed (3) where E is Young s Modules of solid copper, and d is the lattice constant of copper. The simulation is carried out within the framework of the open-source MD simulation code LAMMPS [23] with certain extension and the data visualization is done using VMD [24]. Periodic boundary conditions are applied to x- and y- directions while mirror boundary condition is used for the top boundary. In other words, a reflecting wall is placed at the top of the simulation box, which prevents energy transfer through the interaction between molecules and the wall. This arrangement is consistent with the setup in actual experiment processes [25-27]. The whole simulation consists of three steps. Firstly, the entire water domain is equilibrated to be 298K under the Berendsen thermostat [28]. Secondly, the temperature of copper plate is gradually heated up to 1000 K with phantom atom thermostat method by using NVE time integration with sufficient time steps. Finally, the liquid water at 298 K is suddenly placed on the hot plate which was equilibrated to the temperature of 1000 K in the second step. It should be pointed out that in order to ensure the possibility of forming a water bubble while it is still below the melting point, 1000K is chosen as the temperature for the copper plate. Results and discussions Figure 2 shows temperature variation of copper plate and water during the simulations for four cases that include smooth (I) or square nanostructure (II, III and IV) type copper 3

4 plate. It can be seen that the temperatures suddenly drop from 1000 K to around 750 K for all the cases when the cold water film touches the hot copper plate. In the later period, the temperatures of hot copper recover to 1000 K because of the continuously added heat flux from the thermal reservoir. Meanwhile, the temperatures of water sharply increase from 298 K to around 625K, 675K, 700K and 775K, respectively. It is also found that the temperatures of water finally stabilize to certain values in the later period. For the liquid water, the average temperature dramatically rises in the beginning of rapid boiling, and it starts to decrease once the liquid film detach from the solid surface. The vapor molecules near the solid wall prevent heat flux flowing from hot wall to the liquid film above the vapor due to its lower thermal conductivity. During the following period, it is found that the temperatures are stabilized to certain values up to the end of the simulation. It is also clearly shown that the overall separation temperature, which is defined as the temperature associated with separation of liquid from wall [11] by the time that the liquid water adjacent to solid wall reaches the vaporized temperature, increases with increasing nanostructure size. Due to the presence of nanostructures, the area of solid-liquid interface increases and therefore the water molecules above that copper plate is able to absorb energy from the nanostructures more efficiently. As a consequence, more energy can be transferred and utilized to vaporize water molecules nearby the wall. It can also be found that final temperature of water from the case with nanostructures is apparently higher than the one based on the flat surface. In order to vividly show the dynamic behavior of water film during rapid boiling, snapshots on water molecules spatial distribution at different time for surface type of I-IV are given in Figs. 3 to 6. As shown in Fig. 3, the liquid film detaches from the solid surface at around 60 ps as a large cluster above smooth surface (I). Owing to the high wall temperature, the liquid adjacent to the solid wall reach to the saturation temperature and start to vaporize, while the water above are still in the liquid phase due to lower temperature. Gradually, the entire water domain can be categorized to be three zones: the lower vapor zone near the hot plate, liquid zone above the lower vapor zone, and top vapor zone. Therefore, the high pressure from lower vapor zone lifts the liquid zone up and then the liquid zone leave from the solid wall [11]. With the heat flux continuously flowing into the water molecules, the lower vapor zone keeps expanding up to 110 ps when the water film first collides with the top wall of the simulation box. Consequently, the water liquid film is forced to move backward. During the following period, water film moves upward again due to the large pressure in the lower vapor zone. For the surface type of II, the movement trend of water liquid layer is similar as the case with the smooth surface, as shown in Fig. 4, except that the liquid detaches from solid surface starts at around 50 ps and the first hitting against the top occur at time of 100 ps. Similarly, for the surface type of III, it is observed that the water liquid film also has a similar movement trend and it begins to detach from solid surface at around 40 ps and hit the top wall at round 90 ps, as shown in Fig. 5. Figure 6 indicates that the water film as a tiny cluster first hits against the top wall at time of 50 ps while the others are 110 ps, 100 ps and 90 ps, respectively. Hence, the liquid molecules on surface type IV moves faster than those from other solid surfaces. It can also be concluded that the translational velocities of water molecules increase along with the size of nanostructures in the first 110 ps. With the physically-sound thermostat, the kinetic energy for each copper atom, on average, is the same for all surfaces. According to the average coordination numbers which are defined as the numbers of oxygen atoms that are within a cutoff radius of 12 Å around a copper atom in the plate, as shown in Table 1, the average energy absorbed by each water molecule decreases with the increasing coordination numbers. That is to say, the translational velocity of single water molecule is obviously larger on the surface type of IV than that 4

5 from other surface types. Meanwhile, Figs. 3-6 clearly show that the size of the cluster of liquid on surface type of I is obviously larger than that from other surface types (II-IV). In order to have a closer look at the density variation in the z-direction, the computational domain along the z-direction is divided into 59 bins and the number of molecules in each slab is calculated to obtain the average density of each bin. The density profiles for all the cases at different times are shown in Figs. 7 to 10. It can be clearly seen that for surface type I there is a large liquid cluster in the computational domain that moves away from the solid surface, as shown in Fig. 7 (a). It is worth mentioning that the peak in density profile indicates the locations of the moving liquid water. Meanwhile, the maximum liquid density keeps decreasing during the moving process of liquid water until the liquid cluster hits the top wall. However, the increase in the maximum density which appears at around 110 ps can be explained by the fact the water molecules compression due to their inertia when they hit against the top wall. The figures also give the z-component of coordinate which is representing the location of moving liquid water at different time. For example, at t = 60 ps, the liquid water is located at somewhere between 50 and 75 nm corresponding to the peak value of approximately 0.65 g/cm 3. During the later period, the peak value of density almost does not change and the height of the bulk liquid water nearly keeps constant, as shown in Fig. 7(b); this means that phase change at the liquid-vapor interface is balanced during this period. For the surface types II and III, the curves show the similar trend as flat surface (I), as shown in Fig. 8 and Fig. 9. But at t =60 ps, the location are between 75 and 100 nm, around 100 nm respectively, the corresponding peak value is approximately g/cm 3 and 0.4 g/cm 3. And as shown in Fig. 10, there is no obvious peak in the curves for surface type of IV, which indicates that partial liquid water molecules as tiny cluster move upward and the rest of them moves as an individual molecule due to larger contact area between copper plate and liquid water [15]. And the small cluster peak approximately appears at the location of 225 nm at 50 ps, when the first hit of water molecules against the top wall occur for the surface type of IV. These results indicate that the size of moving liquid water decrease and the moving liquid water travels faster on surface type of IV than that on surfaces type of I, II and III. And the peak value of density decreases with the increasing of nanostructure size. Another important result is that a non-vaporized water layer always exists at somewhere near the solid wall during the whole simulation period for all the surface types, as shown in Figs In this zone, the water molecules distribute on the surface of the copper plate and show a hot gas-like structure which is also observed during vaporization process [29]. The water molecules density in this zone decrease during the period of rapid boiling and gradually stabilize at around 0.15 g/cm 3 and 0.20 g/cm 3 respectively for flat surface and nanostructure surfaces. Conclusions Rapid boiling of water over nanostructure on a hot flat copper plate is investigated by molecular dynamics simulation. For all cases studied, the liquid water molecules above the solid surface go into high temperature which resulting in a rapid phase change for the molecules close to the copper plate. It is found that a cluster of liquid water move up and down repeatedly between the plate surface and top wall of simulation box for all cases. The size of water cluster during phase transition is related to the size of nanostructures. It is found that larger liquid clusters appear in the water domain for all the cases except the one with largest nanostructure (IV). It is also found that the moving velocity of water cluster increases with the increasing of the size of nanostructure. In addition, both the separation temperature, at which water molecules are separating from solid surface and the final stable temperature strongly depend on the size of nanostructure. Furthermore, a non-vaporization molecular layer with constant density forms on the surface of the copper plate even 5

6 continuous heat flux flow through the plate to water zones for all the cases. Moreover, the number of non-vaporization molecules on nanostructure surfaces is larger than that from the smooth surface. Acknowledge The research was financially supported under the grant of the National Nature Science Foundation of China under grant number , the National Nature Science Foundation of China under grant number and the US National Science Foundation under grant number CBET The authors also would like to acknowledge the Join-training PhD Program (No ) sponsored by the China Scholarship Council and hosted by the University of Missouri. Reference [1] Gad-el-Hak, M., 1999, "The Fluid Mechanics of Microdevices The Freeman Scholar Lecture," Journal of Fluids Engineering, 121(1), pp [2] You, S., Simon, T. W., and Bar-Cohen, A., 1992, "A technique for enhancing boiling heat transfer with application to cooling of electronic equipment," Components, Hybrids, and Manufacturing Technology, IEEE Transactions on, 15(5), pp [3] Lin, C., Kim, Y., Niedrach, L., and Ramp, K., 1996, "Electrochemical corrosion potential models for boiling-water reactor applications," Corrosion, 52(8), pp [4] Kandlikar, S. G., 2002, "Fundamental issues related to flow boiling in minichannels and microchannels," Experimental Thermal and Fluid Science, 26(2), pp [5] Mao, Y., and Zhang, Y., 2014, "Molecular dynamics simulation on rapid boiling of water on a hot copper plate," Applied Thermal Engineering, 62(2), pp [6] Faghri, A., and Zhang, Y., 2006, Transport phenomena in multiphase systems, Academic Press. [7] Xu, X., 2002, "Phase explosion and its time lag in nanosecond laser ablation," Applied Surface Science, 197, pp [8] Novak, B. R., Maginn, E. J., and McCready, M. J., 2008, "An atomistic simulation study of the role of asperities and indentations on heterogeneous bubble nucleation," Journal of Heat Transfer, 130(4), p [9] Takamizawa, A., Kajimoto, S., Hobley, J., Hatanaka, K., Ohta, K., and Fukumura, H., 2003, "Explosive boiling of water after pulsed IR laser heating," Physical Chemistry Chemical Physics, 5(5), pp [10] Kudryashov, S. I., and Allen, S. D., 2006, "Submicrosecond dynamics of water explosive boiling and lift-off from laser-heated silicon surfaces," Journal of Applied Physics, 100(10), p [11] Seyf, H. R., and Zhang, Y., 2013 (a), "Effect of nanotextured array of conical features on explosive boiling over a flat substrate: A nonequilibrium molecular dynamics study," International Journal of Heat and Mass Transfer, 66, pp [12] Matsumoto, S. M. T. K. S., and Kimura, Y. Y. T., 1998, "Liquid droplet in contact with a solid surface," Microscale Thermophysical Engineering, 2(1), pp [13] Yi, P., Poulikakos, D., Walther, J., and Yadigaroglu, G., 2002, "Molecular dynamics simulation of vaporization of an ultra-thin liquid argon layer on a surface," International Journal of Heat and Mass Transfer, 45(10), pp [14] Maroo, S. C., and Chung, J., 2008, "Molecular dynamic simulation of platinum heater and associated nano-scale liquid argon film evaporation and colloidal adsorption characteristics," Journal of Colloid and Interface Science, 328(1), pp [15] Seyf, H. R., and Zhang, Y., 2013 (b), "Molecular Dynamics Simulation of Normal and Explosive Boiling on Nanostructured Surface," Journal of Heat Transfer, 135(12), p [16] Maruyama, S., Kimura, T., and Yamaguchi, Y., 1997, "A molecular dynamics 6

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8 Table captions: Table 1 Average coordination number for water molecules around the copper plate 8

9 Figure captions Figure. 1 Structure of the copper plate, three kinds of function atoms are formed within a distance of 3.61Å Figure. 2 Temperature variation of water and hot copper plate for different scenarios Figure. 3 Trajectories of water molecules for the case with surface I Figure. 4 Trajectories of water molecules for the case with surface II Figure. 5 Trajectories of water molecules for the case with surface III Figure. 6 Trajectories of water molecules for the case with surface IV Figure. 7 Z-direction density distribution at various times for the case with surface I Figure. 8 Z-direction density distribution at various times for the case with surface II Figure. 9 Z-direction density distribution at various times for the case with surface III Figure. 10 Z-direction density distribution at various times for the case with surface IV 9

10 Table 1 Surfaces I (smooth) II (a=14.44 Å) III(a=18.05 Å) IV (d=21.66 Å) Coordination numbers

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