MOLECULAR DYNAMICS STUDY OF CONTACT ANGLE EFFECT ON MAXIMUM CRITICAL HEAT FLUX IN NANO-PATTERNED POOL BOILING

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1 Proceedings of the 2nd Thermal and Fluid Engineering Conference, TFEC2017 4th International Workshop on Heat Transfer, IWHT2017 April 2-5, 2017, Las Vegas, NV, USA TFEC-IWHT MOLECULAR DYNAMICS STUDY OF CONTACT ANGLE EFFECT ON MAXIMUM CRITICAL HEAT FLUX IN NANO-PATTERNED POOL BOILING Ricardo Diaz 1, Zhixiong Guo 1* 1 Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA ABSTRACT Molecular dynamics (MD) simulations were employed to investigate the effect of wettability (via contact angle variation) on nanoscale pool boiling heat transfer of a liquid argon thin film on a horizontal copper substrate topped with cubic nano-pillars. The liquid-solid potential was incrementally altered in order to vary the contact angle between hydrophilic (θ~63 ) and super hydrophobic (θ~155 ), and the resulting effect on heat transfer was observed. For each contact angle the superheat was gradually increased to initiate nucleate boiling and eventually pass the critical heat flux (CHF) into the film boiling regime. Results indicate that the maximum CHF is achieved on a somewhat hydrophobic substrate (θ~ ). The data indicates that there is a quadratic relationship between CHF and contact angle, and an optimal contact angle exists that is neither super hydrophilic nor super hydrophobic. As the contact angle increases the superheat required to reach the CHF condition also increases. KEY WORDS: MD simulation; Pool boiling; CHF; Nano-patterning; Liquid argon; Heat transfer. *Corresponding Author: guo@jove.rutgers.edu 1. INTRODUCTION Heat transfer on the micro- and nano-scales continues to be a vital area of research due to the everdecreasing size of electro-mechanical devices and the accompanying increases in power density resulting from the technological advances of the last decade [1-4]. As applications with large power densities increase it will be extremely important to remove excess heat as efficiently as possible. Boiling heat transfer on micro/nanoscale substrates, which has the capacity for rapid large heat flux removal, is an excellent candidate for such applications but requires further research in order to better understand the heat transfer process and mechanism at these small scales. In particular, pool boiling heat transfer enhancement has long been investigated both experimentally and numerically as a means of meeting the high heat flux removal requirements. Various methods of enhancement, including the use of micro/nano-structures, nanofluids, and hydrophilic/phobic substrates, have been employed and their effects on heat transfer have been studied. Recent advances in micro- and nanoscale fabrication techniques have allowed for better customization of substrates via micro/nano-channels, nanostructures, etc. These enhanced topologies passively increase boiling heat transfer via increased surface area and bubble nucleation sites [5-7]. Wang et al. [8] showed that altered bubble dynamics due to micro/nanostructures could also improve critical heat flux (CHF). Cooke and Kandlikar [9] also showed that adding micro-channels to the substrate surface improves the heat transfer coefficient by promoting wetting of the surface and preventing dry out. Nanofluids have also been 1

2 investigated in pool boiling, and shown to improve CHF via enhanced fluid conductivity, surface wetting, and nanoparticle deposition on the substrate, which increases surface roughness [10-12]. Micro-convection via Brownian motion and nanoparticle aggregation have also been postulated as CHF enhancement mechanisms in nanofluid pool boiling [13]. More recently hydrophobic/philic patterning has been investigated experimentally [14-15] and shown to increase bubble nucleation and CHF via increased wetting. After enhancement, several of the pool boiling experiments mentioned have attained heat fluxes greater than 10 kw/cm 2, which is adequate for many electronics cooling applications. The effect of liquid contact angle on CHF has also been investigated in milli-scale experiments [16-17], and others [18-19] proposed correlations for pool boiling CHF that incorporated contact angle, amongst other variables. In general these studies showed that CHF is adversely affected by large contact angles (hydrophobicity), while smaller (hydrophilic) contact angles increase the heat transfer coefficient and improve CHF. It is difficult, however, to perform these types of experiments on the nanoscale while controlling for a number of different variables. On this small a scale larger bubble sizes (radii >= 1 micrometer) are not allowed to form, and the dynamics and heat transfer mechanisms can be very different. Thus in this study Molecular Dynamics (MD) simulations have been utilized to investigate the effect of equilibrium contact angle on CHF. MD simulation is a powerful tool that can be used to investigate nanoscale phenomena with more flexible control than experimental setups [20]. In this study, the substrate topology (roughness), temperature, and pressure were all controlled in order to more clearly view the effect of contact angle on the CHF condition. To date many MD studies have been conducted on both homogeneous and heterogeneous systems in order to investigate heat transfer, phase change, flow properties, etc. Several studies have used flat substrates to investigate evaporation, effect of wettability, etc. [21-23] and there have recently been some studies focused on boiling/evaporation on nano-structured substrates using differently shaped nano-structures and nano-structures with different wettability [24-27], though to the authors knowledge no MD study has been conducted looking at critical heat flux variation with contact angle. In this study, a nanostructured copper substrate is used to heat a liquid argon film. Eight different scenarios were investigated, each with different contact angles ranging from super hydrophilic to super hydrophobic. Simulation of these six arrangements has allowed us to compare the critical heat flux and evaporation characteristics of each to determine heat transfer trends, and investigate mechanisms by which the heat transfer enhancements take place. 2. SIMULATION METHOD The system used in the main simulations was comprised of a horizontal solid copper wall with four vertically oriented nano-pillars, a layer of liquid argon, and argon vapor molecules in a simulation box measuring x x 440 Angstroms (Å). Figures 1 (a), (b) and (c) detail the overall configuration of the simulation box and the enlarged views of the copper wall and nano-pillars, respectively. The wall at the bottom of the simulation box consisted of a base of five monolayers of solid copper totaling 4,000 atoms. As in previous works, this was deemed enough to accurately act as a conduction layer for liquid heating [24, 28-29]. The four nano-pillars were arranged on the base wall in a symmetrical fashion. The nano-pillars were fifteen monolayers high and each measured 25.3 x 25.3 x 25.3 Å. The base wall and nano-pillars totaled 15,160 atoms, and were arranged in an FCC lattice structure corresponding to the (100) plane. For these copper atoms a lattice constant of Å was used, corresponding to a density of 8.9 g/cm 3. Fifteen monolayers of argon molecules were placed just above the copper base wall, covering both the wall and pillars. For the argon liquid atoms a lattice constant of Å was used, corresponding to an initial density of 1.4 g/cm 3. Finally, 342 argon atoms (corresponding to a density of 5.77x10-3 g/cm 3 ) were placed above the liquid, filling the rest of the simulation box. 2

3 (b) (a) (c) Fig. 1 Sketch of simulation model: (a) overall simulation configuration (b) and (c) enlarged views of the copper substrate and nano-pillars. Units: Å Interactions between all atoms were modeled with the standard 12-6 Lennard-Jones potential [30], given by: σ E = 4ε r 12 σ 6 r, for r < r c (1) where ε is the potential well depth, σ is the characteristic length at which the potential becomes zero, r is the interatomic length, and r c is the cut-off distance. The r -12 term governs short-range repulsion, while the r -6 term describes long-range attraction. To reduce the computational cost an r c equal to 4σ Ar-Ar was employed. For interactions between two atoms i and j, it follows that 3

4 σ ij = 1 ( 2 σ i +σ j ) and ε ij = ε i ε j (2) Before the main CHF simulation runs, separate simulations were first carried out using altered interaction potential parameters in order to establish the different contact angles. The ε Cu-Ar interaction value for the 106 o contact angle (i.e. ε Cu-Ar = ev) was calculated via the normal Lorentz-Berthelot mixing rules of Eq. (2), however for most cases the Cu-Ar potential well depth was altered in order to change the interaction strength, and consequently the contact angle. The altered potential well depth is calculated as follows: ε Cu Ar = f ε Cu ε Ar (3) where f is a user-chosen numerical factor. Each case is meant to simulate a copper substrate with altered wetting characteristics (via surface modification, coatings, etc.). Table 1 details the potential parameters and the resulting contact angles of 63 o, 75 o, 88 o, 106 o, 124 o, and 146 o. A smaller ε value indicates a weaker, or more hydrophobic, interaction (i.e. a larger contact angle). For clarity, each case will be referred to with a CA followed by its contact angle value, i.e. CA-63, CA-75, etc. Table 1 Potential well depth parameters and resultant contact angles Case f ε Cu-Ar (ev) Contact Angle (deg) CA CA CA CA CA CA CA CA The separate contact angle simulations were performed on a flat copper substrate with the same dimensions as the substrate used in the CHF simulations. A block of 1,470 liquid argon particles 36.8 Å 3 was initially placed just above the substrate while argon vapor atoms filled the rest of the simulation box. The simulation was run for 3.5 ns with a 5 fs time step while a Langevin thermostat was applied in order to keep all atoms at 60K. In order to calculate the resulting contact angle, the simulation domain was first divided into a grid of boxes 2 Å per side, and the average density was monitored in each and written to a file every 250 ps. The last four data points were then averaged to determine the final density profile, an example of which is shown in Figure 2. As in ref. [31] a small portion of the liquid region near the wall was excluded to remove any influence of the copper wall on the contact angle calculation. Once the profile was calculated, an algebraic circle fit was used to estimate the droplet boundary as well as its intersection with the horizontal substrate. With the circle and intersection point defined, a contact angle could be calculated. 4

5 Fig. 2 Density map of the CA-155 simulation. After the contact angles were established, the CHF simulations were carried out in two phases. Phase I consisted of initialization and equilibration, and was itself broken down into three subphases. First an energy minimization was carried out to determine the minimum energy state of the initial configuration. Once completed, a Langevin thermostat was imposed for on all atoms to establish an equilibration temperature of 90K. After 3 ns the thermostat was removed, and the system was allowed to evolve under the microcanonical ensemble (NVE) for an additional 1 ns. Once the system temperature and energy are stable, Phase II commences and the temperature of the system is steadily increased from 90K to 300K over the course of 7.5 ns (not including the previous 4 ns of Phase I). In this phase the Langevin thermostat was applied to only the second monolayer of the copper base wall, while the first layer was kept immobile to prevent atoms from moving through the bottom of the simulation domain. The rest of the atoms were maintained in the NVE ensemble and allowed to interact as they normally would via the Lennard-Jones potential. Both phases used a velocity Verlet integration algorithm with a 5 fs time step. The simulation domain is periodic in the four sidewalls of both the x and y directions, which helps to prevent finite size effects of the small simulation domain. Per the authors previous work [27] the size of the simulation is suitable, i.e. a larger simulation domain/number of atoms would result in no significant differences in pressure, temperature, or density. The top of the simulation domain is a fixed, adiabatic boundary, which means that any atom that moves outside the boundary by a certain distance is placed back inside the boundary by that same distance, while having the sign of its z velocity reversed. All simulations were run using LAMMPS software (version 16 Feb 2016), a classical molecular dynamics code based on Plimpton s work [32], while system visualization was performed with VMD v1.9.1 [33]. 3. RESULTS AND DISCUSSION During Phase I equilibration the average pressure was monitored in order to determine system stability. The equilibration is meant to take place at atmospheric pressure conditions, while during Phase II the pressure is allowed to evolve as it normally would in a closed system. Figure 3 shows 5

6 the vapor pressure of each case for both Phase I and II. As can be seen, most cases maintain a pressure of about 1 bar during the 4 ns of Phase I before showing a relatively steady pressure increase during Phase II. Cases CA-63 through CA-132 are grouped together until roughly 6 ns, when a slight separation occurs. A short time after this point the two most hydrophobic cases, CA- 144 and CA-155, maintain the highest vapor pressure, while the other cases pressures decrease with decreasing contact angle. In general however, all pressures rise at the same rate during the latter stage of the simulation. Vapor Pressure (bar) CA-63 CA-75 CA-88 CA-106 CA-124 CA-132 CA-144 CA Time (ns) Fig. 3 Argon vapor pressure evolution. Figures 4 (a) and (b) show the temperature history for copper and argon respectively. As expected, the copper temperature is virtually the same for all cases, and after the equilibration at 90K it rises linearly to 300K over the duration of the simulation. The argon temperature follows a similar path, however at around 6.5 ns it begins to follow the copper temperature less closely (there is a 10-20K lag between the copper and argon temperatures) and some separation between the different cases emerges. This is due to the onset of the CHF condition for the various cases, as will be seen in later figures. At the CHF points for CA-106 (~6.2 ns), CA-124 (~6.5 ns), and CA-132 (~6.8 ns) these cases have a slightly higher temperature than the other cases, however by the end of the simulation they have the lowest, excluding the two most hydrophobic cases CA-144 and CA-155. This is most likely due to these two cases reaching their CHF condition at a slightly higher wall temperature than the other cases, before experiencing a more rapid heat flux decline due to stronger vapor layer formation. Each case exhibits this slight increase in temperature rate corresponding to its CHF condition. 6

7 Temperature (K) CA-63 CA-75 CA-88 CA-106 CA-124 CA-132 CA-144 CA Time (ns) Temperature (K) CA-63 CA-75 CA-88 CA-106 CA-124 CA-132 CA-144 CA Time (ns) Fig. 4 Temperature history for a) Copper and b) Argon. Figures 5 and 6 show the density during Phase II and the evaporation number for both phases, respectively. To calculate the density, the simulation domain was divided into boxes encompassing the entire x and y directions and 7.9 Å in the z-direction, and the average density in each box was recorded every 10 ps. The density measurements for all cases were restricted to the liquid region (i.e. less than or equal to 50 Å). Separation is apparent from the very beginning of Phase II, with stronger interaction potentials (i.e. lower contact angles) predictably resulting in higher densities. The separation decreases as each case nears its CHF point, with all but the most hydrophobic cases having a density near 0.9 g/cm 3 at 5.9 ns. The density curves begin as somewhat linearly decreasing, and then move to a region of exponential decrease as the CHF is approached before 7

8 transitioning back to a linear decrease after the CHF. In a macro sense this exponential density decrease is due to the sharp increase in nucleation rate that accompanies the CHF condition [34]. While the small-scale nature of these simulations makes it difficult to directly observe bubble nucleation, the rate of phase change from liquid to vapor can be viewed via the evaporation ratio, shown in Figure 6. This shows the ratio of the evaporation number at a certain time to the initial number of vapor atoms within the liquid region. To distinguish between liquid and vapor atoms a criteria based on coordination number [27] was used, where any argon atom surrounded by less than 12 other atoms (within a radius of 5.3 Å) is considered a vapor atom. In this way the number of liquid and vapor atoms can be tracked and compared between cases. As can be seen, within the liquid there is indeed a spike in the number of evaporated argon atoms coinciding with the CHF near 6 ns, with the CA-132 case having the largest number. It seems that this interaction potential strength promotes the most liquid-to-vapor phase change. Density (g/cm 3 ) CA-63 CA-75 CA-88 CA-106 CA-124 CA-132 CA-144 CA Time (ns) Fig. 5 Phase II density profile. The CHF curve is shown in Figure 7. The total energy (kinetic and potential) of the argon atoms was tracked each time step, then divided by the time step size and surface area of the substrate to calculate the heat flux. Interestingly, both the CHF and the temperature at which the peak flux occurs tend to increase with increasing contact angle up to a point, after which the CHF begins to decrease. The CA-124 and CA-132 cases showed virtually the same CHF (~1.52x10 8 W/m 2 ), which is ~23% higher than that of CA-155 (1.17x10 8 W/m 2 ) and ~14% higher than that of CA-63 (~1.30x10 8 W/m 2 ). The CA-124 and CA-132 peaks again occur at a temperature ~20K higher than that of CA-63, but ~30K less than CA-155. After the peak flux the difference between cases gradually decreases, and by the end of the simulation (well into the explosive boiling regime) there is only a ~2.5% difference between the maximum and minimum values. These fluxes are in line with previous simulations [35], as well as the heat flux limit predicted by evaporative kinetic theory [36]. 8

9 Evaporation ratio (liquid region) CA-63 CA-75 CA-88 CA-106 CA-124 CA-132 CA-144 CA Time (ns) Fig. 6 Evaporation ratio (in the liquid region, z<50 Å). Heat Flux (10 7 W/m 2 ) Heat Flux (10 7 W/m 2 ) Temp (K) CA-63 CA-75 CA-88 CA-106 CA-124 CA-132 CA-144 CA Temperature (K) Fig. 7 CHF curve (Argon heat flux vs. copper temperature). At very low superheats the lower contact angle cases are somewhat favored, however near the CHF the larger contact angle cases emerge with higher fluxes. Although the CHF increases with increasing contact angle, the rate of increase slows as the contact angles become larger, before eventually decreasing. This decrease would be due to the weakening interaction between liquid and substrate no longer allowing efficient kinetic energy exchange. Figure 8 shows this via a plot of the peak flux as a function of contact angle. This seems to be at odds with previous experimental and 9

10 theoretical studies [15,18,37] in which more hydrophilic substrates produced higher flux values, however these investigations were on a more macro length scale. The results of the nanoscale simulations performed in this study might be expected to differ from larger scale work given the different scale of forces/altered dynamics, especially considering the lack of any macro bubble nucleation. Indeed, the critical bubble radius based on the Young-Laplace equation is 20Å and is thus comparable to the film thickness and nano-pillar pitch. This makes it difficult to nucleate stable bubbles to facilitate heat exchange Peak Heat Flux (10 7 W/m 2 ) Peak Flux Contact Angle (deg) Fig. 8 Peak heat flux vs. contact angle 4. CONCLUSION Pool boiling of a thin liquid argon film on a nanostructured copper substrate was investigated via MD simulation. After obtaining CHF curves based on varying contact angle, and monitoring temperature, density, pressure, and evaporation the following observations were made: - It was found that there exists a contact angle that maximizes peak CHF, located in a Goldilocks zone that both promotes phase change via kinetic energy transfer and allows vapor nuclei to escape the liquid film to be replaced by other less energetic atoms. - This is corroborated by the density and evaporation data, which show a higher evaporation ratio and steeper drop in density in the liquid film region for the CA-132 case. - The CA-124 and CA-132 cases showed the highest CHF at a value of 1.52x10 8 W/m 2, which is 14% higher than the CA-63 case, and 23% greater than the super hydrophobic CA- 155 case. - Based on the CHF/contact angle data, the optimal angle for this geometry was determined to be ~124 o -132 o. This is inconsistent with some previous studies that show enhanced CHF for more hydrophilic surfaces, however for the nanoscale investigation here the lack of true bubble nucleation and associated bubble dynamics alters the heat transfer mechanisms. - The temperature at which CHF occurs (and thus the degree of superheat) also increases with increasing contact angle. 10

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