Thermal transport during thin-film argon evaporation over nanostructured platinum surface: A molecular dynamics study

Transcription

1 Original Article Thermal transport during thin-film argon evaporation over nanostructured platinum surface: A molecular dynamics study NANOMATERIALS NANOENGINEERING AND NANOSYSTEMS Proc IMechE Part N: J Nanomaterials, Nanoengineering and Nanosystems 2018, Vol. 232(2-3) Ó IMechE 2018 Article reuse guidelines: sagepub.com/journals-permissions DOI: / journals.sagepub.com/home/pin Mohammad Nasim Hasan, Sheikh Mohammad Shavik, Kazi Fazle Rabbi, Khaled Mosharraf Mukut and Md. Muntasir Alam Abstract Investigation of thermal transport characteristics of thin-film liquid evaporation over nanostructured surface has been conducted using molecular dynamics simulation with particular importance on the effects of the nanostructure configuration for different wall fluid interaction strengths. The nanostructured surface considered herein comprises wallthrough rectangular nanoposts placed over a flat wall. Both the substrate and the nanostructure are of platinum while argon is used as the evaporating liquid. Two different wall fluid interaction strengths have been considered that essentially emulate both hydrophilic and hydrophobic wetting conditions for three different nanostructure configurations. The argon platinum molecular system is first equilibrated at 90 K and then followed by a sudden increase in the wall temperature at 130 K that induces evaporation of argon laid over it. Comparative effectiveness of heat and mass transfer for different surface wetting conditions has been studied by calculating the wall heat flux and evaporative mass flux. The results obtained in this study show that heat transfer occurs more easily in cases of nanostructured surfaces than in case of flat surface. Difference in behavior of argon molecules during and after the evaporation process, that is, wall adsorption characteristics, has been found to depend on the surface wetting condition as well as on presence and configuration of nanostructure. A thermodynamic approach of energy balance shows reasonable agreement with the present molecular dynamics study. Keywords Evaporation, wettability, nanostructures, molecular dynamics simulation Date received: 14 November 2017; accepted: 13 August 2018 Introduction Enhancing phase change heat transfer during boiling, through the use of nanostructures, has been a topic of great interest among researchers in recent times. This study of boiling of thin liquid layer on a solid surface has applications such as nanoelectronics, nanoelectronics cooling, and thermal management. Using nonequilibrium molecular dynamics (NEMD) simulation involving nanostructured surface with different patterns, sizes, and shapes that could influence the behavior of boiling phenomena at the nanoscale level can be explored. The heterogeneous phase transition of liquid has become the center of attention for molecular dynamics (MD) studies. Maroo and Chung 1 conducted MD simulation of argon platinum system to explore thin-film evaporation and colloidal adsorption features. Morshed et al. 2 described the effect of cylindrical nanostructures on phase change characteristics of thinfilm liquid argon laid over platinum wall. This study has confirmed that the phase change as well as heat transfer rate can be substantially improved with inserted nanostructures over the flat solid surface. Geometry and shape of the nanostructures also have significant effect on the heat transfer rate as reported by Seyf and Zhang. 3 They revealed that larger nanoparticles increased the rate of heat transfer during Department of Mechanical Engineering, Bangladesh University of Engineering & Technology (BUET), Dhaka, Bangladesh Corresponding author: Mohammad Nasim Hasan, Department of Mechanical Engineering, Bangladesh University of Engineering & Technology (BUET), Dhaka 1000, Bangladesh. nasim@me.buet.ac.bd

2 84 Proc IMechE Part N: J Nanoengineering and Nanosystems 232(2-3) boiling. Wang et al. 4 studied thin-film liquid boiling on aluminum nanostructured substrate through MD simulation with the conclusion that heat transfer enhancement occurs as the height of the nanopost increases up to some critical value after which it starts to decrease. Yamamoto and Matsumoto 5 performed MD study on initial stage of nucleate boiling. Yu and Wang 6 focused on evaporation characteristics of thin-film liquid argon and evaluated the net evaporative mass flux. Plawsky et al. 7 described evaporation enhancement using structure in microlevel and nanolevel. Diaz and Guo 8 employed MD simulations to study pool boiling heat transfer of thin-film liquid argon on a flat, horizontal copper wall with and without vertical nanoscale pillars with particular emphasis on the efficacy of phobic/philic nanopatterning for boiling heat transfer enhancement during nucleate as well as explosive boiling. Using MD simulation, Li et al. 9 studied nanoscale vaporization and condensation process of a fluid confined between two parallel walls (one is being at constant higher temperature while another is kept at constant lower temperature to induce vaporization and condensation, respectively). They considered two different wall superheats of the hot wall along with cuboid nanostructures placed at the cold wall in order to examine the effect of nanostructure on the condensation process. Bubble generation on a platinum substrate has been reported by Hens et al. 10 with particular focus on the surface pattern. These studies have established that changing of the surface chemistry as well as surface topography in microscale and nanoscale can be used to vividly impact phase change process. This study covers the NEMD simulation of thin-film liquid argon laid over solid platinum surface with or without embedded nanostructure. Nanostructure in the form of rectangular post/rib is placed through across the substrate wall. Three different heights of the rectangular post have been considered to get different configurations of nanostructured surface for two different wall fluid interaction strengths that describe both hydrophilic and hydrophobic surface conditions, based on the study of Hens et al. 10 Simulation method The schematic of the simulation domain used in present MD study is shown in Figure 1. As shown in Figure 1, the lowest segment of the simulation domain is the solid platinum wall over which both the liquid argon and vapor argon atoms coexist. The cuboid simulation domain has a dimension of 7.34 nm in both the x and z directions, and 70.0 nm in the y direction. The solid platinum wall located at the bottom of the simulation domain, consisted of eight monolayers of atom. The bottom atomic layer of the wall was kept fixed to avoid migration of atoms from the simulation box. The immediate two atomic layers above it were set to act as heat source while the next five atomic layers are used Figure 1. Schematic of the simulation domain. Figure 2. Wall configurations adopted in this study: (a) flat surface and (b d) nanostructured surfaces (all dimensions are in nm). to transfer heat to the overlying liquid argon. The platinum atoms were arranged in face-centered cubic (FCC) (1 0 0) lattice structure corresponding to its density of kg/m 3 at 90 K. The liquid argon film laid over the platinum wall is 3.01 nm thick and arranged with a lattice constant corresponding to liquid argon density, kg/m 3 at 90 K. Above the liquid argon film, it is the vapor argon region where 400 argon vapor atoms reside. The total number of atoms in the system varied from 9894 to 12,398 for different nanostructure configurations (surface-1, surface-2, and surface-3) depending on the height of the rectangular nanoposts placed above the substrate wall as shown in Figure 2 with summary mentioned in Table 1. Lennard-Jones potential 11 was used to evaluate the interaction potentials between the atoms and the intermolecular forces s 12 fðþ=4e r r s 6 r ð1þ

3 Hasan et al. 85 Table 1. Various wall configurations adopted in this study. Surface configuration Flat surface 0 Surface Surface Surface Nanopost height (nm) Table 2. Energy parameter and length potential of associated molecules. 2,6. Combination Energy potential, e (ev) Ar-Ar Pt-Pt Ar-Pt (hydrophilic) (hydrophobic) Length potential, s (nm) Here, e and s represent the energy parameter and the length parameter, respectively. Their values for different atomic combinations are tabulated in Table 2. Two different surface wetting conditions has been assumed in this study by changing the wall fluid interaction strength, e Ar-Pt following Hens et al. 10 For e Ar- Ar \ e Ar-Pt, surface was considered hydrophilic and for e Ar-Ar. e Ar-Pt surface was considered hydrophobic by Hens et al. 10 Based on this definition in this study, e Ar- Pt = ev (e Ar-Pt / e Ar-Ar = 2) has been considered to represent the hydrophilic surface case, while e Ar- Pt = ev (e Ar-Pt / e Ar-Ar = 0.5) has been considered to represent the hydrophobic surface case. All computations are made with a cut-off distance of 4s Ar-Ar. Similar values of cut-off distance are considered in the contemporary literature. 2,6 Velocity Varlet algorithm with 5 fs time step has been employed to integrate the equation of motion for every particle. Due to the planer characteristics of the present problem, periodic boundary conditions (PBCs) were used in the x and z directions and a simple non-periodic fixed boundary condition is applied in the y direction with adiabatic and elastic boundary at the top. This set of boundary condition is necessary as the present simulation is conducted in microcanonical (NVE ensemble) framework where the total number of atoms, total energy, and total volume must be conserved. The simulation was performed in three steps. Initially, the Langevin thermostat was turned on and the entire simulation system (both wall and the fluid) was set at a uniform temperature of 90 K. With this condition in place, simulation was run for 1 ns. After that, the Langevin thermostat was turned off, and the system was allowed to reach equilibrium for another 1 ns. To check the thermodynamic equilibrium of the system, variation of system properties such as temperature, energy, pressure, and density profile of argon atoms were examined. The temperature of the argon and solid wall was found to be fluctuating around 90 K for all cases. The equilibrium of the liquid vapor system was also ensured by comparing the density profile of argon with the phase diagram of the Lennard-Jones system. 11 At the end of the equilibrium period, the Langevin thermostat of the wall was then set to rise at 130 K and maintained for the rest of the simulation period using NVT ensemble while the fluid domain was maintained in NVE ensemble in the said period. The simulations were run in this condition for a time period of 5 ns. Necessary simulations of this study were performed using LAMMPS (large-scale atomic/molecular massively parallel simulator) 12 while the required post-processing has been carried out using visual molecular dynamics (VMD). 13 Results and discussion At the end of the equilibration period, as the temperature of the solid wall is abruptly increased from 90 K to 130 K, liquid argon starts heating and argon atoms enter the vapor region as individual atoms from the liquid vapor interface in both cases of hydrophilic and hydrophobic surfaces. Thus, evaporation takes place as shown in the snapshots of the simulation domain of Figure 3. For the case of flat surface, hydrophilic surface condition offers faster evaporation than hydrophobic cases as indicated by the presence of much liquid argon atom near the wall by the end of simulation period (7 ns). The presence of nanostructure in both surface wetting conditions are found to hook up liquid argon atoms around them as shown in Figure 3. The temperature history of the argon atoms for hydrophilic and hydrophobic wetting case has been depicted in Figures 4 and 5, respectively. The argon temperature reaches 130 K very quickly and remains steady after 3 ns for all surface configurations with hydrophilic wetting condition. It is also noticeable that the temperature reaches 130 K quicker in case of nanostructured surfaces than in case of flat surface. With the increase in the height of nanostructure, the time to achieve steady state temperature for argon decreases as evident in Figure 5. This is due to the increased heat transfer rate through nanostructured surfaces. On the contrary, the temperature reaches 130 K rather slowly for hydrophobic surfaces. This again proves that, of the two types of wettability considered, hydrophilic surface transfers energy at a much quicker rate. Variation of argon temperature profile with of nanostructure height for hydrophobic cases as depicted in Figure 5 also follows the same trend as hydrophilic cases. The pressure history of the simulation domain for hydrophilic and hydrophobic surfaces is shown in Figures 6 and 7, respectively. Since, the volume of the system is constant, with the increase in the temperature; pressure also increases in both hydrophilic and hydrophobic cases. In case of hydrophilic surfaces, as seen from Figure 6, this pressure reaches an equilibrium level around the time the temperature became steady in Figure 4 and remains

4 86 Proc IMechE Part N: J Nanoengineering and Nanosystems 232(2-3) Figure 3. Atomic distribution in the simulation domain for hydrophilic (left column) and hydrophobic (right column) case for different surface configurations: (a) flat surface, (b) surface-1, (c) surface-2, and (d) surface-3. steady after that. It was also noted that, on nanostructured surfaces, this equilibrium was reached earlier than on the flat surface. This is also in agreement with the temperature curve of Figure 4 discussed above. In case of hydrophobic surfaces, as seen in Figure 7, the pressure continues to rise and no steady equilibrium level is identified. This corresponds with the observation from Figure 5 where the temperature does not seem to reach steady equilibrium until much later in the simulation period. Figure 8 shows the number density profiles of argon inside the simulation domain at three different instances of time say t = 3, 5, and 7 ns, for both hydrophilic and hydrophobic surfaces. The number density value is

5 Hasan et al. 87 Figure 4. Argon temperature rise for hydrophilic surface condition. Figure 7. Variation of system pressure for hydrophobic surface condition. Figure 5. Argon temperature rise for hydrophobic surface condition. Figure 6. Variation of system pressure for hydrophilic surface condition. greatly reduced with increasing height in the y direction from the substrate wall. This is in agreement with the snapshots displayed in Figure 3. A careful observation of Figure 8, reveals out that for hydrophilic surface wetting condition, the spatial number density profiles does not change much for different surface configurations between times instant 3 and 5 ns. This is an indication that the evaporation reaches in some equilibrium condition. Meanwhile, for hydrophobic surface wetting condition, the spatial number density profiles continue to change in the same time interval, which means evaporation still continues. Careful look at Figures 6 and 7 readily reveal the fact that the spatial number density in the system domain assumes higher values for hydrophobic surface wetting condition than hydrophilic surface wetting condition at any time for nanostructured surface configuration. The reason behind these phenomena is the formation of Non-evaporating layer in case of hydrophilic surface wetting condition. Non-evaporating layers form when liquid atoms adjacent to the heated solid surface stick with the surface. From Figure 3, it was observed that, on hydrophilic surfaces, as the height of the nanostructures increased, thus increasing the heated solid surface area, more argon atoms got attached to the solid walls and formed the nonevaporating layers. This happens exclusively on hydrophilic surfaces, because hydrophilic surfaces have higher solid liquid interaction potential. On hydrophobic surfaces, no such non-evaporating layers are formed, as these surfaces have lower solid liquid interaction potential. This contrast between hydrophobic and hydrophilic surfaces is demonstrated in Figure 9, with a closer look on the evaporating surfaces. Since there is no evaporating layer, there are more argon molecules in the vapor region for hydrophobic surfaces, as evidenced by Figure 3. In hydrophilic wetting condition, more argon molecules get stuck to the solid surface due to higher wall fluid interaction strength. This can also be inferred in the plots of Figure 8(b) and (c). At time instants of 5 and 7 ns, the number density distribution beyond 10 nm in the y direction is much higher for hydrophobic case in comparison to its hydrophilic counterpart. More molecules in the vapor region thus lead to higher number density. Figures 9 and 10 show the net evaporation number (i.e. the number of atom leaving the liquid film to the vapor region) in case of hydrophilic and hydrophobic surfaces, respectively. The net evaporation number increases initially with time for both surfaces. But for hydrophilic surface, this increase is faster and becomes steady after a while, whereas for hydrophobic surfaces, the increase is slower and simply keeps increasing with time. As mentioned earlier, the increase in the nanostructure size increases the rate of temperature rise for solid surfaces. This faster rate of temperature rise results in

6 88 Proc IMechE Part N: J Nanoengineering and Nanosystems 232(2-3) Figure 8. Instantaneous number density profile of argon inside the simulation domain for hydrophilic (left column) and hydrophobic (right column) surface: (a) 3, (b) 5, and (c) 7 ns. Figure 9. Evaporation characteristics for hydrophilic surface wetting condition. Figure 10. Evaporation characteristics for hydrophobic surface wetting condition. faster increase in net evaporation number for nanostructured surfaces 1, 2, and 3, as can be seen in Figure 9. The increase in the nanostructure height from 1.5 to 3 nm results in faster evaporation for both hydrophilic and hydrophobic wetting conditions; however, as the nanostructure height increases from 3 to 4.5 nm, evaporation rate decreases for both hydrophilic and hydrophobic surfaces as shown in Figure 9. Regarding the height of nanostructure, it is noteworthy that embedded nanostructures not only facilitate the heat transfer rate but also result in relatively fewer liquid argon atoms over the nanostructured surface in

7 Hasan et al. 89 Figure 11. Adsorption characteristics of flat and nanostructured surfaces for hydrophilic and hydrophobic wetting condition at 7 ns: (a) flat surface, (b) surface-1, (c) surface-2, and (d) surface-3. Figure 12. Wall heat flux variation with time for hydrophilic surface wetting condition. Figure 13. Wall heat flux variation with time for hydrophobic surface wetting condition. comparison to that over flat surface. So evaporation process ceases much quickly in case of nanostructured wall than the flat wall case. Moreover, with higher nanostructure height, more atoms get attached with them in case of hydrophilic surface (wall/fluid interaction is more dominating), resulting thick Non-evaporating layer, while in case of hydrophobic surface, enhanced heat transfer causes the argon atoms to get away from the surface (wall/fluid interaction is less dominating), resulting in much argon atoms in the vapor region. So, we have different adsorption characteristics for nanostructured hydrophilic and hydrophobic surfaces that have been depicted in Figure 11. Figures 12 and 13 show the wall heat flux profiles in case of hydrophilic and hydrophobic cases, respectively. These profiles follow trends which are similar to the previous studies, as discussed in the previous section. Addition of nanostructures increases the heat flux significantly, and with the increase in the height of the nanostructures, heat flux increases. For hydrophilic case, the value of maximum heat flux for nanostructured surface-3 (920 MW/m 2 ) is almost 1.7 times the value of maximum heat flux observed in case of flat surface (550 MW/m 2 ). However, for hydrophobic surfaces, the value of maximum heat flux in case of nanostructured surface-3 (700 MW/m 2 ) is three times the value of maximum heat flux obtained in case of flat surface (230 MW/m 2 ). So, from the heat flux point of view, the increase in the height of the nanostructures has been more effective in case of hydrophobic surface. Another important point to note is that, the values of the maximum wall heat flux for all cases under consideration are in order with the theoretical value of maximum possible of heat flux, q max,max as obtained by Gambill and Lienhard. 14 To have a deep insight of evaporation characteristics, the time-averaged mass flux from the wall has been calculated from the net evaporation number curves (as

8 90 Proc IMechE Part N: J Nanoengineering and Nanosystems 232(2-3) Table 3. Time-averaged evaporative mass flux for different surface configurations. Surface shown in Figures 9 and 10), and Table 3 demonstrates the evaporative mass flux for different parametric conditions considered in this study. It is quite clear that the mass flux increases significantly for the nanostructure-1 (nanopost height, 1.5 nm). But for other nanostructure configurations (nanopost height, 3.0 nm/ 4.5 nm), the mass flux seems to decrease. As the evolution of the non-evaporating layer tends to increase with the height of the nanostructure as discussed earlier, the enhancement of evaporation can only be observed up to an optimum height. After that, the effect of non-evaporating layer becomes more dominant, which reduces the average evaporative mass flux. It is noteworthy that Yu and Wang 6 and Nagayama et al. 15 have conducted studies on evaporation in hydrophilic confined nanochannels for lower wall temperatures of 110 and 120 K, respectively, while keeping the upper wall temperature at 100 K. The current investigation is done for one-end open nanostructure where evaporation is carried out at 130 K after equilibration at 90 K. The mass flux obtained from these studies follow a similar trend with our study. It should also be noted that the average mass flux and heat transfer are closely related. Equation (2) shows the theoretical relationship between them, where h fg is the latent heat of evaporation q therm = h fg m avg Time-averaged evaporative mass flux, m avg (kg/m 2 s) Hydrophilic Hydrophobic Flat surface Surface Surface Surface ð2þ A comprehensive summary of maximum wall heat flux (q max ), average wall heat flux (q avg ), and average thermodynamic boiling heat flux (q therm ) for different surface configurations as well as surface wetting conditions are presented in Table 4. Interestingly, in all cases q avg agrees reasonably with q therm. Conclusion MD simulation of nanoscale evaporation process of a thin-film liquid argon placed over a solid heated platinum surface with or without nanostructure (rectangular wall-through nanopost) has been conducted for two different wall fluid interaction strengths representing hydrophilic (good wetting) and hydrophobic (bad wetting) surface conditions. Different vaporization as well as absorption behaviors have been observed depending on surface wettability, as well as presence and size of nanostructure. The main outcomes of this study can be summarized as follows: 1. The effect of nanostructure height is more significant in case of hydrophilic surface and increase in the nanostructure height enhances the evaporation phenomena. Non-evaporating layer was found in case of hydrophilic surfaces having nanostructures, while for hydrophobic surfaces, no such layer was found. 2. Formation of Non-evaporating layer over nanostructured surface results in decrease in the evaporation rate and ultimately cessation of evaporation process in case of hydrophilic surfaces. This results in relative low spatial number density in the system domain for hydrophilic surfaces in comparison to for hydrophobic surfaces. 3. The heat flux profiles confirmed that the energy transfer rate is much higher in case of nanostructured surfaces. Also, the maximum heat flux increased more significantly for same nanostructure height in case of hydrophobic nanostructured surface (almost three times), than in case of hydrophilic surfaces (less than two times). 4. The time-averaged evaporative mass flux for hydrophilic surfaces is much higher than hydrophobic surfaces. Inclusion of nanostructured surface enhances evaporation in certain case only. 5. Heat transfer enhancement due to the presence nanostructure have been found to dominate the adsorption characteristics in case of hydrophobic surface wetting condition (weak wall fluid interaction) as indicated by the presence of fewer fluid atoms near the wall at the end of evaporation while stronger wall fluid interaction (due to higher wall fluid interaction strength as well as larger Table 4. Heat flux characteristics from atomistic approach and thermodynamic approach. Surface Surface wetting condition Hydrophilic Hydrophobic q max (MW/m 2 ) q avg (MW/m 2 ) q therm (MW/m 2 ) q max (MW/m 2 ) q avg (MW/m 2 ) q therm (MW/m 2 ) Flat surface Surface Surface Surface

9 Hasan et al. 91 wall fluid interaction area) results in thicker nonevaporating layer in case of hydrophilic surface wetting condition. 6. Energy balance obtained from thermodynamic approach agrees reasonably with the present MD results. Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) received no financial support for the research, authorship, and/or publication of this article. References 1. Maroo SC and Chung JN. Molecular dynamic simulation of platinum heater and associated nano-scale liquid argon film evaporation and colloidal adsorption characteristics. J Colloid Interface Sci 2008; 328: Morshed AKMM, Paul TC and Khan JA. Effect of nanostructures on evaporation and explosive boiling of thin liquid films: a molecular dynamics study. Appl Phys A 2011; 105: Seyf HR and Zhang Y. Molecular dynamics simulation of normal and explosive boiling on nanostructured surface. J Heat Transfer 2013; 135(12): Wang W, Zhang H, Tian C and Meng X. Numerical experiments on evaporation and explosive boiling of ultra-thin liquid argon film on aluminum nanostructure substrate. Nanoscale Res Lett 2015; 10: Yamamoto T and Matsumoto M. Initial stage of nucleate boiling: molecular dynamics investigation. J Therm Sci Technol Jpn 2012; 7: Yu J and Wang H. A molecular dynamics investigation on evaporation of thin liquid films. Int J Heat Mass Transfer 2012; 55: Plawsky JL, Fedorov AG, Garimella SV, et al. Nanoand microstructures for thin-film evaporation a review. Nanosc Microsc Therm 2014; 18: Diaz R and Guo Z. A molecular dynamics study of phobic/philic nano-patterning on pool boiling heat transfer. Heat Mass Transfer 2017; 53: Li L, Ji P and Zhang Y. Molecular dynamics simulation of condensation on nanostructured surface in a confined space. Appl Phys A 2016; 122: Hens A, Agarwal R and Biswas G. Nanoscale study of boiling and evaporation in a liquid Ar film on a Pt heater using molecular dynamics simulation. Int J Heat Mass Transfer 2014; 71: Lennard-Jones JE and Devonshire AF. Critical phenomena in gases. I. Proc R Soc Lond A Math Phys Sci 1937; 163: LAMMPS user s manual. Sandia National Laboratories, (accessed 14 November 2016). 13. Humphrey W, Dalke A and Schulten K. VMD: visual molecular dynamics. J Mol Graph 1996; 117(1): Gambill WR and Lienhard JH. An upper bound for the critical boiling heat flux. J Heat Transfer 1989; 111: Nagayama G, Kawagoe M, Tokunaga A, et al. On the evaporation rate of ultra-thin liquid film at the nanostructured surface: a molecular dynamics study. Int J Therm Sci 2010; 49: Appendix 1 Notation Ar argon h fg Latent heat of vaporization (kj/kg) P pressure (bar) Pt platinum q w Wall heat flux (MW/m 2 ) q max Maximum wall heat flux (MW/m 2 ) q avg Time averaged wall heat flux (MW/m 2 ) q therm Thermodynamic boiling heat flux (MW/m 2 ) r distance between molecules (Å) t time (ns) T temperature (K) x coordinate in x direction y coordinate in y direction z coordinate in z direction e energy parameter of Lennard-Jones (LJ) potential (ev) u energy (ev) s length parameter of LJ potential (A )