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Molecular dynamics study of rapid boiling of thin liquid water film on smooth copper surface under different wettability conditions
International Journal of Heat and Mass Transfer 147 (2020) 118905
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Technical Note
Molecular dynamics study of rapid boiling of thin liquid water film on smooth copper surface under different wettability conditions Nini Wu a,b, Liangcai Zeng a, Ting Fu a,⇑, Zhaohui Wang a, Chang Lu a a Key Laboratory of Metallurgical Equipment and Control Technology (Wuhan University of Science and Technology), Ministry of Education & Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering (Wuhan University of Science and Technology), Wuhan 430081, People’s Republic of China b College of Technology, Hubei Engineering University, Xiaogan 432000, Hubei, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 11 May 2019 Received in revised form 17 September 2019 Accepted 14 October 2019
Keywords: Molecular dynamics Rapid boiling Heat transfer Wettability condition
a b s t r a c t This work aims to present theory of heat transfer on rapid boiling for pure wettability surfaces and mixed wettability surfaces based on molecular simulation. The simulation results showed that the temperature of water increased obviously and the maximum evaporation rate of water reduced significantly with the increase of hydrophilic for pure wettability surfaces. Furthermore, a microfluidic layer which was formed on all cases except hydrophobic surface (surface 4) was conducive to critical heat flux (CHF) improvement. Meanwhile, the attraction of water molecules upon hydrophobic region was smaller than that on hydrophilic region which was conducive to boiling heat transfer coefficient (HTC) improvement. A mixed wettability surface enhances boiling heat transfer by regulating vapor spreading behaviors over the heating copper surface compared with pure wettability surfaces. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Rapid boiling heat transfer technology, which can quickly decrease the surface temperature and take away heat, is widely used in many fields such as thermal power, nuclear energy, solar energy and cryogenic engineering [1]. Over the last decades, many experimental and numerical investigations have conducted to explore that changing wettability was an effective way to enhance boiling heat transfer. Shen and Zhang et al. [2] investigated the heat transfer coefficients of the hybrid wettability surfaces which were higher than the values of the spatially uniform wettability surfaces. Kim et al. [3] designed four types of hydrophobic stripes and showed that the parallel striped surfaces had higher the critical heat flux than the crossed striped surfaces. Hsu et al. [4] indicated that the number of interlaced lines and ratio of two surface wettability affected heat transfer performance of surfaces. Although above scholars had studied experimentally the enhancement of heat transfer about hybrid way of mixed wettability in rapid boiling, many special phenomena in phase change at nanoscales cannot be well described using the classical macroscopic theory due to the breakdown of the continuum assumption. Thus, molecular dynamic(MD) simulation is considered as an effective
⇑ Corresponding author. E-mail address: [email protected] (T. Fu). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118905 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
approach [5] to study effects of wettability on pool boiling duo to its advanced microscopic transfer theory. For the past few years, most of researchers study effects of surface roughness [6–8], uniform wettability [9,10] or mixed wettability of a single fixed ratio of hydrophilic & hydrophobic [11], which did not systematically consider effects of mixed wettability ratio and arrangement. In this work, effects of pure wettability and mixed wettability surfaces on heat transfer were studied by MD simulation, where water was used as the liquid medium. The thermal mechanism of wettability on rapid boiling was explored in nanoscale.
2. Simulation models and methods A simulation box with size of 86.64 Å(x) 86.64 Å(y) 270 Å(z) is created and Fig. 1(a) illustrates the initial configuration of simulation for surface 8. The liquid water used a lattice constant of 4.9 Å corresponding to a density of 1.0 g/cm3 was placed on the copper plate used a lattice constant of 3.61 Å corresponding to a density of 8.9 g/cm3 at a temperature of 298 K under standard atmospheric pressure.The copper plate consisted of six layers of copper atoms arranged horizontally. The bottom two layers were fixed to avoid migration of atoms. The middle two layers were set to be ‘‘phantom atoms” as the heat source maintained at 1000 K via a Langevin thermostat from which heat flux was generated; The top two layers set to be surface with different proportions of wettability were
2
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
Fig. 1. Schematic diagram of (a) initial configuration of simulation system for surface 8, (b) X-Y two-dimensional view of surface 8 and parameters of mixed wettability surfaces scale, (c) X-Z two-dimensional view of surface 8, (d) View of pure wettability surfaces (surface 1–4), (e) View of mixed wettability surfaces (surface 5–10).
considered as the real copper atoms and through which heat was transfer to the liquid water as shown in Fig. 1(d and e). In this work, the well-known Lennard-Jones(L-J) potential function used in Cu-Cu between which an artificial harmonic bond was built to connect neighboring copper atoms. Spring constant k could be estimated with formula below [12]:
k ¼ Ed
ð1Þ
where E = 274–306 GPa is Young’s Modules of solid copper, and d = 3.615 Å is the lattice constant of copper. The interatomic potential between copper–oxygen atoms is given by the well-known Lenard–Jones potential:
12 6 r r U ¼ 4e r r
ð2Þ
where e is the depth of potential well, r is the finite length at which the potential is zero. For interactions between two atoms i and j, eO = 0.00698 eV, eCu = 0.583 eV, rO = 3.16435 Å and rCu = 2.27 Å follow that:
rij ¼
1 ri þ rj 2 pffiffiffiffiffiffiffi
eij ¼ c ei ej
ð3Þ ð4Þ
where c is a user-chosen constant to controlled the depth of potential well eij which presented the mutual attraction between atoms (i and j) [13]. The more hydrophilic surface can be obtained from a bigger eij. In Fig. 2(d) the potential parameter c of surface 1–4 was set as 3, 2, 1, and 0.25, respectively. In Fig. 1(b and e), mixed wettability surfaces were formed by hydrophilic zone(c = 1) and
3
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
Fig. 2. Trajectories of water molecules for pure wettability surfaces: (a) surface 1, (b) surface 2, (c) surface 3, (d) surface 4.
hydrophobic zone(c = 0.25) with different ratios: L was defined as the total length of the copper plate in the X and Y direction; a and b were respectively set as the width of hydrophilic and hydrophobic streaks in the X direction of copper plate; The length of L was equal to the sum of a and b in surface 5–7, and the length of L was equal to twice the sum of a and b in surface 8–10.In surface 5–10 the parameter a was L/2, 2L/3, 3L/4, L/4, L/3 and 3L/8, respectively. L-J with long-range Coulombic interactions is well-accepted used to describe the interaction force between water molecules
consists of the intermolecular interaction between hydrogen atoms, oxygen atoms, or hydrogen and oxygen [14]:
U ab ¼
a X b k q q X c ai bj i
j
r ai bj
þ
a X b X i
j
2
rai bj 4eai bj 4 r ai bj
!12
rai bj r ai bj
!6 3 5
ð5Þ
where a and b represent two different atom types; i and j denote atoms of oxygen or hydrogen in one individual TIP4P molecule;
4
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
Fig. 3. Trajectories of water molecules for mixed wettability surfaces: (a) surface 5, (b) surface 6, (c) surface 7, (d) surface 8 (e) surface 9, (f) surface 10.
qO = 1.04e, qH = 0.52e is the electric charge of oxygen and hydrogen, and raibj is the distance between two atoms; Parameter kc is the electrostatic constant. An accuracy of 106 is used to resolve the longrange effect by PPPM (particle–particle particle-mesh) due to electrostatic potential while the pair potential between oxygen atoms is considered with a cutoff radius of 12 Å. And in order to hold the rigidity of the water molecules, the SHAKE [15] algorithm is used. The boundary conditions of p-p-f were used for the whole system. All these simulations were performed within the framework of open-source package LAMMPS (version 16 Mar 2018) while the data visualization was done with VMD.
3. Results and discussion 3.1. Behavior of water molecules To explicitly show the behavior of liquid water during rapid boiling, the x-z projection of the atomic configuration of pure wettability and mixed wettability surfaces were shown in Figs. 2 and 3, respectively. The velocity of water molecule cluster decreased successively from surface 1 to surface 4 (see Fig. 2). The movement trend of the water liquid clusters for surface 5–10 is similar (see Fig. 3). Meanwhile, these designed mixed wettability surfaces with
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
5
Fig. 4. Temperature variation of (a) water and (b) copper for different surfaces. (c and d) Comparison of number of liquid water molecules as a function of time.
different ratio between hydrophilic and hydrophobic make little difference on movement of water molecular. As shown in Fig. 3, an interesting finding is that the density of water molecules in hydrophilic zone of the mixed wettability surfaces is significantly higher than that in hydrophobic zone. And a microfludic layer which was formed upon all hydrophilic zone from boiling beginning to system stability was marked with red ellipse at 400 ps in Figs. 2 and 3. 3.2. Temperature and number of liquid water molecular variation Effects of different wettability surfaces on the temperature history of the copper plate and water for all the cases were shown in Fig. 4(a and b). As shown in Fig. 4(a), the water temperature rose very rapidly at the beginning of boiling stage and reached the highest value from 50 ps to 100 ps. The temperature of water rose significantly with hydrophilic increasing. The highest temperature of water in surface 1 was 690 K at 30 ps, while the lowest temperature of water in surface 4 was 590 K at 70 ps. However, temperature of water for mixed wettability surfaces between 615 K and 635 K from 40 ps to 100 ps. The temperature of water on surface 9 and surface 10 was the highest about 635 K, while it was 615 K on surface 5 which was the lowest. Meanwhile, Fig. 4(b) shows that the copper walls of all the cases responded very quickly to the temperature rise and reach the target temperature (1000 K) in less than 100 ps. The number of liquid water molecules on different surfaces was compared during the simulation period, as shown in Fig. 4(c and d).
The evaporation rate can be calculated by counting the variation of liquid water molecules number. The number of water molecules on solid surfaces decreased significantly at the beginning of the simulation except surface 4. Fig. 4(c) shows that evaporation rate of water for hydrophobic surface (surface 4) is the highest. Furthermore, the total number of water molecules in the initial state is 6936. Fig. 4(d) shows that the minimum number of water molecules on surface 3, surface 4, and surface 9 are 4938(at 80 ps), 4802(at 192 ps), and 4698(at 88 ps), respectively. What’s more, the evaporation rate of surface 9 (32.3%) is bigger than surface 3 (28.8%) but similar to surface 4(30.8%). And the time of reaching the max evaporation rate of mixed wettability surfaces (90 ps) is all less than surface 4(192 ps).
3.3. Energy and density of water molecules Fig. 5 presents the distribution of density and energy of water molecules on the solid surface within 15 Å of simulation box at 60 ps when the boiling was beginning. It can be seen that on the mixed wettability surfaces (surface5-10) the density of water molecules in the hydrophobic region was significantly less than that in the hydrophilic region due to different interaction between atoms. A reduction in interaction with smaller parameter ‘‘c” between the atoms causes bigger amplitude kinetic energy and smaller attraction (the absolute value of negative potential energy) of water molecules and which make the surface hydrophobic.
6
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
Fig. 5. The density and energy distribution of water molecules on the mixed wettability surfaces at 60 ps: (a) surface 5, (b) surface 6, (c) surface 7, (d) surface 8 (e) surface 9, (f) surface 10.
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
4. Conclusions In the current study we investigate that the thickness of a microfluidic layer which formed in hydrophilic zone increases with interaction enhancement between atoms is conducive to CHF improvement, while the smaller attraction in the hydrophobic region is conducive to evaporation. The increase of evaporation rate of surface 9 is 3.5% compared to surface 3, and the time of reaching maximum evaporation of surface 9 is almost half as fast as surface 4. Surface 9 not only keeps heat transfer speed of hydrophilic surface 3, but also maintains evaporation rate of hydrophobic surface 4. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgement This research was financially supported by National Natural Science Foundation of China (Grant No. 51605345, No. 51975425, No. 51875419 and No. 51575407). References [1] V.P. Carey, Liquid Vapor Phase Change Phenomena: An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment, Taylor&Francis Group, New York, 2008. [2] C. Shen, C. Zhang, Y. Bao, X. Wang, Y. Liu, L. Ren, Experimental investigation on enhancement of nucleate pool boiling heat transfer using hybrid wetting pillar surface at low heat fluxes, Int. J. Therm. Sci. 130 (2018) 47–58, https://doi.org/ 10.1016/j.ijthermalsci.2018.04.011. [3] J.M. Kim, T. Kim, D.I. Yu, H. Noh, M.H. Kim, K. Moriyama, et al., Effect of heterogeneous wetting surface characteristics on flow boiling performance, Int. J. Heat Fluid Flow 70 (2018) 141–151, https://doi.org/10.1016/j. ijheatfluidflow.2018.02.006.
7
[4] C.-C. Hsu, M.-R. Lee, C.-H. Wu, P.-H. Chen, Effect of interlaced wettability on horizontal copper cylinders in nucleate pool boiling, Appl. Therm. Eng. 112 (2017) 1187–1194, https://doi.org/10.1016/j.applthermaleng.2016.10.176. [5] X. Li, I. Cole, J. Tu, A review of nucleate boiling on nanoengineered surfaces – the nanostructures, phenomena and mechanisms, Int. J. Heat Mass Transf. 141 (2019) 20–33, https://doi.org/10.1016/j.ijheatmasstransfer.2019.06.069. [6] W. Wang, S. Huang, X. Luo, MD simulation on nano-scale heat transfer mechanism of sub-cooled boiling on nano-structured surface, Int. J. Heat Mass Transf. 100 (2016) 276–286, https://doi.org/10.1016/j. ijheatmasstransfer.2016.04.018. [7] N. Sankar, N. Mathew, C.B. Sobhan, Molecular dynamics modeling of thermal conductivity enhancement in metal nanoparticle suspendions, Int. Commun. Heat Mass Transf. 35 (7) (2008) 867–872, https://doi.org/10.1016/j. icheatmasstransfer.2008.03.006. [8] T. Fu, Y. Mao, Y. Tang, Y. Zhang, W. Yuan, Molecular dynamics simulation on rapid boiling of thin water films on cone-shaped nanostructure surfaces, Nanoscale Microscale Thermophys. Eng. 19 (2015) 17–30, https://doi.org/ 10.1080/15567265.2014.991480. [9] Y. Chen, Y. Zou, B. Yu, D. Sun, X. Chen, Effects of surface wettability on rapid boiling and bubble nucleation: a molecular dynamics study, Nanoscale Microscale Thermophys. Eng. 22 (2018) 198–212, https://doi.org/10.1080/ 15567265.2018.1475526. [10] S.M. Shavik, M.N. Hasan, A.K.M.M. Morshed, M.Q. Islam, Molecular dynamics study of effect of different wetting conditions on evaporation and rapid boiling of ultra–thin argon layer over platinum surface, Procedia Eng. 105 (2015) 446– 451, https://doi.org/10.1016/j.proeng.2015.05.032. [11] W. Zhou, Y. Li, M. Li, J. Wei, W. Tao, Bubble nucleation over patterned surfaces with different wettabilities: molecular dynamics investigation, Int. J. Heat Mass Transf. 136 (2019) 1–9, https://doi.org/10.1016/j. ijheatmasstransfer.2019.02.093. [12] T. Fu, Y. Mao, Y. Tang, Y. Zhang, W. Yuan, Effect of nanostructure on rapid boiling of water on a hot copper plate: a molecular dynamics study, Heat Mass Transf. 52 (2015) 1469–1478, https://doi.org/10.1007/s00231-015-1668-2. [13] M. Isaiev, S. Burian, L. Bulavin, M. Gradeck, F. Lemoine, K. Termentzidis, Efficient tuning of potential parameters for liquid–solid interactions, Mol. Simul. 42 (2015) 910–915, https://doi.org/10.1080/08927022.2015.1105372. [14] Y. Mao, Y. Zhang, Molecular dynamics simulation on rapid boiling of water on a hot copper plate, Appl. Therm. Eng. 62 (2014) 607–612, https://doi.org/ 10.1016/j.applthermaleng.2013.10.032. [15] J.P. Ryckaert GC, H.J. Berendsen, Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of nalkanes, J. Comput. Phys. 23 (3) (1977) 327–341, https://doi.org/10.1016/ 0021-9991(77)90098-5.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Technical Note
Molecular dynamics study of rapid boiling of thin liquid water film on smooth copper surface under different wettability conditions Nini Wu a,b, Liangcai Zeng a, Ting Fu a,⇑, Zhaohui Wang a, Chang Lu a a Key Laboratory of Metallurgical Equipment and Control Technology (Wuhan University of Science and Technology), Ministry of Education & Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering (Wuhan University of Science and Technology), Wuhan 430081, People’s Republic of China b College of Technology, Hubei Engineering University, Xiaogan 432000, Hubei, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 11 May 2019 Received in revised form 17 September 2019 Accepted 14 October 2019
Keywords: Molecular dynamics Rapid boiling Heat transfer Wettability condition
a b s t r a c t This work aims to present theory of heat transfer on rapid boiling for pure wettability surfaces and mixed wettability surfaces based on molecular simulation. The simulation results showed that the temperature of water increased obviously and the maximum evaporation rate of water reduced significantly with the increase of hydrophilic for pure wettability surfaces. Furthermore, a microfluidic layer which was formed on all cases except hydrophobic surface (surface 4) was conducive to critical heat flux (CHF) improvement. Meanwhile, the attraction of water molecules upon hydrophobic region was smaller than that on hydrophilic region which was conducive to boiling heat transfer coefficient (HTC) improvement. A mixed wettability surface enhances boiling heat transfer by regulating vapor spreading behaviors over the heating copper surface compared with pure wettability surfaces. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Rapid boiling heat transfer technology, which can quickly decrease the surface temperature and take away heat, is widely used in many fields such as thermal power, nuclear energy, solar energy and cryogenic engineering [1]. Over the last decades, many experimental and numerical investigations have conducted to explore that changing wettability was an effective way to enhance boiling heat transfer. Shen and Zhang et al. [2] investigated the heat transfer coefficients of the hybrid wettability surfaces which were higher than the values of the spatially uniform wettability surfaces. Kim et al. [3] designed four types of hydrophobic stripes and showed that the parallel striped surfaces had higher the critical heat flux than the crossed striped surfaces. Hsu et al. [4] indicated that the number of interlaced lines and ratio of two surface wettability affected heat transfer performance of surfaces. Although above scholars had studied experimentally the enhancement of heat transfer about hybrid way of mixed wettability in rapid boiling, many special phenomena in phase change at nanoscales cannot be well described using the classical macroscopic theory due to the breakdown of the continuum assumption. Thus, molecular dynamic(MD) simulation is considered as an effective
⇑ Corresponding author. E-mail address: [email protected] (T. Fu). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118905 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
approach [5] to study effects of wettability on pool boiling duo to its advanced microscopic transfer theory. For the past few years, most of researchers study effects of surface roughness [6–8], uniform wettability [9,10] or mixed wettability of a single fixed ratio of hydrophilic & hydrophobic [11], which did not systematically consider effects of mixed wettability ratio and arrangement. In this work, effects of pure wettability and mixed wettability surfaces on heat transfer were studied by MD simulation, where water was used as the liquid medium. The thermal mechanism of wettability on rapid boiling was explored in nanoscale.
2. Simulation models and methods A simulation box with size of 86.64 Å(x) 86.64 Å(y) 270 Å(z) is created and Fig. 1(a) illustrates the initial configuration of simulation for surface 8. The liquid water used a lattice constant of 4.9 Å corresponding to a density of 1.0 g/cm3 was placed on the copper plate used a lattice constant of 3.61 Å corresponding to a density of 8.9 g/cm3 at a temperature of 298 K under standard atmospheric pressure.The copper plate consisted of six layers of copper atoms arranged horizontally. The bottom two layers were fixed to avoid migration of atoms. The middle two layers were set to be ‘‘phantom atoms” as the heat source maintained at 1000 K via a Langevin thermostat from which heat flux was generated; The top two layers set to be surface with different proportions of wettability were
2
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
Fig. 1. Schematic diagram of (a) initial configuration of simulation system for surface 8, (b) X-Y two-dimensional view of surface 8 and parameters of mixed wettability surfaces scale, (c) X-Z two-dimensional view of surface 8, (d) View of pure wettability surfaces (surface 1–4), (e) View of mixed wettability surfaces (surface 5–10).
considered as the real copper atoms and through which heat was transfer to the liquid water as shown in Fig. 1(d and e). In this work, the well-known Lennard-Jones(L-J) potential function used in Cu-Cu between which an artificial harmonic bond was built to connect neighboring copper atoms. Spring constant k could be estimated with formula below [12]:
k ¼ Ed
ð1Þ
where E = 274–306 GPa is Young’s Modules of solid copper, and d = 3.615 Å is the lattice constant of copper. The interatomic potential between copper–oxygen atoms is given by the well-known Lenard–Jones potential:
12 6 r r U ¼ 4e r r
ð2Þ
where e is the depth of potential well, r is the finite length at which the potential is zero. For interactions between two atoms i and j, eO = 0.00698 eV, eCu = 0.583 eV, rO = 3.16435 Å and rCu = 2.27 Å follow that:
rij ¼
1 ri þ rj 2 pffiffiffiffiffiffiffi
eij ¼ c ei ej
ð3Þ ð4Þ
where c is a user-chosen constant to controlled the depth of potential well eij which presented the mutual attraction between atoms (i and j) [13]. The more hydrophilic surface can be obtained from a bigger eij. In Fig. 2(d) the potential parameter c of surface 1–4 was set as 3, 2, 1, and 0.25, respectively. In Fig. 1(b and e), mixed wettability surfaces were formed by hydrophilic zone(c = 1) and
3
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
Fig. 2. Trajectories of water molecules for pure wettability surfaces: (a) surface 1, (b) surface 2, (c) surface 3, (d) surface 4.
hydrophobic zone(c = 0.25) with different ratios: L was defined as the total length of the copper plate in the X and Y direction; a and b were respectively set as the width of hydrophilic and hydrophobic streaks in the X direction of copper plate; The length of L was equal to the sum of a and b in surface 5–7, and the length of L was equal to twice the sum of a and b in surface 8–10.In surface 5–10 the parameter a was L/2, 2L/3, 3L/4, L/4, L/3 and 3L/8, respectively. L-J with long-range Coulombic interactions is well-accepted used to describe the interaction force between water molecules
consists of the intermolecular interaction between hydrogen atoms, oxygen atoms, or hydrogen and oxygen [14]:
U ab ¼
a X b k q q X c ai bj i
j
r ai bj
þ
a X b X i
j
2
rai bj 4eai bj 4 r ai bj
!12
rai bj r ai bj
!6 3 5
ð5Þ
where a and b represent two different atom types; i and j denote atoms of oxygen or hydrogen in one individual TIP4P molecule;
4
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
Fig. 3. Trajectories of water molecules for mixed wettability surfaces: (a) surface 5, (b) surface 6, (c) surface 7, (d) surface 8 (e) surface 9, (f) surface 10.
qO = 1.04e, qH = 0.52e is the electric charge of oxygen and hydrogen, and raibj is the distance between two atoms; Parameter kc is the electrostatic constant. An accuracy of 106 is used to resolve the longrange effect by PPPM (particle–particle particle-mesh) due to electrostatic potential while the pair potential between oxygen atoms is considered with a cutoff radius of 12 Å. And in order to hold the rigidity of the water molecules, the SHAKE [15] algorithm is used. The boundary conditions of p-p-f were used for the whole system. All these simulations were performed within the framework of open-source package LAMMPS (version 16 Mar 2018) while the data visualization was done with VMD.
3. Results and discussion 3.1. Behavior of water molecules To explicitly show the behavior of liquid water during rapid boiling, the x-z projection of the atomic configuration of pure wettability and mixed wettability surfaces were shown in Figs. 2 and 3, respectively. The velocity of water molecule cluster decreased successively from surface 1 to surface 4 (see Fig. 2). The movement trend of the water liquid clusters for surface 5–10 is similar (see Fig. 3). Meanwhile, these designed mixed wettability surfaces with
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
5
Fig. 4. Temperature variation of (a) water and (b) copper for different surfaces. (c and d) Comparison of number of liquid water molecules as a function of time.
different ratio between hydrophilic and hydrophobic make little difference on movement of water molecular. As shown in Fig. 3, an interesting finding is that the density of water molecules in hydrophilic zone of the mixed wettability surfaces is significantly higher than that in hydrophobic zone. And a microfludic layer which was formed upon all hydrophilic zone from boiling beginning to system stability was marked with red ellipse at 400 ps in Figs. 2 and 3. 3.2. Temperature and number of liquid water molecular variation Effects of different wettability surfaces on the temperature history of the copper plate and water for all the cases were shown in Fig. 4(a and b). As shown in Fig. 4(a), the water temperature rose very rapidly at the beginning of boiling stage and reached the highest value from 50 ps to 100 ps. The temperature of water rose significantly with hydrophilic increasing. The highest temperature of water in surface 1 was 690 K at 30 ps, while the lowest temperature of water in surface 4 was 590 K at 70 ps. However, temperature of water for mixed wettability surfaces between 615 K and 635 K from 40 ps to 100 ps. The temperature of water on surface 9 and surface 10 was the highest about 635 K, while it was 615 K on surface 5 which was the lowest. Meanwhile, Fig. 4(b) shows that the copper walls of all the cases responded very quickly to the temperature rise and reach the target temperature (1000 K) in less than 100 ps. The number of liquid water molecules on different surfaces was compared during the simulation period, as shown in Fig. 4(c and d).
The evaporation rate can be calculated by counting the variation of liquid water molecules number. The number of water molecules on solid surfaces decreased significantly at the beginning of the simulation except surface 4. Fig. 4(c) shows that evaporation rate of water for hydrophobic surface (surface 4) is the highest. Furthermore, the total number of water molecules in the initial state is 6936. Fig. 4(d) shows that the minimum number of water molecules on surface 3, surface 4, and surface 9 are 4938(at 80 ps), 4802(at 192 ps), and 4698(at 88 ps), respectively. What’s more, the evaporation rate of surface 9 (32.3%) is bigger than surface 3 (28.8%) but similar to surface 4(30.8%). And the time of reaching the max evaporation rate of mixed wettability surfaces (90 ps) is all less than surface 4(192 ps).
3.3. Energy and density of water molecules Fig. 5 presents the distribution of density and energy of water molecules on the solid surface within 15 Å of simulation box at 60 ps when the boiling was beginning. It can be seen that on the mixed wettability surfaces (surface5-10) the density of water molecules in the hydrophobic region was significantly less than that in the hydrophilic region due to different interaction between atoms. A reduction in interaction with smaller parameter ‘‘c” between the atoms causes bigger amplitude kinetic energy and smaller attraction (the absolute value of negative potential energy) of water molecules and which make the surface hydrophobic.
6
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
Fig. 5. The density and energy distribution of water molecules on the mixed wettability surfaces at 60 ps: (a) surface 5, (b) surface 6, (c) surface 7, (d) surface 8 (e) surface 9, (f) surface 10.
N. Wu et al. / International Journal of Heat and Mass Transfer 147 (2020) 118905
4. Conclusions In the current study we investigate that the thickness of a microfluidic layer which formed in hydrophilic zone increases with interaction enhancement between atoms is conducive to CHF improvement, while the smaller attraction in the hydrophobic region is conducive to evaporation. The increase of evaporation rate of surface 9 is 3.5% compared to surface 3, and the time of reaching maximum evaporation of surface 9 is almost half as fast as surface 4. Surface 9 not only keeps heat transfer speed of hydrophilic surface 3, but also maintains evaporation rate of hydrophobic surface 4. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgement This research was financially supported by National Natural Science Foundation of China (Grant No. 51605345, No. 51975425, No. 51875419 and No. 51575407). References [1] V.P. Carey, Liquid Vapor Phase Change Phenomena: An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment, Taylor&Francis Group, New York, 2008. [2] C. Shen, C. Zhang, Y. Bao, X. Wang, Y. Liu, L. Ren, Experimental investigation on enhancement of nucleate pool boiling heat transfer using hybrid wetting pillar surface at low heat fluxes, Int. J. Therm. Sci. 130 (2018) 47–58, https://doi.org/ 10.1016/j.ijthermalsci.2018.04.011. [3] J.M. Kim, T. Kim, D.I. Yu, H. Noh, M.H. Kim, K. Moriyama, et al., Effect of heterogeneous wetting surface characteristics on flow boiling performance, Int. J. Heat Fluid Flow 70 (2018) 141–151, https://doi.org/10.1016/j. ijheatfluidflow.2018.02.006.
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