of Missouri, Columbia, Missouri, USA c Key Laboratory of Surface Functional Structure Manufacturing of

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1 This article was downloaded by: [University of Missouri-Columbia] On: 31 August 2015, At: 08:20 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: 5 Howick Place, London, SW1P 1WG Click for updates Nanoscale and Microscale Thermophysical Engineering Publication details, including instructions for authors and subscription information: Molecular Dynamics Simulation on Rapid Boiling of Thin Water Films on Cone- Shaped Nanostructure Surfaces Ting Fu a, Yijin Mao b, Yong Tang c, Yuwen Zhang b & Wei Yuan c a 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, and Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri, USA b Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri, USA c 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 Published online: 26 Feb To cite this article: Ting Fu, Yijin Mao, Yong Tang, Yuwen Zhang & Wei Yuan (2015) Molecular Dynamics Simulation on Rapid Boiling of Thin Water Films on Cone-Shaped Nanostructure Surfaces, Nanoscale and Microscale Thermophysical Engineering, 19:1, 17-30, DOI: / To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.

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3 Nanoscale and Microscale Thermophysical Engineering, 19: 17 30, 2015 Copyright Taylor & Francis Group, LLC ISSN: print / online DOI: / MOLECULAR DYNAMICS SIMULATION ON RAPID BOILING OF THIN WATER FILMS ON CONE-SHAPED NANOSTRUCTURE SURFACES Ting Fu 1, Yijin Mao 2, Yong Tang 3, Yuwen Zhang 2, and Wei Yuan 3 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, and Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri, USA 2 Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri, USA 3 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 Molecular dynamics simulations (MDS) are employed to investigate the effects of the size of a nanocone on rapid boiling of an ultrathin liquid water film that is suddenly heated by a hot aluminum plate. A physically sound thermostat is applied to control the temperature of the aluminum plate and then to heat the water molecules that are placed on the solid surface. The results show that the cone nanostructures drastically enhance heat transfer from the solid aluminum plate to liquid water and the phase change process from liquid water to vapor. They also have significant effects on temperature histories and the density distributions in the system. In all cases studied, the water molecules above the solid surface rapidly boil after contact with an extremely hot aluminum plate and consequently a cluster of liquid water is observed to move upward during the phase change. It is also observed that the separation temperature associated with separation of liquid water film from the solid surface and its final temperature when the system is at equilibrium strongly depend on the height of the nanocone. Furthermore, in all cases, at a specific time after beginning of boiling, a nonvaporized water molecular layer is formed above the surface of the aluminum plate. KEY WORDS: nanostructure, nanocone, molecular dynamic simulation, rapid boiling INTRODUCTION Thermal management of nano-electronics has attracted considerable attention in recent years due to rapid advances in microelectronic fabrication technologies and the promise of emerging nanotechnologies [1 4]. Liquid vapor phase changes, including Manuscript received 20 August 2014; accepted 29 October Address correspondence to Yong Tang, Key Laboratory of Surface Functional Structure Manufacturing of Guangdong High Education Institutes, School of Mechanical and Automotive Engineering, South China University of Technology, 381 Wu Shan Road, Tian He District, Guangzhou , China. ytang@ scut.edu.cn Color versions of one or more of the figures in the article can be found online at 17

4 18 T. FU ET AL. d lattice constant, Å E Young s modules, Gpa k spring constant, ev/å 2 k C electrostatic constant, Å kcal/mol q electron charge, e r ij distance between two atoms i and j, Å t time, ps U potential energy for Al-O, ev U ab potential function for water molecule, ev x coordinate in the x-direction NOMENCLATURE y z coordinate in the y-direction coordinate in the z-direction Greek Symbols ε depth of potential well, ev σ minimal distance between atoms when potential energy is equal to zero, Å Subscripts Al aluminum O oxygen boiling, of thin liquid films on a solid surface are very important in electronic cooling. Rapid boiling [5] is a special kind of boiling process in which the phase change from liquid to vapor occurs very rapidly. During rapid boiling, the liquid is superheated to a degree much higher than the normal saturation temperature, even approaching the thermodynamic critical temperature, which leads to the near-surface region of the materials being rejected rapidly [6]. Over the last decades, many experimental and numerical investigations have been performed to understand certain phenomena, such as clusters formed by bubbles and high superheat, that occur during rapid boiling [7 10]. Park et al. [11] induced rapid thermal expansion and explosive vaporization by a laser beam with a pulse duration of tens of nanoseconds in irradiated water on a solid surface. Ahn et al. [12] experimentally investigated saturated and subcooled pool boiling on a horizontal heater surface with nanostructures to study the effect of nanostructured surfaces on pool boiling. However, experimental research under such small timescales (picosecond) and space scales (nanometer) poses problems in instrumentation. In addition, it is difficult to describe phase change phenomena at such small scales using the classical macroscopic theory due to the breakdown of the continuum assumption, which is essential for continuum mechanics. Due to the limitation of classical macroscopic theory, many special phenomena in phase change cannot be well explained. One promising approach is molecular dynamics simulation (MDS), which goes directly to the molecular level. By solving Newton s equation of motion for each atom in a simulation system, much detailed information on the whole microscopic system can be obtained. Therefore, it is a powerful tool to capture the microscopic view of the heat transfer behavior during rapid boiling near solid wall in the nanoscale. Little [13] and Long et al. [14] studied the evaporation of liquid argon on solid surfaces by MDS and obtained the evaporation rate, which agreed well with the existing theoretical results. Maruyama and Kimura [15] obtained the contact thermal resistance over the solid liquid interface using MDS. The results showed that the temperature jump at the solid liquid interface increased sharply with decreasing surface wettability. Maroo and Chung [16] reported the effect of nanochannel height on liquid thin-film evaporation and heat fluxes in a nanochannel. They showed that both evaporation and heat flux heavily depend on the size of the nanochannel. In addition, in a follow-up work [17], they studied heat and mass transfer and pressure variation using MDS. It was shown that very high heat flux and evaporation rates as well as significant increases in pressure occurred after the formation of a nonevaporating film near the solid surface. Morshed et al. [18] simulated boiling of a liquid argon thin film absorbed on a platinum substrate whose surface is structured by

5 RAPID BOILING OF THIN WATER FILMS 19 cylindrical nanostructures. They reported that their nanostructure had a significant effect on vaporization/boiling of the liquid thin film. Seyf and Zhang [19] performed nonequilibrium MDS to investigate the effects of size of a nanocone array and types of wall material on the explosive boiling of a thin liquid argon film on a nanostructure. They used aluminum and silver separately as wall material and the embedded atom method for interactions between metal atoms. The results showed that the cone-shaped nanostructures drastically enhanced heat transfer from solid to liquid and they had significant effects on temperature, net vaporization, and the density distribution in the system. Mao and Zhang [5] carried out MDS to investigate the rapid boiling behavior of a liquid water film heated by a hot copper plate. They showed that liquid water molecules near the solid copper plate are instantly overheated and undergo a rapid phase change. The geometry and size of nanopatterns are two main factors affecting the heat transfer behaviors during rapid boiling [19]. Experimental studies have shown that using nanostructures on a flat surface enhances the heat transfer coefficient and critical heat flux [20, 21]. However, experimental works may suffer from limitations in handling such small-scale problems with current sophisticated technologies. In addition, most of the simulation works on boiling behavior are focused on heterogeneous phase changes in a liquid on a flat solid surface [5, 22, 23]. Few researchers have investigated phase changes in nanostructures. In addition, the effect of cone-shaped nanostructures and metal type on explosives has rarely been analyzed. Furthermore, the liquid used is commonly argon [24, 25] due to the fact that the interatomic interaction between argon atoms is easy to handle. However, water is one of the most widely used working fluids in engineering systems. Therefore, the main contribution of our work is that conical-shaped nanostructures are designed on a flat metal solid surface to study the rapid boiling phenomena over it and water is used as the working fluid. SIMULATION MODEL The molecular system employed for this simulation consists of a solid aluminum wall and a liquid water film in a cuboid of dimension 8.1 nm (x) 8.1 nm (y) nm (z). The liquid water that lies on the solid plate is initially placed on a face-centered cubic lattice corresponding to a density of 1.0 g/cm 3 at a temperature of 298 K under standard atmospheric pressure. Considering the accuracy in description of water s dynamic and thermal properties, the water liquid molecules are modeled by a four-site water model (TIP4P) [26]. The solid plates that are placed at the bottom of the simulation box are also arranged in a face-centered cubic lattice structure corresponding to a density of 2.7 g/cm 3. In order to model a more physically sound thermostat, six layers of aluminum atoms are constructed to form the flat wall. From the bottom to the top, the first two layers are fixed to avoid migration of atoms; the next two layers are set to be phantom atoms [22] as the heat source from which heat flux is generated; and the last two layers are considered as the real aluminum atoms through which heat is conducted to the liquid. The flat surface (surface type I) is formed by this aluminum model. Four equal-sized cone-shaped nanostructures are placed on top of the flat metallic surface. The thickness of the liquid water film is constant for all simulations and the height of the nanostructure is 5 Å (surface type II), 9 Å (surface type III), and 13 Å (surface type III), respectively. In addition, the base diameters of the nanostructures is 8 Å, as shown in Figure 1. The total number of atoms ranges from 18,516 to 32,448, which corresponds to different nanostructures.

6 20 T. FU ET AL. Figure 1 Structure of the aluminum plate. Three kinds of function atoms are formed within a distance of 4.05 Å. In this work, two different potentials, the well-known Lennard-Jones (L-J) potential and L-J with long-range Coulombic interactions, are used. It should be pointed out that the interaction between aluminum atoms is not considered. Instead, many artificial Al-Al harmonic bonds are built for the plate and nanostructures to introduce an Al-Al spring-like interaction [5, 18]. An artificial harmonic bond is created by connecting neighboring aluminum atoms that are within the shortest distance of 3 Å. It is important to set a reasonable interatomic spring constant k, which is closely related to Young s modulus, to obtain a sufficiently accurate thermostat. This can be estimated by the following formula: k = Ed, (1) where E is the Young s modulus of solid aluminum, and d is the lattice constant of solid aluminum. For the water molecules, the well-accepted potential function, L-J with long-range Coulombic interactions, which consists of contributions from electrostatic, dispersion, and repulsive forces, is used to describe the intermolecular interaction between hydrogen atoms, oxygen atoms, or hydrogen and oxygen [5]: U ab = a i b j k C q ai q bj r ai b j + a i b j [ (σai ) 12 b j 4ε ai b j r ai b j ( σai b j r ai b j ) ] 6, (2)

7 RAPID BOILING OF THIN WATER FILMS 21 where subscripts i and j denote atoms of oxygen or hydrogen in one individual TIP4P molecule. Superscripts a and b represent two different atom types. Parameter k C is the electrostatic constant, q i is the electric charge of site i, and r ai b j is the distance between two atoms. A particle particle particle mesh approach [27] with an accuracy of is used to resolve the long-range effect due to electrostatic potential. In this work, the pair potential only counts the interaction between oxygen atoms with a cutoff radius of 12 Å. The SHAKE [28] algorithm is applied to hold the rigidity of the water molecule. The interaction between aluminum and oxygen atoms is considered using the L-J potential: [ (σ ) 12 ( σ ) ] 6 U = 4ε, (3) r r where ε is the distance of the potential wall and σ denotes the finite distance at which the interatomic potential energy is zero. They are obtained by the following Berthelot mixing rule [29, 30]: ε Al O = ε Al Al ε O O σ Al O = σ Al Al + σ O O. 2 In this simulation, the interactions between aluminum hydrogen and hydrogen hydrogen are not considered [26]. Table 1 provides all of the parameters required in this work. In order to prevent energy transfer through the interaction between molecules and the wall, periodic boundary conditions are applied to the x and y directions and the top boundary is elastic and adiabatic. That is, the water molecules are reflected back to the simulation domain without any loss of momentum or kinetic energy. This method is consistent with the setup in actual experimental processes [24, 31, 32]. All of the simulations are performed using the open-source software LAMMPS [33] with certain extension and the visualization is done using VMD [34]. The equations of motion are integrated using the Verlet algorithm with a 1-fs time step. Before the liquid water is heated by the hot aluminum plate, the whole system is equilibrated using the following two steps: (1) the entire water domain is equilibrated to a stable state at a temperature of 298 K under a Berendsen thermostat [20], and (2) the temperature of the aluminum plate is gradually heated up to 800 K with a phantom atom thermostat while the water molecules are isolated from the integration. After these Table 1 L-J potential parameters for aluminum oxygen and water potential parameters (4) Parameters Values Units ε O-O ev σ O-O Å q H 0.52 e q O 1.04 e ε Al-O ev σ Al-O Å E 69 GPa d 4.05 Å

8 22 T. FU ET AL. preparation steps are completed, the liquid water at 298 K is suddenly placed on the hot plate that was equilibrated to a temperature of 800 K. The entire system is integrated with a number, volume, energy (NVE) ensemble that drives the simulation under Newton s second law during the simulation period. In addition, the aluminum plate is controlled to the desired temperature of 800 K with a phantom atom thermostat. RESULTS AND DISCUSSION To explicitly show the dynamic behavior of the water film during rapid boiling, the x z projection of the water molecule configuration at different times for four cases that includes smooth (I) or cone-shaped nanostructure (II, III, and IV) aluminum plates are presented in Figures 2 to 5. AsshowninFigure 2, liquid water above the smooth surface (I) Figure 2 Trajectories of water molecules for the case with surface I.

9 RAPID BOILING OF THIN WATER FILMS 23 Figure 3 Trajectories of water molecules for the case with surface II. vaporizes first at around 190 ps, which pushes the liquid layer above the surface away and consequently separates from the solid wall. At this point, due to the rapid rise in the wall temperature, liquid water near the aluminum wall reaches its saturation temperature and vaporizes while the water above is still in the liquid phase because of its lower temperature. That is, a low-density vapor region appears at that time, and the entire water domain can be clearly considered as three zones: the lower vapor zone adjacent to the hot solid surface, a liquid water zone above the lower vapor zone, and the top vapor zone. Due to continuous heat flux flowing into the water domain, the lower vapor zone keeps expanding up to 260 ps when the water film first collides with the top wall. For surface types II and III, the movement trends of the water liquid layer are similar to the case with the smooth surface, as shown in Figures 3 and 4, except that the liquid detaches from the solid surface starting at around 120 and 100 ps and the first hit against the top occurs at 190 and 160 ps, respectively. For the surface type IV, the water film, as a tiny cluster, first hits against the top wall at 80 ps; for the other surfaces, this time is 260, 190, and 160 ps, respectively, as shown in Figure 5. In addition, due to the surface tension, the liquid water shows a lower meniscus for

10 24 T. FU ET AL. Figure 4 Trajectories of water molecules for the case with surface III. surface IV before the beginning of boiling; this leads to large liquid vapor interface area, which causes vaporization on the nanostructure to occur more quickly than that on the flat surface. Moreover, it is worth mentioning that because the transfer of energy is only from the bottom for the case of the flat surface, evaporation lasts longer. Furthermore, the translational velocities of water molecules increase along with the size of the nanostructures in the first 260 ps. In addition, for the smooth surface, the liquid layer above the solid surface separates from it as a large cluster of liquid; the size of the liquid cluster differs for cases with nanostructures. With an increase in nanostructure size, the surface area of the solid in contact with the liquid increases, which results in the temperature gradient in the liquid film becoming less extensive than that of the smooth surface. Hence, a smaller cluster of liquid moves upward while the rest of liquid migrates as individual molecules. At the same time, due to the larger heating area in the case of larger nanostructures, the volume of the liquid layer decreases and the liquid moves upward so the separation starts from the upper layer of the liquid.

11 RAPID BOILING OF THIN WATER FILMS 25 Figure 5 Trajectories of water molecules for the case with surface IV. Figure 6 shows the effects of a cone-shaped nanostructure on the temperature history of the aluminum plate and water for these cases. It can be seen that the solid walls respond very quickly to the temperature rise and reach the target temperature in less than 100 ps. Meanwhile, at the beginning of boiling stage, the water temperature rises very rapidly from 298 K to around 600, 625, 650, and 675 K, respectively. At the same time, it should be pointed out that a temperature drop occurs after 200 ps because the kinetic energy is converted to potential energy when bulk liquid hits against the wall. During the following period, it is clearly shown that the temperatures are stabilized to certain values until the end of the simulation. As described earlier, at a specific time the liquid water film near the solid surface vaporizes, which lifts the liquid zone up and then the liquid zone separates from the solid as a cluster of liquid. It is found that the overall separation temperature, which is defined as the temperature associated with separation of the liquid from the wall [19], increases with increasing nanostructure size. Because of increased solid liquid interface area and interaction, the nanostructures lead to quicker energy transfer from the solid wall

12 26 T. FU ET AL. Figure 6 Temperature variation of water and hot copper plate for different scenarios. to the liquid molecules. In addition, due to the presence of cone-shaped nanostructures on the surface, the quick rise in wall temperature causes greater energy transfer to the vapor molecules near the solid wall, which results in an increase in the separation temperature. In order to have a closer look at the density variation in the z-direction for different surface areas of nanostructures, the computational domain along the z-direction is divided into 66 bins and the number of molecules in each bin is calculated to obtain the average density of each bin. The effect of nanostructure on the number density profile for different time periods after the onset of boiling is shown in Figure 7. The number density profiles show as four different zones, which includes a nonevaporative zone near the solid aluminum surface, a liquid-phase zone with a relatively high density, a vapor phase zone, and a vapor liquid interface zone. The domain for high-density peaks appearing in the curves indicates the locations of the moving liquid water molecules. For surfaces I and II there is a large liquid cluster in the computational domain that moves away from the solid surface, whereas for other surfaces there is no obvious peak in the curves, which indicates the existence of a tiny cluster in the system instead of a large cluster. The z-coordinate represents the location of moving liquid water at different times. For instance, at t = 160 ps, for the case of a smooth surface, the liquid water peak value is around 0.7g/cm 3 and it is located somewhere between 75 and 100 Å, which is shown in Figure 7a. For surface II, as shown in Figure 7b, the location is between 150 and 175 Å, and the corresponding peak value is approximately 0.5 g/cm 3. However, for surfaces III and IV, due to a larger heat area and vaporization,

13 RAPID BOILING OF THIN WATER FILMS 27 Figure 7 Z-direction density distribution at various times for all cases. there is no obvious large liquid cluster, which means that partial liquid water molecules as tiny clusters move upward and the rest of them move as individual molecules [35]. Furthermore, there is an obvious high-density zone near the solid wall, which is defined as the nonvaporized water zone [36] during the entire simulation period for all cases. In this zone, the water molecules are distributed near the solid surface and show a hot gas-like structure. In addition, it can be clearly seen that the density profile gradually flattens before and after each peak value, which indicates the disappearance of the vapor liquid phase interface [19]. Figure 8 illustrates the number of liquid water molecules for all surfaces during the simulation period. It is important to note that the evaporation rate in this system is calculated by counting the change in the number of liquid water molecules [18, 19]. It can be seen that after the beginning of boiling, the number of liquid water molecules decreases sharply for all surfaces and finally reaches a constant value. Evaporation occurs at around 140, 80, 50, and 20 ps for surfaces I, II, III, and IV, respectively, which means that most of liquid molecules evaporated in the beginning of the boiling process for nanostructured surfaces. In other words, due to the larger heating area for the nanostructured surfaces, fast evaporation of liquid water molecules occurs in the beginning of boiling and the number of liquid water molecules reaches equilibrium quickly. In addition, at approximately 140 ps < t < 150 ps, the flat surface shows a higher evaporation rate, whereas it occurs at around 80 ps < t < 120 ps, 50 ps < t < 75 ps, and 20 ps < t < 50 ps for nanostructured surfaces II, III, and IV, respectively.

14 28 T. FU ET AL. CONCLUSIONS Figure 8 Number of liquid molecules as a function of time. MDS is carried out to study the rapid boiling of liquid water film over cone-shaped nanostructures on a hot aluminum plate. Four cone-shaped nanostructures with different heights ranging from 5 to 13 Å are studied. Artificial Al-Al harmonic bonds are created for the plate and nanostructures in order to introduce Al-Al interaction and the L-J and L-J with long-range Coulombic interactions potentials are employed to describe the entire simulation system. The results show that the cone-shaped nanostructures enhance the heat transfer from solid to liquid and increase the water temperature and evaporation rate. It is observed that a cluster of liquid water moves upward after the water is suddenly heated to a very high temperature. In addition, the size of the water cluster during the phase change is related to the height of the nanocones. It is found that the velocity of the water cluster strongly depends on the size of the nanocone, which shows as the increasing velocity with an increase in the height of the nanostructure. In addition, the separation temperature associated with separation of the liquid water film from the solid surface also depends on the size of the nanostructure. Furthermore, a nonvaporized water layer always exists somewhere near the solid aluminum surface during the whole simulation period for all cases, including continuous heat flux flow through the plate to water zones. FUNDING This research was financially supported by a grant from the National Nature Science Foundation of China under grant number , the National Nature Science Foundation of China under grant number , and the U.S. National Science

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