Electrifying both stationary and mobile systems requires ultra-compact, lightweight power electronics and electric machines. Increasing the volumetric and gravimetric density of these systems is constrained, however, by the capacity to remove heat from these assemblies. A promising method for extracting heat is jumping droplet condensation, which can address both spatially and temporally changing hotspots. Yet, disagreement exists in the literature about the maximum attainable heat flux for water-based, droplet jumping devices such as vapor chambers, with values ranging from 5 to 500 W/cm2. Here, using thermal measurements and optical imaging in pure vapor conditions, we directly observe the hydrodynamics occurring inside of a jumping droplet vapor chamber. Our experiments show that flooding is the key obstacle limiting jumping droplet mass flux to hot spots, limiting heat transfer to less than 15 W/cm2. These results indicate that past works reporting high heat fluxes benefited from other hot spot cooling pathways such as previously observed liquid bridges formed due to flooding. To test our hypothesis, we characterize progressive flooding on a variety of structured surfaces ranging in length-scale from 100 nm to 10 μm. Progressive flooding was delayed by decreasing the length-scale of the surface structures, which supports recent observations in the literature. Our work not only helps to understand the wide variability of past results quantifying droplet jumping heat transfer, but also provides design guidelines for the development of surfaces that are capable of maintaining enhanced jumping droplet condensation.

Wide-bandgap transistors incorporating gallium nitride (GaN) and silicon carbide (SiC) are catalyzing the development of higher power density and higher efficiency converters.1,2 Yet, as the transistor package size decreases, the surface area for cooling diminishes. Employing thermal interface materials3 constrains improvements in power density and specific power of the complete system due to the necessity for bulky heat sinks.1–6 The integration of efficient cooling with chip-scale wide bandgap transistor packages would improve reliability and device performance by maintaining lower device junction temperatures.1,2,5

To ameliorate this concern, directed cooling mechanisms are required to mitigate hotspots and catalyze further increases in power density.5 One thermal management approach for extracting heat involves liquid-vapor phase-change cooling. Motivated by the recent demonstration of controllable jumping-droplet electronics cooling on suitably designed superhydrophobic surfaces in ambient conditions,6–15 as well as the wide variability of recently reported maximum jumping droplet heat fluxes,16,17 we experimentally investigate the hydrodynamics and heat transfer physics in the pure vapor environment of an open vapor chamber with water as the working fluid to benchmark the thermal management of GaN devices.

Figure 1 depicts the closed-loop behavior of the jumping droplet process and highlights how this scheme can be integrated into a dense electronics assembly for directed cooling. While GaN transistors were selected to represent generic power electronics hotspot generators, these heat-generating devices could be any passive, active, or support logic component. The hotspots are enclosed within the vapor chamber in order to avoid any series thermal impedances from contact mechanisms like solder or thermal interfaces. To avoid safety hazards from high-voltage switches and to ensure a robust, highly reliable design, this scheme requires a thin electrically isolating coating layer for the hot side of the vapor chamber.7 A key benefit of jumping droplet vapor chambers7–17 over other state-of-the-art cooling schemes is wickless liquid transport from the condenser to evaporator.16,17Figure 1 demonstrates how, instead of relying on wick structures, cold droplets jumping independent of gravity from the nanostructured superhydrophobic surface are guided toward the hotspots using externally supplied electric fields, extract heat from the hot spot during evaporation, and return to the cold plate as hot vapor. Thus, the heat transfer process is not limited by the need for external pumping or capillary forces to drive liquid return to the hotspot. The lack of pumping required is a key benefit due to: (1) alleviation of aspect ratio design requirements governed by the need for liquid return,18 (2) elimination of additional thermal resistances from wick structures, and (3) simplified manufacturing and integration.

FIG. 1.

Schematic showing how external electric fields inside of a vapor chamber can be employed to guide jumping droplets toward hotspots independent of gravity. Heat is extracted from the electronics via evaporation, and vapor returns without a wicking structure to the cold surface where it is spread via condensation.

FIG. 1.

Schematic showing how external electric fields inside of a vapor chamber can be employed to guide jumping droplets toward hotspots independent of gravity. Heat is extracted from the electronics via evaporation, and vapor returns without a wicking structure to the cold surface where it is spread via condensation.

Close modal

Building on observations from investigations of jumping droplet cooling in ambient conditions,14,15 we began by exploring the governing physics behind jumping droplet heat transfer inside of a well-controlled vacuum chamber in order to reduce the amount of non-condensable gases.19,20 While the vast majority of vapor chamber research involves assemblies that do not permit imaging of the vapor space, Fig. 2(a) underscores how the custom experimental setup built around a 24″ cube vacuum chamber (Kurt J. Lesker) offers the unique capability to visualize coupling between heat dissipation and hydrodynamics. To observe dynamics within the vapor space, the chamber contains multiple 6″ optical viewports, allowing access to a high-speed camera (Photron FASTCAM Mini AX200 coupled to an InfiniProbe TS-160 lens).

FIG. 2.

(a) Image of the chamber test bed used to conduct the jumping droplet electronics cooling experiments. (b) Copper cold plate having (c) CuO nanostructures with HTMS in order to ensure superhydrophobicity. Each transistor on a (d) custom power device testbed both generated heat and (e) served as a high-sensitivity heat flux sensor.

FIG. 2.

(a) Image of the chamber test bed used to conduct the jumping droplet electronics cooling experiments. (b) Copper cold plate having (c) CuO nanostructures with HTMS in order to ensure superhydrophobicity. Each transistor on a (d) custom power device testbed both generated heat and (e) served as a high-sensitivity heat flux sensor.

Close modal

Automating a large portion of the data collection and instruments for the experimental setup facilitated the rapid testing of different structured surfaces with the electronics testbed shown in Figs. 2(b)–2(d). To ensure the rapid transition from condensation to evaporation, the testbed was designed with the capability of switching between hot and cold liquid loops. As depicted in Fig. 2(a), liquid water flowed through the cold plate at a rate of 22 ± 0.1 LPM (ThermoFisher Scientific SYS III) to ensure minimal thermal resistance from the coolant to the cold plate enabled by highly turbulent flow (ReD 90 000, where D = 5 mm is the cold plate internal channel diameter). Moreover, the chiller-cooling loop can be isolated from the experimental setup with a series of valves and a bypass loop. As a result, hot fluid can be passed through the chamber from a separate heating bath (Polyscience SD07R-20-A12ER) in order to enable non-intrusive cleaning of a flooded surface and repeated tests at the same vapor pressure via thermal cycling of the cold plate. To quantify the heat transfer enhancement from jumping droplets, we used a copper (Cu) cold plate (Wakefield-Vette 120455) functionalized with a nanoengineered superhydrophobic surface21 as depicted in Fig. 2(c) (see supplementary material, Sec. S1 for full fabrication details). Briefly, after cleaning the Cu cold plates, a CuO superhydrophilic surface was created by immersing the cold plate in a heated alkaline bath. Next, chemical vapor deposition of a fluorinated silane (heptadecafluorodecyltrimethoxy-silane, HTMS) yielded a superhydrophobic surface with apparent advancing and receding contact angles of 172.1 ± 1.9° and 168.5 ± 6.7°, respectively, (MCA-3, Kyowa Interface Science Ltd). Figures 2(d) and 2(e) highlight how the GaN transistors served both as hotspots and as heat flux sensors.7,14,15 The junction temperature of the GaN device was tracked in real time during experiments by measuring the dc electrical resistance Rdson, which eliminated the need for attaching thermocouples to the GaN devices.7,14,15 During the experiments, the highest rate of condensation occurred at the condenser locations closest to the hotspot11 since this is the smallest diffusion path for hot vapor to return to the cold plate. Similar to the behavior observed in the ambient environment,14,15 external electric fields enabled enhancement of both heat flux and duration of cooling by offering a larger area for replenishment of cold condenser liquid. Electric fields also help to magnify heat spreading and to reduce the rate of droplet accumulation and ultimate flooding on the superhydrophobic surface. Interestingly, electric fields offer more than three orders-of-magnitude larger force on jumping droplets when compared to magnetic fields (Sec. S2, supplementary material).

Figure 3(a) shows high-speed time-lapse images demonstrating the ability of electric-field-enhanced (EFE) jumping droplet condensation to cool GaN hotspots (see Videos S1 and S2). Interestingly, imaging revealed that the mass flux of droplets reaching the GaN device was <10 000 droplets per second from an area of the cold plate 6 larger than the area of the GaN device. Estimating the average droplet radius as 50 μm using image analysis, this corresponded to a heat flux of q 15 W/cm2 averaged over the enter GaN transistor surface area exposed to the jumping droplets (see Sec. S3, supplementary material). Since the junction temperature, Tj, of each GaN transistor could be tracked with a propagated uncertainty of ± 0.8 °C [Fig. 3(b)] and power dissipated, PD, with an uncertainty of ± 2.1 mW, our heat flux measurements had a resolution of ± 0.02 W/cm2 (Sec. S4, supplementary material). Figure 3(c) shows the normalized temperature difference, ΔTj, defined as ΔTj(t)=Tjt/Tj(t1), where Tj(t1) corresponds to the junction temperature after reaching the calibrated settling value based on the cold plate temperature. The transient cooling of the GaN devices was significantly lower than that expected from theory and past experiments.17Figure 3(c) also highlights that enhanced cooling did not exist for a sustained period of time due to the transition to progressive flooding depicted in the final frames of Fig. 3(a), which results in an increasing jumping droplet departure diameter and an overall decrease in the jumping droplet mass flux. For the experiments conducted here, electrical power was supplied to each GaN transistor prior to vapor supply into the evacuated chamber in order to determine the impact of radiation and to provide a calibration of performance, Tj,vac, as the cold plate was cycled between cold (e.g., 20 ± 0.5 °C) and hot (e.g., 60 ± 0.5 °C) temperatures. Thus, insight about the junction temperature for different input powers and surface temperatures was obtained. Prior to injecting pure water vapor, the hot liquid loop was connected to the sample so that incoming steam did not influence the saturation conditions. Based on the known temperature of the cooling fluid loop (Fig. S4, supplementary material), pure vapor was allowed to flow until the vapor pressure, Pv, ensured that the supersaturation was less than the critical supersaturation, S1.06, for nucleation-mediated flooding.11,13 For example, for Pv 2.5 kPa, the coolant temperature was set to 20 ± 0.5 °C to ensure that jumping droplet condensation would occur once the cold plate temperature decreased. These supersaturation conditions were maintained for other vapor pressures by adjusting the coolant temperature accordingly. Nucleation-mediated flooding does not enable jumping droplets since condensate in the Wenzel state forms within the nanostructures immediately and has larger adhesion to the surface. In contrast, when droplets condense on top of the functionalized surface in the Cassie–Baxter state, jumping does occur and progressive flooding develops over time as the average jumping droplet diameter increases and pinning becomes more prevalent. An additional measurement before starting the investigation of jumping droplets examined the impact of radiation and single-phase convection without phase-change by adjusting the temperature of the hot bath, while keeping the supersaturation below unity to prevent condensation, and tracking the junction temperature for this non-jumping case, Tj,nj. The change in Tj for each GaN switch as well as an array of other temperatures inside of the setup (i.e., back of the printed circuit board (PCB), chamber ceiling, chamber wall near the window, various locations on the cold plate, and inlet/outlet of the cold plate) was captured in real-time during all four phases of a single experimental run. Furthermore, imaging of initial nucleation once the coolant was routed into the cold plate, the period of jumping droplet condensation, the transition to progressive flooding, and the process of fluid evaporating from the cold plate by switching the inlet fluid to the hot supply was observed and recorded. For a single pressure condition, the experimental runs were repeated with and without applied electric fields (100 V/cm). The entire experimental process was implemented for a range of pressures (2.5 kPa–8.8 kPa). To characterize droplet jumping heat flux, Tj was monitored for a given input power before and after jumping. For a fixed loss (input heat flux), we measured how jumping droplets impacted the decrease in Tj from Tj,nj toward Tj(t1) based on the experimental supersaturation conditions for the cold plate. When the surface did not flood, the electrical input was increased until Tj approached the value of the non-jumping measurement, Tj,nj. Combining insights from all of these measurements ensured that the contribution from droplet jumping was accounted for in the heat flux measurement along with the fixed radiative components to the cold plate and convection to the surrounding gas. For all experiments, the maximum dissipated GaN heat flux was < 15 W/cm2, indicating that significant limitations to droplet jumping cooling existed.

FIG. 3.

(a) Time-lapse images (Pv = 5.4 kPa, S = 1.06, q = 10 W/cm2) highlighting a decrease in the number and an increase in the diameter of jumping droplets. (b) Example of real-time data capture highlighting how thermal cycling of the inlet temperature enables several measurements of the jumping droplet cooling of the separate GaN transistors (GaN 1 and GaN 2) to be obtained for the same vapor pressure, Pv. (c) Normalized change in the GaN junction temperature, Tj, with and without an applied electric field (EF) during jumping droplet cooling for q= 15 W/cm2 and S= 1.06 starting 10 s before the inlet temperature changes. The measurements highlight a small increase in the slope of ΔTj for all vapor pressure conditions with the most pronounced improvement for 7.3 kPa.

FIG. 3.

(a) Time-lapse images (Pv = 5.4 kPa, S = 1.06, q = 10 W/cm2) highlighting a decrease in the number and an increase in the diameter of jumping droplets. (b) Example of real-time data capture highlighting how thermal cycling of the inlet temperature enables several measurements of the jumping droplet cooling of the separate GaN transistors (GaN 1 and GaN 2) to be obtained for the same vapor pressure, Pv. (c) Normalized change in the GaN junction temperature, Tj, with and without an applied electric field (EF) during jumping droplet cooling for q= 15 W/cm2 and S= 1.06 starting 10 s before the inlet temperature changes. The measurements highlight a small increase in the slope of ΔTj for all vapor pressure conditions with the most pronounced improvement for 7.3 kPa.

Close modal
FIG. 4.

(a) Image of the experimental setup residing inside the test-bed [Fig. 2(a)] used to obtain top-view images of the condensing samples with a mirror. (b) Top-view scanning electron micrographs of the structured samples used in the experiments. Top-view optical images of the structured samples (c) before and (d) after the injection of vapor in order to demonstrate how structure length-scale impacts flooding characteristics and jumping droplet behavior. All structures transitioned to the flooded condensation regime due to progressive flooding. Time t = 0 is defined as the time when condensate nucleation was first observed.

FIG. 4.

(a) Image of the experimental setup residing inside the test-bed [Fig. 2(a)] used to obtain top-view images of the condensing samples with a mirror. (b) Top-view scanning electron micrographs of the structured samples used in the experiments. Top-view optical images of the structured samples (c) before and (d) after the injection of vapor in order to demonstrate how structure length-scale impacts flooding characteristics and jumping droplet behavior. All structures transitioned to the flooded condensation regime due to progressive flooding. Time t = 0 is defined as the time when condensate nucleation was first observed.

Close modal

A second method providing support to the low heat flux observations involves examination of d(ΔT)/dt [Fig. 3(c)] during experiments and comparing them to other GaN device cooling methods. An aggressive phase-change cooling scheme previously observed to support high heat flux inside of compact vapor chambers involves self-assembled liquid bridges that connect the hot and cold surfaces and enable confined boiling.7 While the d(ΔT)/dt for liquid bridge confined boiling7 in the same experimental embodiment approached 15 K/s, d(ΔT)/dt for radiation/convection and EFE condensation was 0.01 K/s and 0.07 K/s, respectively, representing a difference of over three orders-of-magnitude. Scaling the two results based on the maximum heat flux obtained by liquid bridge confined boiling (100 W/cm2) indicates that heat fluxes during transient cooling of the GaN devices do not exceed 15 W/cm2.

Our heat transfer measurements revealed a measureable improvement in cooling when an external electric field is applied. The maximum difference in heat flux for conditions without and with EFE was 5 W/cm2 for only the first 20 seconds. High-speed video supports this observation, showing surface flooding after 150 s. Note that inverting the orientation of the setup for gravity-assisted jumping did not prevent surface flooding and did not significantly increase the maximum heat flux observed due to jumping droplets. In fact, inversion of the experiment often promoted the formation of liquid bridges. Moreover, repeating the experiments for higher vapor pressures resulted in lower heat fluxes and temperature differences due to faster nucleation mediated flooding.

To explore the impact of flooding, we conducted additional condensation experiments using a variety of structured surfaces having varying length scales. Figure 4(a) depicts how the experimental setup was modified by inclusion of a mirror to observe simultaneously top-view condensation dynamics on five different nanoengineered samples. In order to provide a fair comparison with previous heat transfer characterization, the flooding experiments were conducted for the same pressure range. Figure 4(b) shows top-view scanning electron micrographs of the structured superhydrophobic surfaces, including etched aluminum microstructures (l 10 μm, etched Al), copper oxide microstructures (l 1 μm, CuO), titanium dioxide nanostructures (l 500 nm, TiO2), and aluminum oxy-hydroxide nanostructures (l 100 nm, AlO(OH)). To attain superhydrophobicity and ensure that all samples were coated with identical hydrophobic chemistry, all samples were conformally coated with HTMS. For fabrication details of all samples, see Sec. S1 of the supplementary material. Examining time-lapse images of the samples taken with a DSLR camera (Cannon EOS Rebel T6) at a frequency of 1 Hz [Figs. 4(b) and 4(c)] revealed that flooding occurred first on etched Al (largest length-scale) and last on AlO(OH) (smallest length-scale). As previously hypothesized, the structure length-scale plays a critical role in flooding resistance, with smaller scale structures enabling higher nucleation densities of smaller discrete droplets without coalescence between neighboring unit cells of the structure.13 This observation also agrees with a recently developed model22 highlighting how flooding can be passively delayed by controlling the nucleation density and preventing fluid from pooling inside nanostructure cavities. Although demonstrated here to delay flooding, future work should build on these observations and prior modeling to examine how the use of smaller length-scale structures can help reconcile the difference in heat transfer measurements when compared to previous literature.11,16,17 Water was studied here since superoleophobic and superomniphobic surfaces have not been shown to support condensation-based droplet jumping,23 though recent research in examining how techniques such as macrotexturing can promote droplet shedding and jumping for artificially placed droplets show promise.24 These results are also relevant for the development of nanoengineered structures for routing and repelling low surface tension fluids in self-cleaning and embedded cooling applications.24,25 In summary, our experimental observations highlight critical jumping droplet cooling limitations stemming from the inability of the superhydrophobic surface to eliminate flooding. Both high-speed video and heat transfer measurements support the hypothesis that jumping droplets cannot support high heat fluxes for even short timescales (30 s) with current state-of-the-art nanostructured surfaces. Future research is required to develop nanostructured surfaces that can both decrease the average radius of droplets departing the condensing surface and maintain this average departure radius in order to catalyze higher jumping droplet mass fluxes. In addition to engineering nanostructures of different length-scales and spatially controlled nucleation sites, surface engineering must also ensure that the conformal hydrophobic coatings prevent droplet pinning and degradation.26,27 Our experimental observation of jumping droplet condensation time-dependent progressive flooding points to the need for more efficient removal mechanisms from the condensing surface once droplets depart. Interestingly, for confined, low aspect ratio devices such as vapor chambers, flooding ultimately yields self-assembled liquid bridges. These liquid bridges can support heat fluxes exceeding 100 W/cm2 via confined boiling, which is the most likely mode of heat transfer in vapor chambers as characterized in past literature.7,16,17 Our work signifies that while jumping droplet phase-change cooling holds promise, improvements to prevent flooding are required.

See the supplementary material for a detailed discussion of sample fabrication, the experimental setup, the impact of magnetic and electric fields on the trajectory of jumping droplets, experimental uncertainty, and two videos highlighting electric field enhanced cooling of GaN transistors.

The authors gratefully acknowledge funding from the Power Optimization of Electro-Thermal Systems (POETS) National Science Foundation Engineering Research Center with Cooperative Agreement No. EEC-1449548. T.F. gratefully acknowledges funding support from the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1144245. N.M. acknowledges funding from the International Institute for Carbon Neutral Energy Research (No. WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology. Field emission scanning electron microscopy was carried out in the Materials Research Laboratory Central Facilities and Beckman Institute Microscopy Suite, University of Illinois.

The data that support the findings of this study are available within the article and its supplementary material.

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Supplementary Material