Abstract
The Leidenfrost effect, namely the levitation of drops on hot solids1, is known to deteriorate heat transfer at high temperature2. The Leidenfrost point can be elevated by texturing materials to favour the solid–liquid contact2,3,4,5,6,7,8,9,10 and by arranging channels at the surface to decouple the wetting phenomena from the vapour dynamics3. However, maximizing both the Leidenfrost point and thermal cooling across a wide range of temperatures can be mutually exclusive3,7,8. Here we report a rational design of structured thermal armours that inhibit the Leidenfrost effect up to 1,150 °C, that is, 600 °C more than previously attained, yet preserving heat transfer. Our design consists of steel pillars serving as thermal bridges, an embedded insulating membrane that wicks and spreads the liquid and U-shaped channels for vapour evacuation. The coexistence of materials with contrasting thermal and geometrical properties cooperatively transforms normally uniform temperatures into non-uniform ones, generates lateral wicking at all temperatures and enhances thermal cooling. Structured thermal armours are limited only by their melting point, rather than by a failure in the design. The material can be made flexible, and thus attached to substrates otherwise challenging to structure. Our strategy holds the potential to enable the implementation of efficient water cooling at ultra-high solid temperatures, which is, to date, an uncharted property.
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Data availability
The data that support the findings of this study are available from the corresponding authors.
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Acknowledgements
We acknowledge financial support from the Research Grants Council of Hong Kong (no. 11218321, no. C1006-20WF and no. 11213320), the Tencent Foundation through the XPLORER PRIZE, the Innovation and Technology Council (no. 9440248), the National Natural Science Foundation of China (grant nos. 51975502 and 21621001) and the 111 Project (no. B17020).
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Contributions
Z.W. conceived the research. Z.W., D.Q. and J.Y. supervised the research. M.J. and Y.W. designed the experiments. Y.L., S.W. and C.P. participated in the discussion of the experimental design. H.Z. set up the electrospinning equipment. Y.W. prepared and characterized the membranes. H.D. and S.T. conducted the fabrication of the steel pillar arrays. M.J., Y.W. and F.L. assembled, characterized the samples and carried out the experiments. D.Q. and M.J. built the models with input from Y.W. and Z.W. All authors analysed the data. Z.W., D.Q., J.Y. and M.J. wrote the manuscript with input from the other authors.
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Z.W., M.J. and Y.W. are co-authors on a filed US patent no. 63/072,995, which describes the methods used herein.
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Extended data figures and tables
Extended Data Fig. 1 Preparation of the samples.
a. Fabrication process of steel pillar arrays with U-shaped grooves. The arrays are fabricated using a precision milling process. The tip of the milling cutter is a ball nose with a diameter of 300 µm. The spindle rotational and translational speeds, and depth-of-cut are 60,000 r/min, 150 mm/min and 40 µm, respectively. The desired depth of 400 µm is reached after ten successive cuts (step 1) after which the sample is rotated by 90°, and ten new cuts are performed. The SEM image is a side-view of the pillars with their U-shaped grooves. b. SEM images of the fibrous membranes treated at various temperatures. Images are obtained with a FEI Quanta 450 FEG microscope after membranes were inserted into a tube furnace (GSL-1500X) at the target temperature and calcinated for 1 h in air. c. Fibrous membranes are embedded into pillar arrays at the desired depth using a pre-designed 3D mold. After removing the mold, the obtained STA is consolidated by a sintering step performed at 800 °C for typically 5 min. d. SEM image of the pillars without U-shaped grooves. This material is made for achieving the sample B. It is fabricated using 2-flute end mill with a diameter of 300 µm. During micro-milling, the spindle rotational and translational speeds are 60,000 r/min and 150 mm/min, and the depth-of-cut is 30 µm.
Extended Data Fig. 2 Water drops contacting STA brought to high temperatures.
a. Side view of water contacting STA at T = 500 °C. As water (dyed in red) contacts a STA, it immediately impregnates the membrane, without penetrating the U-shaped channels. The liquid is kept within the membrane by capillarity and by the vapour pressure inside the channels. The scale bar is 0.5 mm. b. Top views of water drops (approximately 17 µL) on STA at T = 800 °C and T = 1150 °C (around 1200 °C, the membrane starts to melt). Drops behave as reported in Fig. 1c (T = 1000 °C). Images framed in red show the formation of non-uniform and isolated bubbles, that break within several milliseconds owing to an intense boiling. The lifetimes of the drop are 0.35 s and 0.28 s, respectively, showing the persistence of wicking even at ultra-high temperature. Scale bars show 2 mm.
Extended Data Fig. 3 Evaporation time τ of a water drop with volume Ω as a function of the temperature T of its substrate.
The respective values of Ω are (from top to bottom) 13, 6, 4, 6, 30 and 17 µL, which affects the absolute value of the time but not its trend. For many data (those of refs. 5, 27,28 and 29), we observe a classical Leidenfrost behaviour, with a strong decrease of τ around the boiling point (BP), followed by a sharp rise of this time at the Leidenfrost transition. Short evaporation times correspond to τ of order 1s, and they are observed in this case between the BP and the LFP. For the data of Ref. 3, the behaviour is different, with a slow decrease of the time τ as a function of temperature. Its values remain above the regime of quick disappearance, except for AAO+nanoparticles where the regime of interest is achieved between 500 °C and 570 °C. By contrast, the STA sample achieves a low τ in a range of 1000 °C, between 200 °C and 1200 °C. Data in our work are mean ± s.d. from at least five independent measurements.
Extended Data Fig. 4 Percentage of the drop volume that heterogeneously boils on the different samples at T = 1000 °C.
Values are obtained from image analysis after at least 30 drops contacted the samples. Data are mean ± s.d. from at least thirty independent measurements.
Extended Data Fig. 5 Schematic showing the temperature measurement.
The thermocouple is inserted in the steel block at a distance δs ≈ 1 mm below the pillar tops. The ratio between the conduction thermal resistance and the convective thermal resistance of steel, defined as the Biot number Bi = δshs/ks (where hs ≈ 2*103 W/m2K is the convection heat transfer coefficient and ks ≈ 25 W/mK is the thermal conductivity of steel), is 0.07 << 1. This suggests that the temperature at the top surface is comparable to that measured with the thermocouple.
Extended Data Fig. 6 Control experiment based on pillar arrays covered by a conductive copper membrane.
High-speed views of the evaporation dynamics of a water drop deposited on pillar arrays covered by a conductive Cu membrane (T = 500 °C). The whole surface has a uniform temperature and the water drop remains in the Leidenfrost state all along its lifetime. The lifetime (in red) is two orders of magnitude larger than on STA, demonstrating that insulating membranes are essential for inhibiting the Leidenfrost effect.
Extended Data Fig. 7 Thermal characteristics of STA surfaces.
a. Temperature map of a STA surface brought to 1000 °C. Temperature is measured with an infrared camera (FLIR T1050sc) operating at 30 Hz, with an emissivity setting at 0.95. At t = 0 ms, temperature is nearly uniform. The tops of the steel pillars are slightly cooler (by 15 °C) than the membrane, which might be due to the embedded position of the membrane. 198 ms after a drop impact, we observe a strong temperature difference (about 290 °C) between pillars and membrane. b. Evaporation time τ of a water drop of 17 µL deposited on STA at T = 1000 °C, as a function of the pillar density ϕ = a2/(a+b)2. c. Mean heat flux q as a function of ϕ. q is deduced from the time τ and from the measured evaporating solid/liquid area. An optimum of performance is found around ϕ = 0.25. Data are mean ± s.d. from at least five independent measurements.
Extended Data Fig. 8 Upper limit of the pore diameter for the insulating membrane embedded in a STA and dimensionless phase plots.
a. Ratio PL/Pv (Laplace pressure in a pore relative to vapor pressure) as a function of the pore diameter d. Between d = 2 µm and d = 21 µm, the STA operates in the wicking regime. However, the ratio PL/Pv becomes smaller than unity at high d. As a result, vapor can penetrate the wicked membrane and a mixed state is observed. For all tests, the STA temperature is 1000 °C and the U-shaped channel height ε is 150 µm. b. Dimensionless phase plots showing τ/τo (evaporation time relative to the wicking time) as a function of PL/Pv, at fixed ε = 150 μm, and for a STA temperature of 1000 °C. The data show that STA operates in the domains expected from our models (PL/Pv > 1, τ/τo > 1). As a complement, we can estimate the numbers τ/τo and PL/Pv for liquid nitrogen on STA at 30 °C or at 1000 °C (Supplementary Video 2). For the parameters of liquid nitrogen (R ≈ 1.2 mm, L ≈ 2∙ 105 J/kg, η ≈ 0.17 mPa s, γ ≈ 9 mN/m, d ≈ 3 µm), we find at 30 °C (kv ≈ 17 mW/m/K, ηv ≈ 12 µPa s, ρv ≈ 1.8 kg/m3) τ/τo ≈ 1.3 and PL/Pv ≈ 600 – all quantities larger than unity; at 1000 °C (kv ≈ 57 mW/m/K, ηv ≈ 37 µPa s, ρv ≈ 0.4 kg/m3), the latter values become τ/τo ≈ 2.3 andPL/Pv ≈ 3 – still larger than unity.
Extended Data Fig. 9 Schematic showing the fabrication of U-shaped channels.
a. Fabrication of U-shaped channels with different heights (50 µm, 100 µm, 120 µm). Arc-shaped grooves with a height of 50 µm, 100 µm and 120 µm are obtained with a flat milling cutter with a tip diameter of 300 µm that provides grooves with a depth of 340 µm, 290 µm and 270 µm, respectively, as shown in Steps 1–3. Then, the flat bottom cutter is replaced with a ball nose cutter with a diameter of 200 µm to further fit the profile of the arcs, as shown in Steps 4-5. b. Making pillars with a wire electrical discharge machine (WEDM). In Step 1, the steel workpiece moves under the molybdenum wire with a diameter of 180 µm, which results in U-shaped grooves. Then, the workpiece is rotated by 90o and Step 1 is repeated. The current, voltage and machining compensation are 2 A, 80 V and 80 µm, respectively.
Extended Data Fig. 10 Cooling performances of large-scale and curved STA.
a. Optical image of STA fabricated on a steel block of 40 x 40 x 10 mm. b. Comparison of time-dependent heat dissipating abilities of STA and sample A at 1000 °C. Samples are cooled by a water flow (rate of approximately 150 mL/min) released from 4 nozzles placed 5 cm above the surface. Within about 20 s, the temperature on STA drops by 850 °C, whereas temperature hardly changes on A. c. Corresponding heat flux as a function of time on both samples. d. Optical image of a curved STA sample, with width 2 cm, height 1 cm, and radius of curvature of the top surface 2.5 cm. e. Heat dissipating abilities between the curved STA and bare sample. Under a water flow of 20 mL/min, there is a 900 °C drop on the STA sample within 1 minute, whereas there is no appreciable cooling on the bare sample. f. Corresponding heat fluxes as a function of time for both samples.
Supplementary information
Supplementary Video 1
Behaviours and lifetimes of water drops deposited on samples A, B and STA brought to T = 1,000 °C. The volume of the water drops is approximately 17 µl. On pillar arrays (sample A), drops exhibit a typical Leidenfrost state, with a long evaporation lifetime. On the pillar/membrane without channels (sample B), drops are in a mixed wicking/Leidenfrost state. By contrast, drops on STA persistently wick the membrane, which generates constant boiling and a 50-fold reduction in their lifetime.
Supplementary Video 2
Behaviours and lifetimes of liquid nitrogen drops on sample A at room temperature, STA at room temperature and STA at T = 1,000 °C. The impact velocity and diameter of the drops are approximately 45 cm s–1 and 2.4 mm, respectively. Liquid nitrogen adopts a Leidenfrost state on A at room temperature. By contrast, a complete wicking with intense boiling is observed on STA, both at room temperature and at 1,000 °C, with respective lifetimes of approximately 130 ms and 240 ms.
Supplementary Video 3
Cooling performances of large-scale samples A and STA at T = 1,000 °C, due to continuous water drops. Both samples are fabricated on steel, and have dimensions of 40 × 40 × 10 mm3. Water is released from four nozzles placed 5 cm above the surface, with a flow rate of approximately 150 ml min–1.
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Jiang, M., Wang, Y., Liu, F. et al. Inhibiting the Leidenfrost effect above 1,000 °C for sustained thermal cooling. Nature 601, 568–572 (2022). https://doi.org/10.1038/s41586-021-04307-3
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DOI: https://doi.org/10.1038/s41586-021-04307-3
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