Dropwise Evaporative Cooling of Heated Surfaces with Various Wettability Characteristics Obtained by Nanostructure Modifications
 Jiannan Chen^{1},
 Zhen Zhang^{2},
 Xiaolong Ouyang^{1} and
 Peixue Jiang^{1}Email author
Received: 3 February 2016
Accepted: 7 March 2016
Published: 22 March 2016
Abstract
A numerical and experimental investigation was conducted to analyze dropwise evaporative cooling of heated surfaces with various wettability characteristics. The surface wettability was tuned by nanostructure modifications. Spraycooling experiments on these surfaces show that surfaces with better wettability have better heat transfer rate and higher critical heat flux (CHF). Single droplet impingement evaporative cooling of a heated surface was then investigated numerically with various wettability conditions to characterize the effect of contact angle on spraycooling heat transfer. The volume of fluid (VOF) model with variabletime stepping was used to capture the timedependent liquidgas interface motion throughout the computational domain with the kinetic theory model used to predict the evaporation rate at the liquidgas interface. The numerical results agree with the spraycooling experiments that dropwise evaporative cooling is much better on surfaces with better wettability because of the better liquid spreading and convection, better liquidsolid contact, and stronger liquid evaporation.
Keywords
Background
Gordon Moore proposed that the transistor density on chips will double every 2 years in 1965 [1]. This classical Moore’s Law has been accurate for the last four decades. The tremendous enhancement in chip functionality, e.g., higher transistor density, higher speeds, and more sophisticated functions, have resulted in increasing amounts of heat generated per unit chip surface area. More effective cooling schemes are needed for many industrial applications, such as electronic systems, highenergy lasers, and aerospace satellites. Phase change cooling schemes have attracted the most attention because of the large latent heats of the liquidvapor phase change. Spray cooling, with its high heat dissipation capability, precise temperature control, low cost, and reliable longterm stability, has played an important role in high heat flux applications as one of the most promising thermal management methods. Heat fluxes in excess of 1000 W/cm^{2} can be removed from surfaces using water spray cooling at low coolant flow rates with low superheats [2].
Spraycooling heat transfer is influenced by many factors such as the droplet parameters [2, 3], nozzletosurface distance [4], inclination angle [5], and working fluid [6]. Surface morphology is another critical factor affecting the spraycooling heat transfer. Enhanced surfaces, such as millistructured surfaces [7] and micro structured surfaces [8], have been shown to effectively improve the heat transfer. As material science and nanofabrication technologies develop, nanostructured engineering surfaces are becoming more common. Nanostructured surfaces have shown different heat transfer performance for dropwise evaporative cooling. Zhang et al. [9] did spraycooling experiments with CNT films deposited on surfaces with the heat transfer rate improved by the better wettability. Alvarado and Lin [10] investigated single droplet cooling of nanostructured surfaces and observed lower minimum wall temperatures for similar heat fluxes, better heat transfer curves, and lower temperature gradients on the nanostructured surfaces than those on a bare surface. Thus, nanostructures can improve the heat transfer rate by effectively changing the surface wettability which directly affects the liquidvapor phase change process. This study experimentally investigates spraycooling heat transfer on surfaces with various wettability characteristics obtained by nanowire modification.
Spray cooling is affected by many factors with complex heat transfer mechanisms. The droplet parameters are the most important factor. The Sauter mean droplet diameter, the mean droplet velocity, and the droplet density are the three main droplet parameters. The inability to independently control the drop size, drop velocity, and mass flux makes it almost impossible to thoroughly investigate heat transfer mechanism experimentally [7]. Some researchers have studied spray cooling by proposing theoretical and numerical models of single droplet evaporative cooling by independently controlling the droplet parameters numerically. “Before predictions of the heat transfer to a spray can be determined, the fluid dynamics of a single droplet impacting a heated surfaces must be known” [11]. The heat transfer mechanism for how the surface wettability affects the spray cooling can be initially investigated using a numerical model of single droplet impingement cooling of heated surfaces with various wettability characteristics. The flow and evaporation of a single droplet on a surface have been studied extensively with most numerical models based on many assumptions and simplifications of the fluid flow [12, 13], droplet shape [14], and liquid evaporation [15]. The liquidgas interface tracking method and the liquidvapor phase change model are key parts of accurate simulations of droplet impingement cooling. In addition to the experimental study of spray cooling on surfaces with different wettabilities, this paper also presents a numerical study of droplet impingement evaporative cooling of surfaces with different wettabilities using the explicit volume of fluid (VOF) model with variabletime stepping to capture the timedependent liquidgas interface motion throughout the computational domain and the kinetic theory model to predict the evaporation rate at the liquidgas interface.
Methods
Experimental Investigation
SprayCooling System
Test Heater Fabrication
The heating sections were made of 7.4 mm × 7.4 mm, doubleside polished, 490μmthick silicon dies. Chromium, platinum, and titanium (thickness proportions of approximately 1:10:1) were applied to the bottom surface of the silicon dies using positive photoresist liftoff in a serpentine pattern with a total thickness of 241 nm. A 150nmthick PECVD SiO_{2} film was also added on top of the metals for electrical passivation. Four platinum heaters were arranged in serpentine patterns on the bottom surface of each silicon die to reduce the voltage input for safety considerations with each platinum resistance being 300~400 Ω. The SiO_{2} film and the titanium were removed on the eight pads by wet etching to expose the platinum before the silicon die was mounted on a temperatureresistant PCB circuit board. Eight 40μm gold wires connected the four platinum heaters with the circuit board by wire bonding. A DCstabilized voltage source was then used to supply power to the platinum heaters through the eight wires soldered to the circuit board. The currents in each wire were also measured so that the resistances of the platinum heaters could be calculated to determine the heater temperature. Thus, the serpentine platinum heaters acted as the heaters and RTDs. The heat flux was calculated by dividing the input power by the surface area. As the input power increased, surface temperature increased, and at a certain point, test surface temperature increased rapidly and the test sample was burning out. This point was defined as the critical heat flux (CHF) point.
Test Surface Modification
The surface wettability depends on both the surface morphology and the surface chemical energy, so the surface wettability can be tuned by changing these two parameters. Artificial structures are often fabricated on surfaces to change the surface morphology with nanostructures being especially favored.
ZnO nanowires were synthesized on the surface by hydrothermal methods to modify the surface wettability. Surfaces with different wettabilities were obtained by controlling nanowire size. The basic method and growth mechanisms were described by Xu and Wang [17]. A thin zinc metal film was deposited on top of the silicon die by magnetron sputtering as a seed layer for the ZnO growth. The growth solution was prepared by dissolving zinc nitrate hexahydrate (Zn(NO_{3})_{2} 6H_{2}O, 99 %) in deionized water as the source for the ZnO nanowires. Ammonia hydroxide (28 wt% NH_{3} in water, 99.99 %) was added to adjust the pH of the growth solution. Then, the hydrothermal ZnO nanowires were grown by suspending the silicon dies upside down in the growth solution. A variety of parameters such as the Zn^{2+} concentration, the pH, and the growth temperature was tuned to control the properties (mainly the nanowire lengths and diameters of the nanowires) of the final product.
Numerical Simulation
Conservation Equations

α _{ q } = 0: The cell is empty (of the qth fluid).

α _{ q } = 1: The cell is full (of the qth fluid).

0 < α _{ q } < 1: The cell contains the interface between the qth fluid and one or more other fluids.
Interface Conditions
The mass transfer at a liquidgas interface is essentially due to molecular movement. Above absolute zero temperature, every molecule has a certain kinetic energy which is directly related to the temperature. The kinetic energies of the molecules in a liquid are not the same for all molecules. Molecules in the liquid tend to remain together because they are bound to their neighbors by intermolecular forces. At a liquid and air interface, the liquid molecules have less neighbors than those inside the liquid. Therefore, the bond to their neighbors is not as strong as that inside the liquid. Molecules with relatively high kinetic energies can then escape from the liquid into the air. Molecules in the vapor phase move at relatively high velocities and sometimes collide with each other. Some of the vapor molecules may also return into the liquid when they collide with the interface while others are reflected back into the air. Evaporation occurs when the number of the molecules escaping from the liquid is larger than the number of molecules entering the liquid.
Source terms appearing in conservation equations
Equations  Source terms 

VOF (liquid phase)  S _{ αl } = −m′′′ 
VOF (gas phase)  S _{ αg } = m′′′ 
Momentum  \( {S}_m=\left(12{\alpha}_l\right){m}^{\prime \prime \prime}\overrightarrow{v} \) 
Energy  S _{ e } = −m′′′h _{ fg } 
Species (vapor)  S _{ i } = m′′′ 
Solution Method
The commercial CFD software Ansys Fluent 13 was used to perform the numerical simulations. Ansys Fluent uses the control volume method to discretize the governing equations on an unstructured grid. The secondorder upwind scheme was used to discretize the transport equations. The pressure values at the cell faces were obtained using the PRESTO! discretization scheme. The SIMPLEC algorithm was used for pressurevelocity coupling.
Numerical method validation
The numerical results are compared against experimental data in Fig. 5b. The numerical model accurately predicts the evaporation process, so this model can be used to simulate droplet flow dynamics, heat transfer, and evaporation.
Results and discussion
Experimental Results
Simulation Results and Discussions
Weber number and Ohnesorge number are often used to analyze droplet impact dynamics. Droplet impact dynamics is classified into four different regimes according to We and Oh [25]. In regime I, where We > 1 and Oh < 1, kinetic energy dominant motion prevails; in regime II, where We < 1 and Oh < 1, capillary force drives the motion; in regime III, where We < 1 and Oh > 1, capillary effect is dominant and the viscosity is also important; and in regime IV, where We > 1 and Oh > 1, kinetic energy dominates and the viscous force is important as well. In the present simulation, We = 23 and Oh = 0.0086, droplet impact dynamics is in regime I. As kinetic energy dominates in regime I, droplets may spread, recoil, oscillate, and even rebound depending on the surface characteristics.
The heat transfer rate is relatively small in the quasistatic evaporation phase compared to that in the dynamic forced convection phase as can also be seen in Fig. 12 when the slopes of the curves during the dynamic phase are larger than those in the quasistatic phase. The total heat transfer in the dynamic phase, however, is not large because the spreading lasts only tens of microseconds with more heat removed during the relatively long evaporation. This result can be used to explain the Estes and Mudawar spraycooling experiment [3] where the evaporation efficiency was higher with light sprays than with dense sprays, since the droplet evaporation needs a relatively long time and the droplets evaporate more in light sprays by avoiding the frequent impacts of other droplets.
Droplet impingement cooling on surfaces with better wettabilities has much better heat transfer rates as seen in Figs. 11 and 12. During the dynamic phase, the with better wettability has faster liquid spreading, stronger convection, and larger heat transfer areas that all increase the heat transfer.
The numerical results agree well with spraycooling experiments which show that dropwise evaporative cooling on surfaces with better wettabilities is much better because of the better liquid spreading and convection, better liquidsolid contact, and stronger liquid evaporation. The droplet impingement cooling simulations reveal the mechanisms for spray cooling of surfaces with various wettabilities based on simulations of a single droplet.
Conclusions
 1.
Nanostructures significantly affect the surface wettability. The spraycooling experiments show that surfaces with better wettability have higher heat transfer rates during the whole process and higher CHF. The experiments indicate that both the liquid forced convection and the liquid evaporation are enhanced for surfaces with better wettability.
 2.
The numerical simulations agree well with the spraycooling experiments which show that the dropwise evaporative cooling on surfaces with better wettability are much better because of the better liquid spreading and convection, better liquidsolid contact, and stronger liquid evaporation.
 3.
The numerical simulations give more detailed evidence to explain the experiment results. The droplet impingement cooling process is subdivided into a dynamic phase and a quasistatic phase. Surfaces with better wettabilities have faster spreading and larger maximum spreading radii which result in stronger liquid convection during the dynamic phase. Droplets on surfaces with worse wettabilities recoil more after their maximum spreading radii and even rebound from the surface. Surfaces with better wettabilities have large liquid wetting areas during the quasistatic phase, so the liquid evaporation is increased because of larger liquidvapor interfaces and thinner liquid films.
 4.
Marangoni convection in the droplets on surfaces with different wettabilities was also studied in the numerical simulations. A modified Marangoni number was presented to explain the simulation results showing that Marangoni convection is stronger inside droplets on a surface with smaller contact angles.
Nomenclature
CHF critical heat flux
D binary diffusion coefficient
D _{0} droplet diameter
E energy
\( \overrightarrow{F} \) surface tension body force
J _{ i } mass flux of molecules impacting the liquid surface
J _{ c } mass flux of molecules condensing onto the liquid
J _{ r } mass flux of molecules rebounding from the surface
J _{ e } mass flux of molecules evaporating from the surface
J _{ t } net liquid evaporation mass flux
m′′′ evaporation rate of unit cell
Ma Marangoni number
Oh Ohnesorge number = \( \mu /\sqrt{D_0\sigma \rho } \)
P _{ v } vapor partial pressure
P pressure
\( {S}_{\alpha_q} \) VOF equation source term
S _{ m } momentum equation source term
S _{ E } energy equation source term
S _{ i } species equation source term
T cell temperature
\( {t}_{\frac{1}{2}} \) droplet half lifetime
U _{Ma} Marangoni velocity scale
U _{0} droplet impact velocity
We Weber number = \( \rho {D}_0{U}_0^2/\sigma \)
y mass fraction
Greek symbols
α volume fraction
σ surface tension
μ viscosity
ρ density
Subscripts
n normal vector
q the qth phase
t tangential vector
Declarations
Acknowledgements
This program was supported by the National Basic Research Program of China (Grant No. 2012CB933200), the Science Fund for Creative Research Groups of the NSFC (No. 51321002), and the National Natural Science Foundation of China (No. 51406100).
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 Moore GE (1965) Cramming More Components onto Intergrated Circuits. Electronics 38:114–117Google Scholar
 Yang J, Chow LC, Pais MR (1996) Nucleate boiling heat transfer in spray cooling. Journal of Heat Transfer 118(3):668–671View ArticleGoogle Scholar
 Estes KA, Mudawar I (1995) Correlation of Sauter mean diameter and critical heat flux for spray cooling of small surfaces. International Journal of Heat and Mass Transfer 38(16):2985–2996View ArticleGoogle Scholar
 Mudawar I, Estes KA (1996) Optimizing and predicting CHF in spray cooling of a square surface. Journal of Heat Transfer 118(3):672–679View ArticleGoogle Scholar
 Visaria M, Mudawar I (2007) A systematic approach to predicting critical heat flux for inclined sprays. Journal of Electronic Packaging 129(4):452–459View ArticleGoogle Scholar
 Duursma G, Sefiane K, Kennedy A (2009) Experimental studies of nanofluid droplets in spray cooling. Heat Transfer Engineering 30(13):1108–1120View ArticleGoogle Scholar
 Silk EA, Kim J, Kiger K (2006) Spray cooling of enhanced surfaces: Impact of structured surface geometry and spray axis inclination. International Journal of Heat and Mass Transfer 49(25–26):4910–4920View ArticleGoogle Scholar
 Zhang Z, Jiang PX, Ouyang XL, Chen JN, Christopher DM (2014) Experimental Investigation of Spray Cooling on Smooth and MicroStructured Surfaces. International Journal of Heat and Mass Transfer 76:366–375View ArticleGoogle Scholar
 Zhang Z, Jiang PX, Christopher DM, Liang XG (2015) Experimental investigation of spray cooling on micro, nano and hybridstructured surfaces. International Journal of Heat and Mass Transfer 80:26–37View ArticleGoogle Scholar
 Alvarado J L, Lin Y. Nanostructured surfaces for enhanced spray cooling. 27th Army Science Conference 2010; No. MP10.Google Scholar
 Healy WM, Hartley JG, AbdelKhalik SI (2001) On the validity of the adiabatic spreading assumption in droplet impact cooling. International Journal of Heat and Mass Transfer 44:3869–3881View ArticleGoogle Scholar
 Marzo MD, Tartarini P, Liao Y, Evans D, Baum H (1993) Evaporative cooling due to a gently deposited droplet. International Journal of Heat and Mass Transfer 36(17):4133–4139View ArticleGoogle Scholar
 Seki M, Kawamura H, Sanoka K (1978) Transient temperature profile of a hot wall due to an impinging liquid droplet. Journal of Heat Transfer 100:167–169View ArticleGoogle Scholar
 Ruiz OE, Black WZ (2002) Evaporation of Water Droplets Placed on a Heated Horizontal Surface. Journal of Heat Transfer 124:854–863View ArticleGoogle Scholar
 Srotos G, Manolis G, Theodorakakos A, Bergeles G (2011) Numerical investigation of the evaporation of twocomponent droplets. Fuel 90:1492–1507View ArticleGoogle Scholar
 Chen J N, Zhang Z, Jiang P X. Experimental Investigation of Enhanced Spray Cooling on Nano and Hybrid Micro/NanoStructured Surfaces. Proceedings of the 15th International heat transfer conference, Kyoto, Japan, 2014, IHTC9821.Google Scholar
 Xu S, Wang ZL (2011) Onedimensional ZnO nanostructures: solution growth and functional properties. Nano Research 4(11):1013–1098View ArticleGoogle Scholar
 Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39(1):201–225View ArticleGoogle Scholar
 Schrage RW (1953) A Theoretical Study of Interphase Mass Transfer. Columbia University Press, New YorkGoogle Scholar
 Fuller EN, Schettler PD, Giddings JC (1966) A new method for prediction of binary gasphase diffusion coefficients. Industrial and Engineering Chemistry 5(58):19–27Google Scholar
 Daïf A, Bouaziz M, Chesneau X, Chérif AA (1999) Comparison of multicomponent fuel droplet vaporization experiments in forced convection with the Sirignano model. Experimental Thermal and Fluid Science 18:282–90View ArticleGoogle Scholar
 Kim S, Kim HD, Kim H, Ahn HS, Jo H, Kim J, Kim MH (2010) Effects of nanofluid and surfaces with nano structure on the increase of CHF. Experimental Thermal and Fluid Science 34:487–495View ArticleGoogle Scholar
 Šikalo Š, Marengo M, Tropea C et al (2002) Analysis of impact of droplets on horizontal surfaces. Experimental Thermal and Fluid Science 25(7):503–510View ArticleGoogle Scholar
 Kim H, Lee C, Kim MK, Kim J (2012) Drop Impact Characteristics and Structure Effects of Hydrophobic Surfaces with Micro and/or Nanoscaled Structures. Langmuir 28:11250–11257View ArticleGoogle Scholar
 Schiaffino S, Sonin AA (1997) Molten droplet deposition and solidification at low Weber numbers. Physics of Fluids 9:3172–3187View ArticleGoogle Scholar