Device‐Scale Nanochannel Evaporator for High Heat Flux Dissipation

High heat flux values in thin film evaporation experiments are typically attained based on short wicking distance, ranging from tens to hundreds of micrometers between the meniscus and the liquid reservoir, thus making such devices vulnerable to quick drying out while also limiting their real‐world applicability. Here, the performance of a nanochannel (122 nm depth and 10 µm width) based evaporator with FC72 is demonstrated as working fluid. FC72 is an ideal fluid for electronics cooling as it is nonpolar and dielectric with a low boiling point. The 1 mm thick evaporator consists of more than 1000 nanochannels connecting two micro‐reservoirs 4.8 cm apart. Thin film evaporation experiments are conducted for four different power inputs, and the steady‐state wicking distance varied from 21 to 8 mm depending on the evaporator's working temperature. Direct weight measurement of evaporated FC72 is used to estimate the interfacial evaporative heat flux. Such a technique mitigates the need for contact angle measurement in micro/nano confined space, a methodology commonly used in literature studies that is prone to error and uncertainties. The maximum evaporative heat flux is 0.93 kW cm−2 at ≈65 °C hot spot temperature. Interestingly, the product of wicking distance and evaporative heat flux remain constant for all power inputs. Numerical simulations are performed to quantify heat loss and effectiveness of the evaporator.


Introduction
Phase change heat transfer is ubiquitous in nature [1,2] (e.g., transpiration, surface evaporation) as well as in numerous industrial applications [3,4] such as power generation and desalination. Thermal management solutions for integrated circuits (ICs) used in electronic devices frequently use evaporation, [5][6][7] a multiphase heat transfer mechanism, to maintain the temperature of such devices in the operational range. Ongoing DOI: 10.1002/admi.202300129 miniaturization [8,9] of ICs would require evolution of effective thermal management strategies to dissipate localized heat generation and attain 1 kW cm −2 of heat flux removal in near future. Additionally, space constraints in such devices require small form factor cooling solutions and have led to several approaches, including microchannel heat sinks, [10][11][12] embedded cooling, [13] nano/micro-structured heat pipes, [14,15] and graphene heat spreaders, [16] among others. Regardless of device type or design, thin film evaporation-based [17] cooling approach using heat pipes is considered one of the prominent techniques, prompting several studies [18][19][20] to address the on-chip hot spot thermal management. Such devices rely on the passive capillary-driven flow of working fluids, such as water, refrigerants, and alcohol, among others, enabled by porous wicks.
Numerous wick materials and fabrication techniques namely metallic pillars, [21,22] sintering, [23] and 3D printed metal [24] have been investigated to improve the thermal performance of evaporators in heat pipes. Recent studies [18][19][20] reporting interfacial evaporative heat flux ≈0.5-11 kW m −2 K −1 provide insight into the potential of thin-film evaporation-based devices for effective thermal management. However, the accuracy of evaporative heat flux [25,26] calculation with any fluid-wick structure combination directly depends on the reliability of contact angle (CA) measurement at the meniscus because it governs the pressure gradient required for capillary flow. The CA acquired from the meniscus image [18] or Young-Laplace equation [19] in the confined space may not be accurate because it is susceptible to errors in the detection of the three-phase contact line and the limitations associated with the camera/microscope field of view. Consequently, other studies have used the augmented Young-Laplace model, [25] interferometry, [26] and different contact angles for top and side walls of high-aspect-ratio wicks [27] to capture accurate apparent contact angle of fluid. In addition to the reliability of CA measurement, high interfacial heat flux is typically reported for wick distance of just a few microns, [18][19][20][28][29][30] however, such designs are prone to dry out and also may be limited for real-world applications. The evaporative performance relies heavily on maintaining the thin liquid film at the interface governed by capillary pressure and viscous pressure drop in wick/porous structure. www.advancedsciencenews.com www.advmatinterfaces.de Although a decrease in the geometrical parameters of the wick design enhances capillarity, increased viscous resistance restricts fluid flow. [17] For a characteristic length of "L" of a typical wick structure with wick distance "D" between liquid source and evaporation zone, capillarity scales as L −1 , in contrast, hydrodynamic resistance scales as DL −2 . Therefore, momentum transport poses a significant challenge in evaporator design of a heat pipe. Further, the choice of working fluid is dictated by its physical properties, the requirement for heat dissipation, suitability for the application site, and potential risks. Although water offers high surface tension and high latent heat relative to its viscosity, the choice of a low-viscosity working fluid is desirable for electronics applications and can even perform better than water. [20] Among these fluids, 3M Fluorinert electronic liquid FC72 with its dielectric properties, has been found to be a suitable working fluid in oscillating heat pipes [31,32] and has demonstrated superior heat transfer performance over water using gas-assisted thin film evaporation. [33] At lower film thickness, the volatility benefit of FC72 over water plays a critical role in attaining a relatively higher heat flux even with its low thermal conductivity.
In this work, we utilize thin-film evaporation in 1D nanochannels to develop a two-dimensional flat evaporator with FC72 as working fluid. We have devised a novel approach to estimate interfacial evaporative heat flux (q ev ) that, unlike the aforementioned studies, does not depend on contact angle measurements in confined spaces and associated uncertainties. The maximum q ev in our work was ≈0.93 kW cm −2 . Further, the maximum and steady wicking distance obtained was ≈21 mm, well beyond the values reported in the literature of a few microns. Herein, we propose a systematic approach to fabricate, assess and analyze the effectiveness of a steady-state thin film evaporation-based thermal management device. The 1 mm thick evaporator consists of an array of 48 mm-long 1100 nanochannels (122 nm by 10 μm) with micro reservoirs (20 μm by 22 mm) at both ends. This nanochannel-based evaporator will be referred to as nc-EVAP in the remainder of the text. Maroo et al. [34] proposed a similar kind of passive device having multiple channels connected to liquidfilled reservoirs capable of on-chip thermal management. We show that in the absence of thermal load, FC72 wicks from one reservoir of nc-EVAP to the other end, overcoming the hydraulic resistance as observed from a progressive decline in liquid front velocity. While testing at a higher temperature (≈88°C), significantly greater than the boiling point (≈56°C) of FC72, nucleation inside the nanochannel was not observed. At lower temperature (<56°C), menisci were observed to achieve steady state with wicking distance being dependent on the supplied heat flux. The current performance of nc-EVAP was evaluated against evaporative efficiency (ƞ ev ) and heat losses associated with this device were quantified, which also remain unexplored in previous studies. Maximum ƞ ev obtained was only ∼ 0.64% which highlights the importance of estimating heat losses. Thus, numerical simulations on COMSOL Multiphysics were also performed to quantify energy losses from the nc-EVAP. Interestingly, the interfacial evaporative heat flux (q ev ) was found to vary inversely with the wicking distance, such that the product of both appears to be constant for all four supplied heat flux values. The current study demonstrates the performance of a nanochannel-based evaporator at working scale as well as the quantification of parameters associated with it. Figure 1a shows the 3D model of the nc-EVAP. FC72 entered the device through openings fabricated in glass right over the micro-reservoirs. Details for nc-EVAP fabrication methodology are discussed in Supporting Information ( Figure S1 and Note S1, Supporting Information). Depending on the experimental requirement, either single or both openings could be used to supply FC72. Heater is attached in the center and bottom of nc-EVAP along with a thermocouple ( Figure S2, Supporting Information). Atomic force microscopy (performed during fabrication) on a channel cross-section, and depth variation are shown in Figure 1b,c, respectively. The average depth of a nanochannel was ≈122 nm with width ≈10 μm. Micro-reservoirs were of dimension 22 mm × 6 mm and length of nanochannels connecting them was ≈48 mm. The top view of nc-EVAP used in experiments is shown in Figure 1d. Yellow tape pieces covering the openings kept the micro reservoirs clean until the tube reservoirs were attached ( Figure S2, Supporting Information) before the experiments. Micrograph of a portion of nc-EVAP ( Figure 1e) showed the alternating nanochannels (light shade) and silicon ridges (dark shade), each of width ≈10 μm. Figure 2a shows the schematic of the experimental setup that has tube reservoirs with sealing plugs, heater, plastic support, and aluminum base plate attached to the nc-EVAP. The meniscus movement was tracked and visualized under the microscope (Figure 2b), and the location of the meniscus from the microreservoir (i.e., wicking distance) was determined using a reference scale placed beside the nc-EVAP. The left tube reservoir in Figure 2b was longer than the right one because it was primarily used to hold the FC-72 during nc-EVAP experiments, and the scale markings (least count: 0.01 mL) on its curved surface estimate the amount of FC72 evaporated during the experiments. At each input heat flux, nc-EVAP was first observed under a microscope, then temperature was monitored using an infrared (IR) camera ( Figure 2c). Temperature distribution on the nc-EVAP was recorded for 120 s after achieving steady state (≈20 min after heat flux supply). Figure 2d depicts successive images of FC72 wicking (at no supplied heat flux) in the nanochannels, as shown by the shift in color and contrast during the process. FC72 gradually floods the nanochannels all the way to the other microreservoir. Details of the nc-EVAP fabrication procedure, materials used, characterization, and other procedural details are presented in below.

Fabrication of Nanochannel Evaporator
Fabrication of the nanochannel evaporator started with a 4-inch 500 μm thick silicon wafer involving dedicated photolithography procedures. The detailed procedure and methodology are provided in Supporting Information ( Figure S1 and Note S1, Supporting Information). Nanochannels fabricated orthogonally to the micro-reservoirs of dimension 22 mm × 6 mm by 20 μm. Borofloat glass wafer underwent anodic bonding with silicon wafer such that openings in glass wafer were over micro-reservoirs. After dicing, each bonded wafer yielded two nanochannel evaporator samples. The heater attached to the bottom of the evaporator was fabricated separately. Heater fabrication started with a silicon wafer on which a 90 nm thick indium tin oxide (ITO) film was deposited by physical vapor deposition (PVD). Then a 500 nm thick copper layer was deposited as electrodes. The ITO between the copper electrodes acts like a Joule heater when a direct current passes through it.

Materials and Characterization
Electronic liquid FC 72 used as working fluid in the evaporator was procured from 3M. Plastic tubes acting as reservoirs attached above the micro-reservoir opening were commercially available thin syringes trimmed to the required size. Micrographs of the nanochannel sample were captured using an upright microscope (Nikon, Eclipse-LV150NL). The surface topography of the sample was analyzed by atomic force microscopy (AFM) using Vecco Icon AFM tool. The weight measurements were recorded using Pioneer analytical (Model: PX224/E, least count: 0.1 mg) weighing scale connected to a computer. A high-speed camera (Phantom, V611) captured the FC 72 wicking in the nanochannels that was later used to obtain liquid front velocity by performing image analysis through a custom MATLAB script. The temperature was recorded using a combination of K-type thermocouple connected to the data acquisition system (National instruments, NI 9211). An infrared (IR) camera (A6753SC, FLIR Systems) was used to record the evaporator temperature distribution at different input heat flux. www.advancedsciencenews.com www.advmatinterfaces.de

Heating and Meniscus Stability
Heat flux was provided by a resistive heater attached to the bottom of the evaporator, powered by a DC power supply. The performance of the evaporator was analyzed using either a microscope to visualize the menisci behavior or an infrared camera to monitor the temperature distribution. Menisci steady state was achieved when the stable liquid front was confirmed under the microscope, which generally occured after 20 minutes of any change to the supplied heat flux. Videos were captured for 2 minutes after reaching steady state. Furthermore, at each heat flux, the experiment was repeated under an IR camera to record the temperature distribution.

COMSOL Analysis
Numerical analysis to compute heat losses during experiments was performed in COMSOL Multiphysics. Further explanation of domains, boundary conditions, and methodology is provided in the Supporting Information ( Figure S3 and Note S5, Supporting Information). Built-in surface integral of heat flux function was used to calculate the natural convection heat losses (from the aluminum base plate (Q al ), reservoir tubes (Q pt ), plastic base under evaporator (Q pb ), evaporator bottom (Q wb ), and evaporator top (Q wt )) associated with the model at steady state.

Wicking Under No Supplied Power
The wicking of liquids in nanochannels is attributed to capillary pressure, [35,36] and the motion of liquid inside is given by the Lucas-Washburn [37] L wd = Kt 0.5 (1) where L wd is wicking distance, t is the elapsed time, and K is a constant depending on the geometrical properties [36] of the capillary tube and physical properties of the liquid. Coefficient K for high aspect ratio (width >> depth, as in present case) channels is given by following equation [36] K = (h cos ∕3 ) 0.5 (2) where h is the nanochannel height, is FC72 surface tension, is the advancing contact angle of FC72 meniscus inside nanochannels, and μ is the dynamic viscosity of FC72. Linear variation of wicking distance with t 0.5 given in Equation 1 has been verified to hold valid for meniscus wicking inside nanochannels. [27,38] In the present study FC72 is filled in from only one of the reservoirs (Movie S1, Supporting Information) of nc-EVAP keeping the other empty. A high-speed camera captures wicking video, which is later processed using MATLAB script to obtain continuous wicking distance (Figure 3a) confirming the linear relation between the wicking distance and t 0.5 proposed by Equation 1. Furthermore, liquid front velocity (V wf ) during the wicking process is shown in Figure 3b and is also obtained by image processing (Note S2, Supporting Information). The flow of liquid through nanochannels leads to the occurrence of disjoining pressure [27] and the development of ultra-thin stagnant layers on the solid surface. [36] V wf drastically diminishes within ≈250 s of wicking (L wd ≈ 19 mm) due to viscous resistance, and approaches ≈15 μm s −1 toward the end. After complete wicking, the nc-EVAP was kept on a computerconnected weighing scale to record the weight loss due to the evaporation of FC72 as shown in Figure 3c. The tube reservoirs are arranged so that the long tube (inset, Figure 3c) with scale marking containing FC72 is kept plugged (i.e., closed) to prevent surface evaporation, while the other tube reservoir is left open to the atmosphere. The recorded weight loss (Figure 3c) over a period of 2 h was then calibrated against the drop in the level of FC72 in the right reservoir. The weight loss obtained from the weighing scale was 113.9 mg over 2 h, compared to a drop in FC72 level of 0.07 mL (or 117.6 gm of FC72). This equates to a difference of only ≈3.2% between them (Note S3, Supporting Information). This weight change-based approach of finding evaporative mass flux and subsequent evaporative heat flux (for localized heating, see next section) is rather unconventional and independent of contact angle-based methodology extensively used in literature. Deviating from macroscale to nanoscale, meniscus shape, and hence contact angle accuracy, depend on numerous factors such as the resolution of the image, refractive index of glass, molecular interaction between fluid-solid surfaces, and contamination in confined spaces. Certainly, edge detection of the microscopic image of the liquid-vapor interface may not be an accurate technique for finding the contact angle. Studies [25,39] show that there exist inherent issues in confinement, such as significant variation between the actual and apparent contact angle and potential deformation of tmicrostructure at the three phase contact line under negative pressure. Although the current weight loss approach does not capture details of the interfacial phenomena, it does account for the macroscopic performance of nanochannels. Evaporative mass flux (m ev ) in the absence of active heat flux was ≈12.8 kg m −2 s −1 obtained from the following equation: where, ∆m is mass change of FC72 in the tube reservoir (kg), t ev is the total evaporation time (s), and A nc is the total cross-sectional area of nanochannels (m 2 ). Please note that A nc does not include nonfunctional/blocked nanochannels that were found to be 84 (out of total of 1100). Prior to evaluating the performance of nc-EVAP, emissivity (ɛ) calibration of evaporator top surface was performed as shown in Figure 3d. The temperature recorded by the IR camera and thermocouple matches well at ɛ = 0.92, and this value of ɛ has been used in this work.

Heating and Meniscus Stability
Initially, both the reservoirs were filled with FC72 and allowed sufficient time to completely wick into the nanochannels (like Figure 2d) with sufficient additional FC72 present in reservoirs. Subsequently, the sample was heated beyond its normal boiling point (≈56°C) by supplying 5.53 W (11.8 W cm −2 ) while continuously monitoring the nanochannels under the microscope. Interestingly, despite the surface of nc-EVAP at ≈88°C (Figure 4a), no sign of nucleation was observed. On the contrary, vigorous boiling was seen at the opening of the micro-reservoirs (Movie S2, Supporting Information). Nucleation does not occur in the nanochannel primarily due to combination of disjoining pressure and the associated increase in energy required to increase pressure and displace liquid. [27,40] Instead, heat from the heater is conducted laterally along the silicon wafer causing the surface temperature at micro-reservoirs to rise above boiling point. Following the dry out at the reservoirs, the menisci receded rapidly (Figure 4a) from reservoir at one end s to the other (Movie S3, Supporting Information).
To obtain stable menisci under heated conditions, FC72 was filled in only one of the reservoirs.
Stable menisci refer to very little change ≈±0.64 μm s −1 (maximum observed) in meniscus position after 20 min of steady power supply. Depending upon the supplied power, stable menisci were achieved (Figure 4b) regulated by FC72 evaporation rate and subsequent momentum transport governing the FC72 flow to the liquid-vapor interface. Four levels of power input at heater: 0.64, 0.92, 1.63, and 2.20 W (corresponding heat flux: 1.36, 1.96, 3.48, 4.69 W cm −2 ) were utilized in nc-EVAP performance analysis. The distance at which the menisci attain a steady state is called wicking distance (L wd ) which is measured after confirming the meniscus stability under the microscope (Movie S4, Supporting Information). The temperature recorded by IR camera for Q = 2.2 W near the left reservoir (L), right reservoir (R), and above the heater (C) is shown in Figure 4c. The temperature near the right reservoir is lower than the left counterpart due to the presence of FC72 in the right one. m ev and L wd for all four supplied power levels are shown in Figure 5a. At 2.20 W, extremely highm ev ≈105.4 kg m −2 s −1 was recorded. Increased power supply to 2.20 Wcaused a reduction in L wd from 21 mm (at 0.64 W), however nc-EVAP maintained L wd = 8 mm (at 2.20 W) at temperature ≈52°C (measured near meniscus) and close to the boiling point of FC72. At steady state, the contribution of interfacial evaporation in cooling (Q ev ) is given by: where is the density of FC72 (1.68 g cm −3 ), ∆V is the change in FC72 volume in the tube reservoir (mL), h fg is the latent heat of vaporization of FC72 (88 J g −1 ), and t ss is the experiment duration after achieving steady state. ∆V is acquired over t ss = 30 min. Steady state interfacial evaporative heat flux (q ′′ ev ) for each supplied heat power is written as: A nc = 1.24 × 10 −05 cm 2 is the total cross-sectional area of nanochannels (cm 2 ). Details on uncertainty analysis and numerical values are presented in Note S4 and Table S1 (Supporting Information), respectively. For a moving meniscus, q ′′ ev is also given by: where v f is the liquid front velocity and for a flow thorough rectangular channel, it can be approximated as [18] v f ∝ h 2 ΔP L wd (7) where h is the height of the nanochannel, ∆P is the capillary driving pressure over L wd , and μ is dynamic viscosity of the liquid. The inverse relationship between v f and L wd can be observed in Figure 3a,b. From Equations 6 and 7, following observations can be made: Equation 8 implies that even though q ′′ ev increases with supplied heat input (Figure 5b), the product of interfacial evaporative heat flux and wicking distance remains uniform as verified with experimental results shown in Figure 5b. In the current study, maximum q ′′ ev obtained was 0.93 kW cm −2 and average q ′′ ev L wd was ≈0.73 ± 0.02 kW cm −1 . So, a similar nc-EVAP designed to maintain a shorter wicking distance L wd ≈ 100 μm can theoretically achieve q ′′ ev ≈ 73 kW cm −2 , which is within the kinetic theory predictions [17] of maximum q ′′ ev ≈ 110 kW cm −2 . The efficiency of nc-EVAP (Figure 5c) is written as: where Q is supplied power to nc-EVAP. While local interfacial evaporative heat flux (q ′′ ev ) can attain ≈1 kW cm −2 or higher as reported studies, its efficiency in actual device cooling is typically restricted or not reported. In the current study, ƞ ev for all four  levels of supplied power was <1% due to the high q ′′ ev restricted only to a minuscule interfacial area inside nanochannels. This aspect of nanostructured-based evaporators should also be investigated to enhance ƞ ev apart from the primary focus on achieving higher q ′′ ev .

Heat Loss Estimation
While evaporative heat flux contributed <1% to the thermal management, other factors such as conduction through silicon and subsequent heat loss via natural convection reduced hotspot temperature. We performed COMSOL simulation to examine the hot spot temperature and associated convection heat losses in presence of nc-EVAP by comparing experimental and simulation temperature values.
3D model and temperature distribution (for Q in = 0.64 W) on the experimental setup obtained using COMSOL simulation are shown in Figure 6a. Additional details related to the simulation for other power levels are discussed in Figure S3 and Note S5 (Supporting Information).
A comparison of maximum surface temperature obtained from simulation results and experiments (both by IR and thermocouple) for each of the supplied powers is shown in Figure 6b. There is excellent agreement between IR measurements, thermocouple data and the COMSOL results, and corresponding percentages of the natural convection heat loss from various sources are shown in Figure 6c. The convection losses were from the aluminum base plate (Q al ), reservoir tubes (Q pt ), plastic base under the evaporator (Q pb ), bottom silicon surface of the evaporator (Q wb ), and top glass surface of the evaporator (Q wt ), which were estimated by performing COMSOL simulations. As expected, heat loss from the top surface of nc-EVAP (Q wt ) contributes the most in each case. Even though the maximum q ev was ≈0.93 kW cm −2 for Q in = 2.2 W, net cooling provided only by evaporation was ≈11.5 mW, and cooling was predominantly accomplished by heat losses via natural convection on the experimental setup. Similarly, previous studies [6,18,19,28] that demonstrate very high q ev utilizing various types of porous structures, nanoporous membranes, and porous wicks, among others, to enhance evap-orative heat flux require a new perspective to assess the net effect of such q ev improvements on device cooling and associated heat losses through other components.

Conclusion
A systematic approach of fabricating a practical nanochannelbased evaporator (nc-EVAP) was presented, and its performance was evaluated with dielectric FC72 as the working fluid. The nc-EVAP device included 1100 nanochannels of cross-sectional area 122 nm × 10 μm running across a length of ≈48 mm between two micro-reservoirs. nc-EVAP was designed to facilitate the direct measurement of the change in mass during evaporation of FC72, and thus the interfacial evaporative heat flux (q ′′ ev ) was estimated without contact angle measurement of the meniscus in nanochannels and the associated uncertainties that accompany such an approach. When the channels and both reservoirs were filled with FC72, nucleation was not observed even at temperature of ≈88°C, well beyond the boiling point of FC72. When the channels were filled with FC72 using only one reservoir while the other reservoir was open to the atmosphere, stable evaporating menisci were obtained for different power inputs. At lower input heat flux, a maximum steady state q ′′ ev ≈ 0.93 kW cm −2 was achieved at maximum surface temperature of ≈63°C. The maximum variation of temperature in the nc-EVAP was ≈11°C from the central hot spot to the micro-reservoir at 2.20 W. Depending on the given heat flux, the wicking distance ranged from 21 to 8 mm. The product of the steady q ′′ ev and the wicking distance was found to be nearly constant for all power inputs. This suggests the possibility of achieving high q ′′ ev by tailoring wicking distance even under steady state as compared to superior heat transfer performance during transient meniscus variation as reported in the literature. Another aspect of such an evaporator is the evaporative efficiency, i.e., the absolute contribution of the thermal management solution to the cooling of a hot spot, which is found to be restricted to < 1% due to the limited meniscus area in nanochannels. Numerical simulations were performed to calculate the contribution of different components of heat losses in the nc-EVAP system. As a result, appropriate modifications in nanochannel design, such as incorporating nanostructures, are required to improve the interfacial area. The cross-section of the nanochannels can vary depending on the thermal load since it governs the transport of FC-72 from reservoir to the hot spot. Further, nanochannels can be designed with a reduced length (≈2 cm) that corresponds to the maximum stable wicking distance at the desired working power, which would not only minimize the convection heat losses from the surface but also provide the additional benefits of compact size and being lightweight. These suggested modifications in the future could have a significant impact on thermal management in electronic systems.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.