Abstract

Boiling heat transfer has been a popular topic for decades because of its ability to remove a significant amount of thermal energy while maintaining a low wall superheat during the liquid phase change. Such boiling mechanisms can be tailored by engineering new boiling substrates through surface wettability modification and/or microscale feature installation. Here, we create new types of heterogeneous boiling surfaces that integrate vertical gradient micropores on macroscale fins by using a template-free electrodeposition method. The gradient morphology and corresponding gradient wettability simultaneously enable bubble nucleation on the top pores and capillary wicking through the bottom pores. With these unique wetting characteristics, we find that the gradient pores installed at the trench bottom demonstrate the most significant boiling enhancement in critical heat flux and heat transfer coefficients by 160% and 600%, respectively. This enhancement can be attributed to the microflow-enhanced nature of bubble departures around the fins while isolating bubble nucleation and liquid supply through gradient pores. These results provide fundamental insights into boiling mechanisms using porous media and the potential for future works that can optimize the design of multidimensional heterogeneous surfaces to engineer flow patterns and boiling mechanisms accordingly.

1 Introduction

Boiling is the rapid vaporization of a liquid and is utilized in various energy-intensive industrial applications, such as nuclear power plants, electronic cooling systems for high-power-density devices, and heat pumps [14]. To evaluate boiling performances, two main parameters, critical heat fluxes and heat transfer coefficients, are often discussed. Critical heat flux (CHF) describes the heat flux limit where a phase change occurs during the nucleate boiling regime. Once the boiling surface is heated beyond a critical point, vapor films or vapor blankets form on the boiling surface, which suddenly decreases heat transfer efficiency. The formation of the vapor blanket prevents the resupply of the liquid to the boiling surface and decreases the capability of transferring heat from the boiling surface [57]. Heat transfer coefficient (HTC) describes the efficiency of boiling heat transfer; higher HTC values represent efficient boiling performances with smaller temperature differences between the saturation temperature and heated surface. Therefore, the overarching goal of the boiling community is focused on improving either or both CHF and HTC values.

In this context, various efforts have been devoted to discussing the impact of boiling surfaces in terms of their boiling performances [513]. In relation to surface wettability, previous studies have shown that the incipience of bubble nucleation on hydrophobic surfaces achieves more efficient boiling at earlier regimes. On the other hand, surface hydrophilicity provides liquid replenishment to bubble nucleation sites by promoting vapor removal from the boiling surface and by preventing surface dry-out [1418]. Due to those two competing characteristics, hybrid surfaces that integrate both hydrophilic and hydrophobic characteristics have shown superior boiling performances by simultaneously introducing bubble nucleation on hydrophobic regions and enabling liquid resupply through hydrophilic regions [1922].

Three-dimensionally (3D) designed porous structures have been widely discussed for boiling enhancements by taking advantage of morphology-enhanced bubble nucleation [2325], higher nucleation density [2628], capillary-enabled liquid supply [2932], and sizeable surface–volume ratio [33,34]. In detail, the pores provide numerous nucleation sites and facilitate bubble generation under lower heat fluxes owing to the existence of vapor embryos within the porous structures. The interconnected voids can deliver liquid to the boiling surface via capillary wicking and provide pathways for both vapor and liquid phases, delaying the vapor blanket formation in the porous structure and resulting in higher CHF values [35,36]. In addition, these structures enlarge the contact area between the solid and liquid phases for more effective thermal energy transfer. Templated electrodeposition is the most common strategy to fabricate 3D porous structures, which involves constructing sacrificial templates that have complicated structures [3739]. However, the templated electrodeposition method requires relatively complex procedures and high fabrication costs associated with template construction, sintering, and removal through multiple chemical processes. To overcome these challenges, recent studies have introduced a bubble-templated electrodeposition that can fabricate biporous copper structure through a simple, template-free electrodeposition process [32,4042]. The resulting porous structures from the bubble-templated electrodeposition, called as-fabricated biporous copper (BPCu) structures, are often fragile and require postprocessing, such as sintering or two-step electrodeposition [43,44], to enhance structural strength and durability to be used in thermal management systems.

Other efforts have explored macroscale patterns with dimensions ranging from hundreds of micrometers to millimeters. The patterns can lead to the formation of nonuniform temperatures along with varying thermal resistances over the entire surface, which can facilitate early bubble nucleation at selective locations [4547]. For example, bubbles generally tend to grow on the bottom of trenches because of the lower thermal resistance between the heater and trench bottoms. Therefore, CHF values are strongly dependent on the design of fins, including their morphology, dimensions, and the liquid–solid interfacial area [48,49].

This study converges the benefits of various strategies above-mentioned that pursue both CHF and HTC enhancements (Fig. 1) [44,5055] by integrating microscale pores with macroscale patterns. Here, the two-step electrodeposition is adopted to enhance structural strength of BPCu introduced in our previous work [53,54], and the process results in the formation of multiple-layered biporous copper (MLBPCu) with vertically varying morphology. The MLBPCu structures are selectively implemented on copper fins to encompass different integration styles between micro- and macroscale features. Depending on the location of deposited copper particles on the fin structure, bubble nucleation and their removal mechanisms associated with convective flows may vary, which affects the boiling performances. The bubble dynamics of each configuration will be visualized and investigated to correlate with convective microscale flow patterns.

Fig. 1
Fig. 1

2 Experimental Section

2.1 Fabrication Process of Samples

2.1.1 Fin Fabrication.

This research discusses the boiling performances of different boiling surfaces: plain surface (bare copper), copper fins, MLBPCu, and MLBPCu-fin structures. In particular, the fabrication process of the MLBPCu-fin structures consists of the fin fabrication with two-step templated electrodeposition (that integrates the bubble-templated electrodeposition followed by Galvanostatic electrodeposition). The 1 mm-thick copper sheets (copper alloy 101) are machined to the dimensions of 10 mm $×$ 10 mm. As shown in Fig. 2(a), the 0.5 mm-height fins are milled on the copper substrate with a constant 2 mm pitch, where the fin width Wfin varies from 0.8 mm to 1 mm (say, 0.8 mm fin and 1.0 mm fin in this study, respectively). The copper substrates are first placed in hydrochloric acid for 15 min to remove the oxidation layer and further cleaned with isopropyl alcohol and de-ionized water in series.

Fig. 2
Fig. 2

2.1.2 Two-Step Bubble-Templated Electrodeposition.

After the fin fabrication, microscale porous structures can be integrated into the fin structures through the bubble-templated electrodeposition technique. Here, the copper substrates are assembled with a customized polycarbonate (PC) holder and attached to a cathode during the deposition. Another copper sheet of 15 mm × 10 mm is connected to the anode for copper ion dissipation. The anode and the copper substrates are placed horizontally in favor of hydrogen bubble departure where the vertical distance is fixed at 35 mm. The electrodeposition is performed in an electrolyte (0.4 M Cu2SO4 + 1.8 M H2SO4) where a direct current (DC) power supply serves as the power source (with a current density of 1 A/cm2 for the first 30 s). First, the bubble-templated electrodeposition initiates the stochastic growth of copper microscale particles on the surface while it produces vigorous hydrogen bubbles as the by-product of the process. The hydrogen bubbles serve as a template to create void portions between the deposited copper particles, which results in the formation of 3D porous copper structures with microscale pores. The following Galvanostatic electrodeposition (with a current density of 0.1 A/cm2 for 30 min) helps the copper microparticles start fusing with adjacent microparticles, which reinforces the structural strength and durability to be used in other thermal systems (Fig. S2 available in the Supplemental Materials on the ASME Digital Collection). The additional details of this fabrication process are illustrated in the Supplemental Material S1 on the ASME Digital Collection. Furthermore, during the sample preparation, the process parameters of the two-step electrodeposition remain consistent to create identical morphologies for the MLBPCu structures, such as structural thickness, pore distribution, and porosity. This consistent fabrication enables the investigation into how microscale flow patterns vary depending on the micropore-fin combinations by isolating the morphological impact of micropores.

2.2 Pool Boiling Measurements.

As shown in Fig. 3, the boiling performances are experimentally measured using a customized pool boiling setup composed of a heating block, a temperature data acquisition, a water reservoir, and a high-speed camera. The heating block integrates a rectangular copper block with four cartridge heaters (connected to an alternating current (AC) power supply to control the input power) and four K-type thermocouples (connected to a data acquisition system to record temperature distributions). The Ti represents the temperature value measured at location i; and ΔXij and ΔTij represent the distance and temperature difference between two locations i and j, respectively. The temperature gradients, dT/dX, are calculated by taking averages of ΔTijXij along the heat transfer direction. By using the temperature profile, the net heat flux q″ passing through the system can be calculated based on the one-dimensional Fourier's Law in thermal equilibrium. To support this one-dimensional conduction assumption, a ceramic fiber blanket and Teflon block are used to insulate the heating block from the ambient. In the customized water reservoir, a guard heater maintains the saturation temperature Tsat, which is monitored by another thermocouple placed in the water reservoir. The calculation of superheat ΔTwall can be thereby expressed as
$ΔTwall =[T1−q″(R″solder+ΔXs1+δsamplekCu)]−Tsat$
(1)
where Rsolder, ΔXs1, and δsample represent the thermal interface resistance of the solder (8 × 10−6 m2K/W), the vertical distance between location 1 and the top surface of the copper block (7.1 mm), and the thickness of the tested sample (1 mm). The HTC is calculated as
$HTC=q″ΔTwall$
(2)
Fig. 3
Fig. 3

Uncertainties of K-type thermocouples, power input, and machining tolerance are ±0.2 K, ±1 W, and ±10−4 m, resulting in the uncertainties on the measured q″ and HTC of ±2.8% and ±5.4%, respectively. To exploit the bubble dynamics during boiling conditions, the high-speed camera (Mini AX50, Photron FASTCAM, CA) records bubble nucleation, growth, and departure at 2000 fps with 1024 × 1024 pixels resolution.

3 Results and Discussion

3.1 Design of Experiments.

To fully exploit the impact of structured surfaces on their boiling performances, we design multidimensional configurations that integrate microscale MLBPCu, fin structures, and their combinations. In this study, a total of ten boiling surfaces are tested including the baseline references (i.e., bare copper surface, homogeneous micropores, and copper fins), with Table 1 summarizing the characteristics of each sample. The physical descriptors of samples are characterized using SEM images, contact angle measurements, and capillary wicking measurements.

Table 1

CHF and HTC enhancement for all tested surfaces in this study

Fin pitch, P (mm)Height, H (mm)Fin width, W (mm)CHF (W/cm2)Enhancement (%)HTC (W/cm2 K)Enhancement (%)
Bare copper105.26.6
MLBPCu213.5103.08.427.1
1.0 mm fin2.00.51.0182.173.112.386.4
1.0 mm all2.00.51.0246.3134.114.5119.7
1.0 mm top2.00.51.0262.0149.015.9141.0
1.0 mm bot2.00.51.0272.8159.324.1280.3
0.8 mm fin2.00.50.8185.075.914.0112.1
0.8 mm all2.00.50.8241.2129.315.4133.3
0.8 mm top2.00.50.8253.2140.719.7198.5
0.8 mm bot2.00.50.8278.3164.546.6606.1
Fin pitch, P (mm)Height, H (mm)Fin width, W (mm)CHF (W/cm2)Enhancement (%)HTC (W/cm2 K)Enhancement (%)
Bare copper105.26.6
MLBPCu213.5103.08.427.1
1.0 mm fin2.00.51.0182.173.112.386.4
1.0 mm all2.00.51.0246.3134.114.5119.7
1.0 mm top2.00.51.0262.0149.015.9141.0
1.0 mm bot2.00.51.0272.8159.324.1280.3
0.8 mm fin2.00.50.8185.075.914.0112.1
0.8 mm all2.00.50.8241.2129.315.4133.3
0.8 mm top2.00.50.8253.2140.719.7198.5
0.8 mm bot2.00.50.8278.3164.546.6606.1

Note: The boldface values represent heterogenous boiling surfaces with highest CHF and HTC enhancements.

The time-dependent characteristics of two-step electrodeposition result in vertically gradient microstructures, which is different from the homogeneous BPCu fabricated via the bubble-templated electrodeposition solely, as shown in SEM images in Fig. 2(b). The average feature size of MLBPCu increases from 10 μm to 100 μm as the structural height increases from 80 μm to 300 μm. Given the cross-sectional SEM images, we can extract the physical descriptors, such as the structural thickness or structural porosity of the MLBPCu by using this expression [31]
$ϕ=1−mρδAproj$
(3)

where m is the total mass of MLBPCu structure, ρ is the copper density, δ is the average structural thickness, and Aproj is the projected area of MLBPCu structure. The calculated porosity of MLBPCu of ∼86% is smaller than the porosity of other BPCu structures reported elsewhere [53,54] due to the emergence of copper dendrite. More details regarding the porosity estimation can be found in the Supplemental Material S3 on the ASME Digital Collection.

The nature of the two-step electrodeposition leads to a vertically gradient morphology and therefore gradient wettability in the growth direction. In detail, larger bottom pores show more hydrophilic characteristics, whereas smaller top pores become less hydrophilic. To quantify these wetting characteristics, we exploit out-of-plane droplet infiltrations and in-plane capillary wicking using sessile-droplet and liquid-rise measurements, respectively (Fig. 4). Once a sessile droplet is dispensed from a tip, the droplet contacts the top pores that possess the largest feature size with the lowest structural porosity. After 50 ms, the droplet starts penetrating to bottom pores. These wetting characteristics can be characterized with three phases (that are increasing drawing area, constant drawing area, and decreasing drawing area) of the droplet infiltration model [56]. The identification of three phases allows for the extraction of the advancing contact angle (θadv), static contact angle (θs), and receding contact angle (θrec) for the MLBPCu structures, which range from 71 deg to 76 deg. The existence of the gradient morphology of MLBPCu and larger pores at the top shows less hydrophilic characteristics (compared to other hydrophilic structures in previous studies [50,57]). To quantify the effective wettability of MLBPCu along the in-plane direction, the rate-of-rise experiments are conducted. These measurements quantify the capillarity, which is the ratio of the permeability to the effective pore radius (K/Reff) of MLBPCu, as 1.1 $×$ 10−7 m based on the Lucas-Washburn equation [58,59] (Figs. 4(c) and 4(d)). The lateral wicking measurements show that the MLBPCu enables capillary wicking through microstructures and provides liquid to the boiling surface.

Fig. 4
Fig. 4

3.2 Boiling Performances.

The boiling curves for the baselines (i.e., bare copper, MLBPCu, and fin structure) are extracted, as shown in Figs. 5(a) and 5(b). In particular, the CHF of the bare copper can be compared with Zuber's correlation [60] that predicts the CHF of a plain surface:
$q″CHF=CZhLvρv(σLg(ρL−ρv)ρv2) 14$
(4)

where hLv represents the enthalpy of vaporization, ρL and ρv are the density for liquid and vapor, respectively, σL stands for the liquid surface tension, and g is the gravitational acceleration. With the Zuber's constant CZ of 0.149 [61], the estimated CHF of the bare copper surface (111 W/cm2) shows a good agreement with the measured value (105 W/cm2).

Fig. 5
Fig. 5

Compared to the bare copper, the MPBPCu or fin samples show the improvements in boiling performances, as displayed in Figs. 5(a) and 5(b). To further discuss the CHF enhancement introduced by the fins, we calculate CHFnorm by normalizing the extracted CHF over the fin area to account for extended surface effect on boiling performances. It should be noted that the temperature discrepancy over the fin surface is expected and assumed to be minimal (≤3%), considering the dimension of trench depth (0.5 mm) and the high thermal conductivity of copper (∼400 W/mK). Here, the CHFnorm of the fin structures (∼120 W/cm2) shows similar values with the measured values for bare copper, which suggest that the increase in the surface area can be considered as the main contribution for CHF enhancement of fin structures.

To predict the CHF of the MLBPCu, a theoretical CHF model [13] based on bubble force balance on a planar hydrophilic boiling surface can be employed
$q″CHF=hLVρV12[σLV (1+cosθ)Hb+12g(ρL−ρV)Hb]$
(5)
However, this model underestimates the transient characteristics of dynamic bubbles such as state transitions between the Cassie-Baxter and the Wenzel states, which are a result of the competition between vapor phase expansion and liquid replenishment. For example, the capillary wicking through micro/nanostructures allows for the transitions from the Wenzel bubbles to the Cassie-Baxter bubbles, whereas the bubble expansion will promote the opposite transition from Cassi-Baxter to Wenzel bubbles. Therefore, the contribution of capillary wicking should be included in the modified model to estimate the theoretical CHF of structured surfaces. The following model postulates that the CHF occurs when the momentum of vapor-phase expansion surpasses the summation of constrain and the capillary wicking forces, which results in dry-out on both top and bottom layers of the structure and demonstrates “Wenzel state” bubbles near the CHF (Fig. S5 available in the Supplemental Materials on the ASME Digital Collection) [62,63]
$q″CHF=hLvρv12[σLvg(ρL−ρv)]14(1+cosθ16)[(2π×1+rcosθrec1+cosθ)+π4(1+cosθ)]12$
(6)

where r and θrec are the roughness factor and the receding contact angle, respectively. By considering the characteristics of surface properties and fluid properties, the predicted CHF of MLBPCu is calculated as 218.6 W/cm2, showing a good agreement with the measured CHF with a 2.3% deviation.

To further explore the mechanisms responsible for HTCs, the bubble dynamics are carefully visualized using a high-speed camera, see high-speed images in Figs. 5(c) and 5(d) and Figure S6 available in the Supplemental Materials on the ASME Digital Collection for the three different regimes that include a low heat flux around the onset of nucleate boiling, a medium heat flux (10-20 W/cm2), and a high heat flux (100–150 W/cm2). The microconvection model predicts the HTC values based on mainly bubble characteristics [64]
$HTC =Chtc (kLρLcpL)0.5nDb2f0.5$
(7)

where kL and cpL represent the thermal conductivity and the specific heat of working liquid; n, Db, and f are the bubble number, the departure diameter, and the departure frequency, respectively. This expression implies that it is imperative to maintain efficient and continuous bubble nucleation during boiling conditions. For the fin structures, the bubble nucleation is initiated on selective locations (e.g., trench bottoms), whereas other surfaces with homogeneous microstructures (e.g., MLBPCu) have bubble generations dominantly at the interface between the structure and the polydimethylsiloxane sealant with less vigorous nucleation. This makes the fin structures have consistently higher HTCs over the entire regime. Therefore, the advantages of each MLBPCu and fin structure on CHF and HTC, respectively, motivate us to integrate two different structures resulting in the creation of MLBPCu-fin structures.

3.3 Effect of Microscale Convective Flow on Boiling Heat Transfer.

To further enhance boiling performances, we create heterogeneous MLBPCu-fin structures that integrate gradient microscale pores and macroscale fins. In detail, MLBPCu structures are selectively deposited on the desired location of copper fins (e.g., all over the surface, fin tops, and trench bottoms), identified as All, Bottom, and Top configurations in Fig. 6(a). The boiling curves for the 1.0- and 0.8-mm MLBPCu-fin structures with three configurations are shown in Figs. 6(b)6(e). For the MLBPCu-fin structures, the CHF values increase by 130%–160%, and the HTC values increase by 120%–600% compared to the bare copper. Also, it should be noted that the MLBPCu-fin structures consistently show superior performances to other references (i.e., bare copper, copper fins, and planar MLBPCu) as summarized in Table 1.

Fig. 6
Fig. 6

The representative boiling mechanisms associated with bubble nucleation locations can be captured by high-speed bubble visualizations, as shown in Fig. 7 and Fig. S7–S9 available in the Supplemental Materials on the ASME Digital Collection. The All and Top designs show similar mechanisms to the fin-only configurations (explained in the earlier section), where individual bubbles generate on the trench bottoms. This phenomenon helps to produce more bubbles at earlier boiling stages with corresponding smaller onset of nucleate boiling than other configurations. Here, the liquid replenishes the surface from the fin tops to the trench bottoms with bubbles generated on the trench bottoms, leading to bottom-initiated flow patterns. However, the boiling curves with such bottom-initiated flow patterns can be less efficient because the bubbles continue to grow or coalesce and clog the routes for liquid resupply in higher heat flux regimes (>100 W/cm2). Contrarily, Bottom configurations show bubble nucleation on the fin tops, which causes a contrasting convective flow pattern in comparison to the other two MLBPCu-fin configurations. The top-initiated flow pattern of the Bottom configuration successfully preserves both liquid and vapor pathways via isolating liquid pathway below the fin tops to bubble nucleation site and facilitate bubble cyclical dynamics, resulting in a superior heat transfer efficiency, in particular, in high heat flux regimes [44]. In addition, the fin dimensions' effects on the boiling performances can be minimal for the CHF (showing only 2%–3% variations) but more significant for improving the HTC values (showing 40–80% changes). This investigation indicates that the fin dimension has a more substantial impact on how efficiently the bubbles dissipate heat from boiling surfaces than increasing the overall heat flux limit.

Fig. 7
Fig. 7

The regime map in Fig. 8 demonstrates the normalized boiling performances of MLBPCu-fin structures over the bare copper compared with other boiling surfaces, including porous structures or macroscale features [31,35,43,48,6567]. The normalized values are discussed because the extracted CHF and HTC values could slightly vary depending on different experimental setups and procedures conducted by different research groups. The regime map showcases the impact of surface wettability modification on boiling performances can be minimal if the features are relatively large; therefore, our boiling performances show neither hydrophilic nor hydrophobic characteristics with narrower bandwidths. Depending on different structure designs, surface wettability, structural materials, the MLBPCu-fin structures show varying bubble dynamics and corresponding boiling heat transfer augmentations in both hydrophilic and hydrophobic categories. The MLBPCu-fin structures from this study successfully couple boiling mechanisms and demonstrate remarkable enhancements in boiling efficiency.

Fig. 8
Fig. 8

4 Conclusion

This study investigates and discusses the mechanism-dependent boiling performances by testing multiple configurations that include heterogeneously integrated micropore-fin designs. To do this, we employ a two-step electrodeposition consisting of bubble templates and Galvanostatic electrodeposition, which allows for the fast and straightforward manufacturing of microstructures. The nature of the two-step process results in the gradient morphology of MLBPCu structures in the growth direction. The corresponding gradient wetting characteristics help both bubble nucleation on the top pores and liquid replenishment through the bottom pores. The enhancements in bubble dynamics allow MLBPCu-fin designs to consistently perform superior boiling performances. Top designs show the early onset of boiling at lower heat fluxes; and Bottom designs demonstrate the highest CHF and HTC values of 280 W/cm2 and 50 W/cm2K, respectively, suggesting 160% and 600% improvements compared to the bare copper. In addition, we reveal that the microscale convective flow patterns can facilitate efficient bubble nucleation and departure in a cyclic manner. This study suggests potential for multidimensional structural modification that can pursue optimal boiling performance in real thermal applications.

Funding Data

• National Chung Shan Institute of Science and Technology, Taiwan.

Nomenclature

• A =

area

•
• C =

constant

•
• cp =

specific heat

•
• D =

bubble diameter

•
• f =

bubble departure frequency

•
• g =

gravitational acceleration

•
• h =

phase-change enthalpy

•
• H =

height

•
• k =

thermal conductivity

•
• K =

permeability

•
• m =

mass

•
• n =

number of nucleation sites

•
• q″ =

heat flux

•
• r =

roughness factor

•
• R =

pore radius

•
• R″ =

thermal resistance (per unit area)

•
• T =

temperature

•
• X =

vertical distance

•
• W =

fin width

Greek Symbols

Greek Symbols

• δ =

structural thickness

•
• θ =

contact angle

•
• ρ =

density

•
• σ =

surface tension

•
• φ =

structural porosity

Subscripts

Subscripts

• adv =

advancing

•
• b =

bubble

•
• eff =

effective

•
• fin =

fin

•
• htc =

heat transfer coefficient

•
• i, j =

measured location on the heating block

•
• L =

liquid

•
• norm =

area-normalized

•
• proj =

projected

•
• rec =

receding

•
• s =

static

•
• sample =

tested sample

•
• sat =

saturation

•
• solder =

solder

•
• V =

vapor

•
• wall =

wall superheat

•
• z =

Zuber

References

1.
Mudawar
,
I.
,
2013
, “
Recent Advances in High-Flux, Two-Phase Thermal Management
,”
ASME J. Thermal Sci. Eng. Appl.
, 5(2), p.
021012
.10.1115/1.4023599
2.
Mudawar
,
I.
,
2011
, “Two-Phase Micro-Channel Heat Sinks: Theory, Applications and Limitations,”
ASME
Paper No. AJTEC2011-44005.10.1115/AJTEC2011-44005
3.
Mudawar
,
I.
,
2011
, “
Two-Phase Microchannel Heat Sinks: Theory, Applications, and Limitations
,”
ASME J. Electron. Packag.
, 133(4), p.
041002
.10.1115/1.4005300
4.
Mudawar
,
I.
,
2001
, “
Assessment of High-Heat-Flux Thermal Management Schemes
,”
IEEE Trans. Compon. Packag. Technol.
, 24(2), pp.
122
141
.10.1109/6144.926375
5.
Seon Ahn
,
H.
, and
Hwan Kim
,
M.
,
2012
, “
A Review on Critical Heat Flux Enhancement With Nanofluids and Surface Modification
,”
ASME J. Heat Transfer-Trans. ASME
, 134(2), p.
024001
.10.1115/1.4005065
6.
Xie
,
S.
,
Shahmohammadi Beni
,
M.
,
Cai
,
J.
, and
Zhao
,
J.
,
2018
, “
Review of Critical-Heat-Flux Enhancement Methods
,”
Int. J. Heat Mass Transfer
, 122, pp.
275
289
.10.1016/j.ijheatmasstransfer.2018.01.116
7.
Mori
,
S.
, and
Utaka
,
Y.
,
2017
, “
Critical Heat Flux Enhancement by Surface Modification in a Saturated Pool Boiling: A Review
,”
Int. J. Heat Mass Transfer
, 108(B), pp.
2534
2557
.10.1016/j.ijheatmasstransfer.2017.01.090
8.
Shi
,
J.
,
Jia
,
X.
,
Feng
,
D.
,
Chen
,
Z.
, and
Dang
,
C.
,
2020
, “
Wettability Effect on Pool Boiling Heat Transfer Using a Multiscale Copper Foam Surface
,”
Int. J. Heat Mass Transfer
, 146, p.
118726
.10.1016/j.ijheatmasstransfer.2019.118726
9.
Teodori
,
E.
,
Valente
,
T.
,
Malavasi
,
I.
,
Moita
,
A. S.
,
Marengo
,
M.
, and
Moreira
,
A. L. N.
,
2017
, “
Effect of Extreme Wetting Scenarios on Pool Boiling Conditions
,”
Appl. Therm. Eng.
, 115(25), pp.
1424
1437
.10.1016/j.applthermaleng.2016.11.079
10.
Liang
,
G.
, and
Mudawar
,
I.
,
2018
, “
Pool Boiling Critical Heat Flux (CHF) – Part 2: Assessment of Models and Correlations
,”
Int. J. Heat Mass Transfer
, 117, pp.
1368
1383
.10.1016/j.ijheatmasstransfer.2017.09.073
11.
Liang
,
G.
, and
Mudawar
,
I.
,
2018
, “
Pool Boiling Critical Heat Flux (CHF) – Part 1: Review of Mechanisms, Models, and Correlations
,”
Int. J. Heat Mass Transfer
, 117, pp.
1352
1367
.10.1016/j.ijheatmasstransfer.2017.09.134
12.
Zhang
,
C.
,
Zhou
,
W.
,
Wang
,
Q.
,
Wang
,
H.
,
Tang
,
Y.
, and
Hui
,
K. S.
,
2013
, “
Comparison of Static Contact Angle of Various Metal Foams and Porous Copper Fiber Sintered Sheet
,”
Appl. Surf. Sci.
, 276, pp.
377
382
.10.1016/j.apsusc.2013.03.101
13.
Kandlikar
,
S. G.
,
2001
, “
A Theoretical Model to Predict Pool Boiling CHF Incorporating Effects of Contact Angle and Orientation
,”
ASME J. Heat Transfer-Trans. ASME
, 123(6), pp.
1071
1079
.10.1115/1.1409265
14.
Bourdon
,
B.
,
Rioboo
,
R.
,
Marengo
,
M.
,
Gosselin
,
E.
, and
De Coninck
,
J.
,
2012
, “
Influence of the Wettability on the Boiling Onset
,”
Langmuir
,
28
(
2
), pp.
1618
1624
.10.1021/la203636a
15.
Bourdon
,
B.
,
DiMarco
,
P.
,
Rioboo
,
R.
,
Marengo
,
M.
, and
DeConinck
,
J.
,
2013
, “
Enhancing the Onset of Pool Boiling by Wettability Modification on Nanometrically Smooth Surfaces
,”
Int. Commun. Heat Mass Transfer
, 45, pp.
11
15
.10.1016/j.icheatmasstransfer.2013.04.009
16.
Bourdon
,
B.
,
Bertrand
,
E.
,
DiMarco
,
P.
,
Marengo
,
M.
,
Rioboo
,
R.
, and
DeConinck
,
J.
,
2015
, “
Wettability Influence on the Onset Temperature of Pool Boiling: Experimental Evidence Onto Ultra-Smooth Surfaces
,”
Adv. Colloid Interface Sci.
, 221, pp.
34
40
.10.1016/j.cis.2015.04.004
17.
Jo
,
H. J.
,
Kim
,
H.
,
Ahn
,
H. S.
,
Kim
,
S.
,
Kang
,
S. H.
,
Kim
,
J.
, and
Kim
,
M. H.
,
2009
, “
Experimental Study of Boiling Phenomena by Micro/Milli Hydrophobic Dot on the Silicon Surface in Pool Boiling
,”
ASME
Paper No. ICNMM2009-82221.10.1115/ICNMM2009-82221
18.
Jo
,
H. J.
,
Kim
,
H.
,
Ahn
,
H. S.
,
Kang
,
S.
,
Kim
,
J.
,
Shin
,
J. S.
, and
Kim
,
M. H.
,
2010
, “
Experimental Study of Pool Boiling for Enhancing the Boiling Heat Transfer by Hydrophobic Dots on Silicon Surface
,”
Trans. Korean Soc. Mech. Eng. B
, 34(6), pp.
655
663
.10.3795/KSMEB.2010.34.6.655
19.
Choi
,
C. H.
,
David
,
M.
,
Gao
,
Z.
,
Chang
,
A.
,
Allen
,
M.
,
Wang
,
H.
, and
Chang
,
C. H.
,
2016
, “
Large-Scale Generation of Patterned Bubble Arrays on Printed Bi-Functional Boiling Surfaces
,”
Sci. Rep.
, 6, p.
23760
.10.1038/srep23760
20.
Dai
,
X.
,
Huang
,
X.
,
Yang
,
F.
,
Li
,
X.
,
Sightler
,
J.
,
Yang
,
Y.
, and
Li
,
C.
,
2013
, “
Enhanced Nucleate Boiling on Horizontal Hydrophobic-Hydrophilic Carbon Nanotube Coatings
,”
Appl. Phys. Lett.
,
102
(
16
), p.
161605
.10.1063/1.4802804
21.
Hsu
,
C. C.
,
Chiu
,
W. C.
,
Kuo
,
L. S.
, and
Chen
,
P. H.
,
2014
, “
Reversed Boiling Curve Phenomenon on Surfaces With Interlaced Wettability
,”
AIP Adv.
, 4, p.
107110
.10.1063/1.4897953
22.
Hsu
,
C. C.
,
Lee
,
M. R.
,
Wu
,
C. H.
, and
Chen
,
P. H.
,
2017
, “
Effect of Interlaced Wettability on Horizontal Copper Cylinders in Nucleate Pool Boiling
,”
Appl. Therm. Eng.
, 112, pp.
1187
1194
.10.1016/j.applthermaleng.2016.10.176
23.
Zhang
,
C.
,
Palko
,
J. W.
,
Rong
,
G.
,
Pringle
,
K. S.
,
Barako
,
M. T.
,
Dusseault
,
T. J.
,
Asheghi
,
M.
,
Santiago
,
J. G.
, and
Goodson
,
K. E.
,
2018
, “
Tailoring Permeability of Microporous Copper Structures Through Template Sintering
,”
ACS Appl. Mater. Interfaces
,
10
(
36
), pp.
30487
30494
.10.1021/acsami.8b03774
24.
Zhang
,
C.
,
Rong
,
G.
,
Palko
,
J. W.
,
Dusseault
,
T. J.
,
Asheghi
,
M.
,
Santiago
,
J. G.
, and
Goodson
,
K. E.
,
2015
, “
Tailoring of Permeability in Copper Inverse Opal for Electronic Cooling Applications
,”
ASME
Paper No. IPACK2015-48262.10.1115/IPACK2015-48262
25.
Zhang
,
C.
,
Palko
,
J. W.
,
Barako
,
M. T.
,
Asheghi
,
M.
,
Santiago
,
J. G.
, and
Goodson
,
K. E.
,
2018
, “
Enhanced Capillary-Fed Boiling in Copper Inverse Opals Via Template Sintering
,”
Adv. Funct. Mater.
,
28
(
41
), p.
1803689
.10.1002/adfm.201803689
26.
Webb
,
R. L.
,
1983
, “
Nucleate Boiling on Porous Coated Surfaces
,”
Heat Transfer Eng.
, 4(3–4), pp.
71
82
.10.1080/01457638108939610
27.
Cieiliński
,
J. T.
,
2002
, “
Nucleate Pool Boiling on Porous Metallic Coatings
,”
Exp. Therm. Fluid Sci.
, 25(7), pp.
557
564
.10.1016/S0894-1777(01)00105-4
28.
El-Genk
,
M. S.
, and
Ali
,
A. F.
,
2010
, “
Enhanced Nucleate Boiling on Copper Micro-Porous Surfaces
,”
Int. J. Multiphase Flow
, 36(10), pp.
780
792
.10.1016/j.ijmultiphaseflow.2010.06.003
29.
Pham
,
Q. N.
,
Barako
,
M. T.
,
Tice
,
J.
, and
Won
,
Y.
,
2017
, “
Microscale Liquid Transport in Polycrystalline Inverse Opals Across Grain Boundaries
,”
Sci. Rep.
,
7
(
1
), p. 10465.10.1038/s41598-017-10791-3
30.
Stein
,
A.
,
2003
, “
Advances in Microporous and Mesoporous Solids - Highlights of Recent Progress
,”
Adv. Mater.
,
15
(
10
), pp.
763
775
.10.1002/adma.200300007
31.
Wang
,
Y. Q.
,
Luo
,
J. L.
,
Heng
,
Y.
,
Mo
,
D. C.
, and
Lyu
,
S. S.
,
2018
, “
Wettability Modification to Further Enhance the Pool Boiling Performance of the Micro Nano Bi-Porous Copper Surface Structure
,”
Int. J. Heat Mass Transfer
,
119
, pp.
333
342
.10.1016/j.ijheatmasstransfer.2017.11.080
32.
Li
,
S.
,
Furberg
,
R.
,
Toprak
,
M. S.
,
Palm
,
B.
, and
Muhammed
,
M.
,
2008
, “
Nature-Inspired Boiling Enhancement by Novel Nanostructured Macroporous Surfaces
,”
Adv. Funct. Mater.
,
18
(
15
), pp.
2215
2220
.10.1002/adfm.200701405
33.
Mandrusiak
,
G. D.
, and
Carey
,
V. P.
,
1989
, “
Convective Boiling in Vertical Channels With Different Offset Strip Fin Geometries
,”
ASME J. Heat Transfer-Trans. ASME
, 111(1), pp.
156
165
.10.1115/1.3250638
34.
Jaikumar
,
A.
,
Gupta
,
A.
,
Kandlikar
,
S. G.
,
Yang
,
C. Y.
, and
Su
,
C. Y.
,
2017
, “
Scale Effects of Graphene and Graphene Oxide Coatings on Pool Boiling Enhancement Mechanisms
,”
Int. J. Heat Mass Transfer
, 109, pp.
357
366
.10.1016/j.ijheatmasstransfer.2017.01.110
35.
Lee
,
H.
,
Maitra
,
T.
,
Palko
,
J.
,
Kong
,
D.
,
Zhang
,
C.
,
Barako
,
M. T.
,
Won
,
Y.
,
Asheghi
,
M.
, and
Goodson
,
K. E.
,
2018
, “
Enhanced Heat Transfer Using Microporous Copper Inverse Opals
,”
ASME J. Electron. Packag.
, 140(2), p.
020906
.10.1115/1.4040088
36.
Ha
,
M.
, and
Graham
,
S.
,
2017
, “
Pool Boiling Characteristics and Critical Heat Flux Mechanisms of Microporous Surfaces and Enhancement Through Structural Modification
,”
Appl. Phys. Lett.
,
111
(
9
), p.
091601
.10.1063/1.4999158
37.
Barako
,
M. T.
,
Sood
,
A.
,
Zhang
,
C.
,
Wang
,
J.
,
Kodama
,
T.
,
Asheghi
,
M.
,
Zheng
,
X.
,
Braun
,
P. V.
, and
Goodson
,
K. E.
,
2016
, “
Quasi-Ballistic Electronic Thermal Conduction in Metal Inverse Opals
,”
Nano Lett.
,
16
(
4
), pp.
2754
2761
.10.1021/acs.nanolett.6b00468
38.
Yeo
,
S. J.
,
Choi
,
G. H.
, and
Yoo
,
P. J.
,
2017
, “
Multiscale-Architectured Functional Membranes Utilizing Inverse Opal Structures
,”
J. Mater. Chem. A
,
5
(
33
), pp.
17111
17134
.10.1039/C7TA05033J
39.
Hatton
,
B.
,
Mishchenko
,
L.
,
Davis
,
S.
,
Sandhage
,
K. H.
, and
Aizenberg
,
J.
,
2010
, “
Assembly of Large-Area, Highly Ordered, Crack-Free Inverse Opal Films
,”
Proc. Natl. Acad. Sci.
,
107
(
23
), pp.
10354
10359
.10.1073/pnas.1000954107
40.
Shin
,
H. C.
,
Dong
,
J.
, and
Liu
,
M.
,
2003
, “
Nanoporous Structures Prepared by an Electrochemical Deposition Process
,”
Adv. Mater.
,
15
(
19
), pp.
1610
1614
.10.1002/adma.200305160
41.
Shin
,
H. C.
, and
Liu
,
M.
,
2004
, “
Copper Foam Structures With Highly Porous Nanostructured Walls
,”
Chem. Mater.
,
16
(
25
), pp.
5460
5464
.10.1021/cm048887b
42.
Li
,
J.
,
Fu
,
W.
,
Zhang
,
B.
,
Zhu
,
G.
, and
Miljkovic
,
N.
,
2019
, “
Ultrascalable Three-Tier Hierarchical Nanoengineered Surfaces for Optimized Boiling
,”
ACS Nano
,
13
(
12
), pp.
14080
14093
.10.1021/acsnano.9b06501
43.
Rishi
,
A. M.
,
Gupta
,
A.
, and
Kandlikar
,
S. G.
,
2018
, “
Improving Aging Performance of Electrodeposited Copper Coatings During Pool Boiling
,”
Appl. Therm. Eng.
, 140, pp.
406
414
.10.1016/j.applthermaleng.2018.05.061
44.
Patil
,
C. M.
, and
Kandlikar
,
S. G.
,
2014
, “
Pool Boiling Enhancement Through Microporous Coatings Selectively Electrodeposited on Fin Tops of Open Microchannels
,”
Int. J. Heat Mass Transfer
,
79
, pp.
816
828
.10.1016/j.ijheatmasstransfer.2014.08.063
45.
Ayub
,
Z. H.
, and
Bergles
,
A. E.
,
1987
, “
Pool Boiling From GEWA Surfaces in Water and R-113
,”
Wärme Stoffübertragung
,
21
(
4
), pp.
209
219
.10.1007/BF01004023
46.
Chan
,
M. A.
,
Yap
,
C. R.
, and
Ng
,
K. C.
,
2010
, “
Pool Boiling Heat Transfer of Water on Finned Surfaces at Near Vacuum Pressures
,”
ASME J. Heat Transfer-Trans. ASME
, 132(3), p.
031501
.10.1115/1.4000054
47.
Zhong
,
D.
,
Meng
,
J.
,
Li
,
Z.
, and
Guo
,
Z.
,
2015
, “
Critical Heat Flux for Downward-Facing Saturated Pool Boiling on Pin Fin Surfaces
,”
Int. J. Heat Mass Transfer
,
87
, pp.
201
211
.10.1016/j.ijheatmasstransfer.2015.04.001
48.
Seo
,
H.
,
Lim
,
Y.
,
Shin
,
H.
, and
Bang
,
I. C.
,
2018
, “
Effects of Hole Patterns on Surface Temperature Distributions in Pool Boiling
,”
Int. J. Heat Mass Transfer
, 120, pp.
587
596
.10.1016/j.ijheatmasstransfer.2017.12.066
49.
Yu
,
C. K.
,
Lu
,
D. C.
, and
Cheng
,
T. C.
,
2006
, “
Pool Boiling Heat Transfer on Artificial Micro-Cavity Surfaces in Dielectric Fluid FC-72
,”
J. Micromech. Microeng.
, 16(10), pp.
2092
2099
.10.1088/0960-1317/16/10/024
50.
Lee
,
J.
,
Suh
,
Y.
,
Dubey
,
P. P.
,
Barako
,
M. T.
, and
Won
,
Y.
,
2019
, “
Capillary Wicking in Hierarchically Textured Copper Nanowire Arrays
,”
ACS Appl. Mater. Interfaces
,
11
(
1
), pp.
1546
1554
.10.1021/acsami.8b14955
51.
Lee
,
J.
,
Shao
,
B.
, and
Won
,
Y.
,
2019
, “
Droplet Jumping on Superhydrophobic Copper Oxide Nanostructured Surfaces
,”
IEEE Trans. Compon., Packag. Manuf. Technol.
, 9(6), pp.
1075
1081
.10.1109/TCPMT.2018.2889091
52.
Pham
,
Q. N.
,
Suh
,
Y.
,
Shao
,
B.
, and
Won
,
Y.
,
2019
, “
Boiling Heat Transfer Using Spatially-Variant and Uniform Microporous Coatings
,”
ASME
Paper No. IPACK2019-6307.10.1115/IPACK2019-6307
53.
Lin
,
C. H.
, and
Won
,
Y.
,
2020
, “
Pressure-Dependent Thermal Characterization of Biporous Copper Structures
,”
IEEE Trans. Compon., Packag. Manuf. Technol.
, 10(4), pp.
568
576
.10.1109/TCPMT.2019.2956722
54.
Lin
,
C. H.
,
Izard
,
A. G.
,
Valdevit
,
L.
, and
Won
,
Y.
,
2021
, “
Mechanically Compliant Thermal Interfaces Using Biporous Copper-Polydimethylsiloxane Interpenetrating Phase Composite
,”
Adv. Mater. Interfaces
,
8
(
1
), p.
2001423
.10.1002/admi.202001423
55.
Mahamudur Rahman
,
M.
,
Pollack
,
J.
, and
Mccarthy
,
M.
,
2015
, “
Increasing Boiling Heat Transfer Using Low Conductivity Materials
,”
Sci. Rep.
, 5, p.
13145
.10.1038/srep13145
56.
Hilpert
,
M.
, and
Ben-David
,
A.
,
2009
, “
Infiltration of Liquid Droplets Into Porous Media: Effects of Dynamic Contact Angle and Contact Angle Hysteresis
,”
Int. J. Multiphase Flow
, 35(3), pp.
205
218
.10.1016/j.ijmultiphaseflow.2008.11.007
57.
Pham
,
Q. N.
,
Shao
,
B.
,
Kim
,
Y.
, and
Won
,
Y.
,
2018
, “
Hierarchical and Well-Ordered Porous Copper for Liquid Transport Properties Control
,”
ACS Appl. Mater. Interfaces
,
10
(
18
), pp.
16015
16023
.10.1021/acsami.8b02665
58.
Washburn
,
E. W.
,
1921
, “
The Dynamics of Capillary Flow
,”
Phys. Rev.
,
17
(
3
), pp.
273
283
.10.1103/PhysRev.17.273
59.
Lucas
,
R.
,
1918
, “
Ueber Das Zeitgesetz Des Kapillaren Aufstiegs Von Flüssigkeiten
,”
Kolloid-Z.
,
23
(
1
), pp.
15
22
.10.1007/BF01461107
60.
Zuber
,
N.
,
1959
, “
Hydrodynamic Aspects of Boiling Heat Transfer
,” Physics and Mathematics, Los Angeles, CA, AEC Report No. AECU-4439.
61.
Incropera
,
F. P.
,
2013
,
Fundamentals of Heat and Mass Transfer
, 6th ed.,
Wiley
, Hoboken, NJ.
62.
Ahn
,
H. S.
,
Jo
,
H. J.
,
Kang
,
S. H.
, and
Kim
,
M. H.
,
2011
, “
Effect of Liquid Spreading Due to Nano/Microstructures on the Critical Heat Flux During Pool Boiling
,”
Appl. Phys. Lett.
,
98
(
7
), p.
071908
.10.1063/1.3555430
63.
Chu
,
K. H.
,
Enright
,
R.
, and
Wang
,
E. N.
,
2012
, “
Structured Surfaces for Enhanced Pool Boiling Heat Transfer
,”
Appl. Phys. Lett.
, 100(24), p.
241603
.10.1063/1.4724190
64.
Pioro
,
I. L.
,
Rohsenow
,
W.
, and
Doerffer
,
S. S.
,
2004
, “
Nucleate Pool-Boiling Heat Transfer. I: Review of Parametric Effects of Boiling Surface
,”
Int. J. Heat Mass Transfer
, 47(23), pp.
5033
5044
.10.1016/j.ijheatmasstransfer.2004.06.019
65.
Righetti
,
G.
,
Doretti
,
L.
,
Sadafi
,
H.
,
Hooman
,
K.
, and
Mancin
,
S.
,
2020
, “
Water Pool Boiling Across Low Pore Density Aluminum Foams
,”
Heat Transfer Eng.
, 41(19–20), pp.
1673
1682
.10.1080/01457632.2019.1640464
66.
Brumfield
,
L. A.
, and
Park
,
S.
,
2012
, “
The Effects of Asymmetric Micro Ratchets on Dynamic Contact Angle and Pool Boiling Performance
,”
ASME
Paper No. IMECE2012-87176.10.1115/IMECE2012-87176
67.
Pham
,
Q. N.
,
Zhang
,
S.
,
Hao
,
S.
,
Montazeri
,
K.
,
Lin
,
C. H.
,
Lee
,
J.
,
Mohraz
,
A.
, and
Won
,
Y.
,
2020
, “
Boiling Heat Transfer With a Well-Ordered Microporous Architecture
,”
ACS Appl. Mater. Interfaces
,
12
(
16
), pp.
19174
19183
.10.1021/acsami.0c01113