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Decoupled hierarchical structures for suppression of Leidenfrost phenomenon Nazanin Farokhnia, Seyed Mohammad Sajadi, Peyman Irajizad, and Hadi Ghasemi Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b00163 • Publication Date (Web): 21 Feb 2017 Downloaded from http://pubs.acs.org on February 24, 2017

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Decoupled hierarchical structures for suppression of Leidenfrost phenomenon Nazanin Farokhnia, Seyed Mohammad Sajadi, Peyman Irajizad, and Hadi Ghasemi* Department of Mechanical Engineering, University of Houston, 4726 Calhoun Rd, Houston, Texas, 77204-4006, USA E-mail: [email protected] Keywords: (Leidenfrost phenomenon, Hierarchical structures, nano membranes, Heat dissipation, Evaporation, droplets)

Abstract

Thermal management of high temperature systems through cooling droplets is limited by the existence of the Leidenfrost point (LFP), at which the formation of a continuous vapor film between a hot solid and a cooling droplet diminishes the heat transfer rate. This limit results in a bottleneck for the advancement of the wide spectrum of systems including high-temperature power generation, electronics/photonics, reactors, and spacecraft. Despite a long time effort on development of surfaces for suppression of this phenomenon, this limit has only shifted to higher temperatures, but still exists. Here, we report a new multi-scale decoupled hierarchical structure that suppress the Leidenfrost state and provide efficient heat dissipation at high temperatures. The architecture of these structures is composed of a nano membrane assembled on top of a deep

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micro-pillar structure. This architecture allows to independently tune the involved forces and to suppress LFP. Once a cooling droplet contacts these surfaces, by re-routing the path of vapor flow, the cooling droplet remains attached to the hot solid substrates even at high temperatures (up to 570 oC) for heat dissipation with no existence of Leidenfrost phenomenon. These new surfaces offer unprecedented heat dissipation capacity at high temperatures (two orders of magnitude higher than the other state-of-the-art surfaces). We envision that these surfaces open a new avenue in thermal management of high-temperature systems through spray cooling.

Introduction

Evaporation and boiling are fundamental and core phenomena in a broad range of disciplines including power generation and refrigeration systems1–9, desalination10,11, distillation12, electronic/photonic cooling13–28, chemical reactors, aviation systems29, and even biosciences30–32. Here, we are interested in cooling of a hot object through spray droplets33,34 (e.g. nuclear reactors exposed in an accident condition or petrochemical reactors). Heat dissipation through direct contact of bulk liquid with a hot solid substrate (pool boiling) is extensively studied before35–38 and still ongoing matter of study39–41, but it is not focus of this work. Boiling heat transfer is characterized by the large dissipated heat flux for a small given superheat as it relies on the latent heat of the cooling fluid. Recently, Liang and Mudawar42 reported a comprehensive review on the droplet phase change on heated walls. At low surface superheats, direct contact of the droplet with the solid substrate allows for very high heat dissipation capacity. However, at high surface superheats, formation of an insulating vapor layer at the solid-liquid interface limits the heat dissipation and the droplet levitates on a layer of vapor43–50. The onset temperature of this phenomenon is denoted by the Leidenfrost point (LFP)51–56. Under such conditions, the heat


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transfer rate is minimal and the temperature of the substrate can reach dangerous levels, such as those experienced in the Fukushima disaster. The limit of LFP has stalled abilities for thermal management of high-temperature devices and has impacted a broad spectrum of systems. The ability to raise LFP or to eliminate LFP opens a new path for breakthroughs in these systems.

A range of surface engineering approaches has been created to tune LFP. The earlier approaches included exploring different surface materials57–59, tuning the roughness of surfaces60–62, and using porous surfaces63,64. Recently, the dynamic field of nanotechnology has promised new avenues for surface engineering to tune LFP further. The later approaches included nanorough surfaces9, nanofiber mats65, micro/nano structured surfaces66–73 and hierarchical surfaces66,74. In addition to surface engineering, other parameters such as tuning ambient pressure75–77, chemical modification of the cooling medium62,78–83, actuating inertia of the droplets84–88 and active approaches (e.g. electrical fields89–91) are exploited to boost LFP. However, surface engineering is more appealing as other solutions are often constrained. We have summarized the reported LFP and their suggested physics for a water droplet with radius of 1.1-1.9 mm in Supplementary Information, Table S1. The maximum reported LFPs of a water droplet is for hierarchical structures in value of 453 oC74 and 400 oC66. In both of these structures, micro-pillars of Si were coated with nanoparticles (NPs) to provide a multi-scale structure to boost LFP. Kim et al.74 suggested a mechanism for superior performance of hierarchical structures. Once a droplet approaches a hierarchical surface, if the thickness of the features on the surface is less than the thickness of the insulating vapor film, the features will only increase the shear resistance for vapor flow and consequently thicken the vapor film. In this case, the surface features do not play any role in the increase of LFP. However, as the droplet evaporates, the thickness of Leidenfrost film decreases with the rate of /

55

and the droplet ultimately forms contact with


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the surface. Note that denotes the radius of the droplet. Upon contact, the heterogeneous nucleation of bubbles can occur if cavities are available for nucleation. To introduce these cavities on the surface, Kim et al.74 used nano-particles on the micro-posts of hierarchical structures to show the role of these nano-features on the transition from film boiling to nucleate boiling. Thus, both length scales on the surface contribute to boost LFP. Despite a long time effort, a rational approach for suppression of LFP is missing. This suppression will be a breakthrough in thermal management of high-temperature systems.

Experimental Section Development of deep-Si microstructure: 2” Si wafers, which are coated with 2 µm SiO on top, were obtained from NOVA Electronic Materials; the photolithography masks were developed by Outputcity; the AZ1512 and AZ300 developer were purchased from Integrated Micro Materials; HMDS was purchased from Ultra Pure Solutions. As we needed to fabricate deep microstructures, we could not use polymer as an etching mask. Thus, we used SiO as etching mask, which has relatively high selectivity to the silicon (>100). To provide high adhesion between AZ1512 and SiO , a thin film of HMDS was coated on the SiO through spin coating. On top of this film, a layer of photoresist material, AZ1512 was coated through spin coating as well. The thickness of photoresist layer measured by the profilometer was 2 ± 0.1 µm. ABM mask aligner in contact mode was used to pattern the photoresist. The time for development of the pattern in AZ 300 developer was 50 s. After, to remove the residue of HMDS on SiO , we used 60 s of oxygen plasma cleaning. In order to transfer the pattern to the SiO film, we used a RIE180 machine and etched the SiO layer using O and CHF at 15 oC to avoid polymerization of AZ1512. After transferring the pattern to the SiO , the remaining photoresist material was removed by acetone and plasma cleaning. The SiO becomes the new mask for etching of the Si


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wafer. As we needed to develop deep microstructures (depth of 85-100µm), we used Bosch process and modified it to get the best result for etching. In the Bosch process, we used SF to etch for 13 s and C H for passivation for 7 s. The etch rate in this process was around 2.5 µm/min. Deposition of SiO2 NPs. Ludox(R) sm colloidal Silica particles (30% wt suspension in H2O) were obtained from Sigma Aldrich with an average diameter of 7 nm. We dip coated the decoupled hierarchical in the solution 3 times (~10 min). The coated sample was baked at a temperature of 550 oC for 3 hrs.

Results and Discussion In Leidenfrost phenomenon, the de-wetting upward force is caused by the pressure gradient of the vapor flow underneath of the droplet. This force keeps the cooling droplet suspended and impedes contact of the droplet with the hot solid substrate. Here, we have developed a new paradigm and corresponding material structure for suppression of Leidenfrost phenomenon. Through decoupled hierarchical structures, we re-route the vapor flow and keep the cooling droplet in contact with the hot solid at extremely high temperatures. These new structures are composed of two components, a nano-membrane and a deep microstructure, Figure 1a. Once a cooling droplet sits on the nano membrane, the generated vapor enters the deep microstructure and flows radially, while the nano membrane keeps the cooling droplet in contact with the hot solid through the capillary force. The de-wetting upward force by the vapor is only a function of dimensions of the microstructure, but downward capillary force, which keeps the droplet in contact with the hot solid, is only a function of pore dimensions in the nano membrane. As these


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forces are decoupled and independent, by tuning of these forces, the droplet can be kept in contact with the hot solid substrate even at high temperatures. At Leidenfrost state, the insulating vapor layer impedes the direct contact of a cooling droplet and a hot substrate and significantly drops the dissipated heat flux. The thickness of static Leidenfrost film for small droplets is determined through the balance of interfacial mass flux and shear flow of vapor in the vapor film and is written as52,55 ∆ / / =( ) ℎ

(1)

where denotes the thermal conductivity of the vapor, ∆ the temperature difference between the solid substrate and the saturation temperature of liquid at the given pressure, the viscosity of the vapor, the density of liquid, the gravitational acceleration, ℎ the enthalpy of the liquid-vapor phase change, the density of vapor phase, and the surface tension of the liquidvapor interface. On the other hand, for droplets with a radius larger than the capillary length, the thickness of Leidenfrost film is proportional to /. Snoeijer et al.50 and Sobac et al.92 developed a more comprehensive and general model to predict the shape of vapor film underneath of a Leidenfrost droplet. Their model predicts the radial dependence of film thickness, which was not considered in the earlier models. As shown in Figure 1a, the decoupled hierarchical structure includes a superhydrophilic nano membrane, which is joined on top of a deep Si micro-pillar structure. The height of pillars in the deep microstructure should be high enough to reduce the developed pressure by shear flow of the vapor in the microstructure. Through simulation of vapor flow, we found that the pillars with a height of

> 95 µm is required to suppress LFP at high temperatures (Supplementary

Information, Figure S1). Once a droplet contacts the nano membrane, the capillary force per unit area by the nano-pores, which is ΔP"#$%#&' = 2 cos , /-$ , keeps the droplet in contact


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with the nano membrane. Note that , and -$ denote the contact angle of liquid meniscus formed in the nano-pores and radius of the nano-pores, respectively. Liquid forms spherical meniscus in the nano-pores as the dimension of nano-pores is much smaller than the capillary length of the liquid. At the liquid-vapor interface, evaporation occurs to dissipate heat flux by the hot solid substrate. The generated vapor flows in the microstructure radially and leaves the structure from the sides. Note that the shear loss for vapor upward flow through nano-pores is proportional to the thickness of the membrane divided by the square of pores’ diameter. This shear loss is 2-3 orders of magnitude higher than the shear loss through the microstructure. Thus, the generated vapor flows predominantly radially in the microstructure. If the de-wetting force by vapor flow overcomes the capillary force, the droplet will detach from the substrate and adopt the Leidenfrost state. Note that these forces are decoupled and independent. These forces can be modified independently to tune the LFP. We simulated the vapor flow in the microstructure to obtain an insight on pressure field of vapor. The details of simulation are given in the Supplementary Information. Also, we provide an approximate analytical solution of maximum pressure generated by the vapor flow in the Supplementary Information. In Figure 1b, the velocity field of the vapor in the microstructure is shown. Although the vapor velocity reaches high values, the assumption of laminar flow field is still valid. We examined the cooling effect of pillars by the vapor. For the vapor flow in the microstructure, we calculated the Reynolds numbers. The hydraulic diameter of the microstructure is D/ = 75 2. The calculated Reynolds number is 4 ≤ ≤ 540. Thus, flow of the vapor in the microstructure is laminar. For this given Reynolds number, the hydrodynamic entry length is LeHydrodynamic = (0.05 DH Re), which is 15 2-2 mm. Thus, flow in the microstructure is not fully developed. Also, the thermal entry length for the vapor is written as LeThemal= (0.05 DH Re Pr), which is 15 2-2 mm as well. Pr denotes


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Prandtl number. The Nusselt number for the configuration of undeveloped hydrodynamic and thermal boundary layers is calculated by T. Irvine et al.93 as a function of length of vapor flow. Given these Nusselt numbers and thermal conductivity of steam (789#: = 0.018 Wm-1k-1), we determined the values of heat transfer coefficient as shown in the Table 1. We calculated the Biot number in the structure (;< =

= > ?@A

), where B denotes the width of micro-pillars, and C% the

thermal conductivity of Si, 148 Wm-1k-1. The maximum Biot number is 0.00014 suggesting that the pillars are isothermal. The cooling heat flux by the vapor flow is written as D7 = ℎ (7 − : ), where 7 denotes the surface temperature of pillars, and : the mean temperature of vapor. In Table 1, we compared the ratio of cooling heat flux to the total heat flux (D7 /D8F8# ) as a function of radial length underneath of the droplet for different surface temperatures. As shown, as low values of superheat, the convective cooling by the vapor can be up to 20% of the total heat flux, but at high temperatures, this cooling effect becomes negligible. Also, the vapor flow on the nano-membrane can lead to a temperature gradient in the nano-membrane, as the thermal conductivity of this membrane is low. Given the heat transfer coefficient by the vapor phase and its mean temperature (Table 1), one can determine the cooling heat flux on the membrane at different temperatures. Using Fourier definition of heat flux and length scale of distance between pillars, the change in temperature of nano-membrane induced by vapor cooling effect is 4-9 oC, which has a small effect on local evaporation rate. Through the simulations, we determined the generated pressure field in the microstructure during the vapor flow as shown in Figure 1c. If the maximum generated pressure in the microstructure is less than the induced capillary pressure by the nano membrane, the droplet will remain attached to the nano membrane and the Leidenfrost state is suppressed. Through these simulations, we can compare the ratio of pressures by the shear flow of vapor and the capillary of


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nano pores at different temperatures. This ratio is shown in Figure 1d for several dimensions of nano membranes. Note that for all the considered nano membranes, no Leidenfrost state occurs even up to temperature of 700 oC. As the required microstructure should be deep (height of 95 ± 2 µm), we developed a customdesigned micro-fabrication procedure for these structures. The details of this approach are provided in the Experimental Methods. After fabrication of the microstructure, we used a sintering approach to attach the nano membrane to the Si micro pillars. A schematic of this approach is shown in Figure 2a. In this approach, one utilizes Au as the interlayer between the membrane and the microstructure94. One side of the membrane is coated with Au in the e-beam evaporator with a thickness of 300 nm. Also, the top of the micro pillars is coated with a thin layer of Au having a thickness of 500 nm. To open the nano pores, the nano membrane is physically etched using RIE180. The coated samples are assembled on top of each other and a pressure of 2 MPa was applied to the sample. The sample is sintered at a temperature of 600 oC. The picture of the developed microstructure in this work is shown in Figure 2b. We used Anodic Aluminum Oxide (AAO) as the nano membrane. These membranes with varied pore diameters were obtained from Synkera Technologies Inc. These membranes have a diameter of 25.4 mm, a thickness of 50 µm and a pore density of 10% reported by the manufacturer. Scanning Electron Microscopy (SEM) is used to probe the structure of nano membrane, Figure S2. As we needed to develop a structure to be used for high temperatures, the AAO membrane were heat treated by the manufacturer for operating temperature of up to 1000 oC. Although as-made AAO membranes are amorphous and have low thermal conductivity, the heat treated AAO membrane by Synkera Technologies Inc. are crystalline α and γ alumina phases and have thermal conductivity of approximately 30 Wm-1K-1.95 We needed the contact angle of water in the nano


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pores to determine capillary pressure in these pores. To do so, as shown in Figure 2c, we measured the contact angle of a water droplet on a pre-cleaned nano membrane and used this contact angle to determine the capillary pressure in the pores. The nano-membrane was cleaned with plasma cleaner (Harrick Plasma PDC-001-HP) before these measurements. The measured contact angle of a water droplet on these nano membranes is 3 ± 1o. The final developed structure is shown in Figure 2d. The penetration of liquid through the nano-membrane to the microstructure is a time-dependent process. Once a droplet is deposited on the nano-membrane, the wicking rate is governed by the balance between the capillary force and the shear force of the fluid in the nano-pores (i.e. Washburn’s law96). The time scale for liquid wicking is written as 2 J G>%"?%H ~ - cos ,

(2)

where denotes the dynamic viscosity of liquid, t the thickness of nano-membrane, the surface tension of liquid, - the radius of nano-pores and , contact angle. In the decoupled hierarchical structures, the thickness of nano-membrane is 50 m. For the pore radius of 40 nm, the penetration time is in order of 10 s. We have demonstrated this wicking phenomenon in Supplementary Video 1. At room temperature, a nano membrane was placed on a smooth Si wafer. After deposition of a liquid droplet, it takes several seconds before wetting of the underneath substrate occurs. At high temperatures, while liquid wicks in the nano-pores, it also evaporates. The time scale for evaporation of liquid in a pore is written as G9#$ ~

J ℎ DK

where denotes density of liquid, ℎ the enthalpy of phase-change and DK the heat flux. The heat fluxes in the experiments are in order of 105-107 Wm-2, Figure S5. Thus, G9#$ is in order of 10-


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2

-1 s. The time scale for evaporation is smaller than wicking time and consequently the liquid

cannot wick to the microstructure and vapor phase occupies the microstructure domain. Once the decoupled hierarchical structure was developed, we examined the heat dissipation by these new structures. The developed experimental setup is shown in the Figure 3. Each structure was thoroughly cleaned by plasma cleaning and was placed on the heating stage. Through fluid dispensing systems, droplets of DI water with a volume of 30 L were introduced on the structure at a height of 4 mm (We~4.4). We minimized the distance between the droplet and the structure to suppress the role of droplet inertia on the droplet spreading. The temperature of the structure was measured close to the droplet deposition coordinate with two independent thermocouples. These thermocouples are attached to the structure with a thermal paste (OMEGA THERM 201). We measured the phase change characteristics of the water droplets as a function of temperature on these surfaces. These characteristics are captured using a high-speed camera (V711, Vision Research). Initially, we examined phase-change characteristics on Si microstructure and nano membrane individually as shown in Figures S3 and S4. The LFP for these two structures are 270 oC and 290 oC, respectively. The phase change characteristics on decoupled hierarchical structures are shown in Figure 4. As shown in Figure 4a, at low value of superheat, the droplet is attached to the surface through the capillary force and thin film evaporation occurs underneath of the droplet (Supplementary Video 2). As the porosity of the studied membrane is only 10%, the evaporation rate of the droplet is small. As we increase the temperature, the phase-change characteristic enters a new regime in which nucleate boiling and thin-film evaporation occur simultaneously (Supplementary Video 3). Thus, the evaporation time of the droplet is reduced. We have shown the phase-change characteristics of a water droplet for four temperatures. Note that even up to a temperature of 540 oC, we did not observe


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the Leidenfrost state. Note that the maximum measured Leidenfrost temperature on state-of-theart surfaces is 453 oC74. The common approach to determine LFP and heat dissipation characteristics of a surface is measurement of the evaporation time as a function of temperature97. In Figure 4b, we plotted water droplet evaporation time as a function of temperature on the decoupled hierarchical structures. We developed these decoupled hierarchical structures with two nano membrane pore dimensions and examined their phase-change characteristics as shown in Figure 4b. As the porosity of the nano membranes are the same, the difference in the evaporation rate cannot be related to the enhanced surface area for evaporation. We expect that the observed difference in the evaporation rate is caused by the non-uniform distribution of pores on the surface. As the characteristic curve shows, through decoupling of the de-wetting force of vapor flow and the capillary force, Leidenfrost state is suppressed. However, the evaporation time of the droplets on these surfaces is higher than the state-of-the-art surfaces. This high evaporation time is caused by two effects: low thickness of nano membrane and inadequate active site for heterogeneous nucleation of vapor bubbles on the smooth nano membrane surface. Phase-change process occurs through nucleate boiling on the flat surface of nano membrane and evaporation in the nano pores. Heat for phase-change process is transferred through Si pillars and then laterally in the nano membrane between pillars. Low thickness of nano membrane reduces the heat capacity of the structure and consequently the total heat flux for phase-change in the decoupled hierarchical structures. Before contact of the droplet with the de-coupled hierarchical structure, the thermal resistance through convection and radiation is much higher than the conduction thermal resistance in the hierarchical structure (see supplementary information). Thus, the structure is approximately at a uniform temperature. The reported temperature is the temperature on the membrane surface.


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However, the surface temperature underneath of the droplet will drop as the droplet touches the surface. We emphasize that the temperature of droplet cannot exceed the spinodal decomposition temperature of water at ambient pressure98–100 (321 ± 17 oC). To overcome the shortcoming of high evaporation time on these smooth decoupled structures, we enhanced the nucleation sites of bubbles on the nano membranes through deposition of NPs. We deposited a layer of SiO2 NPs on the decoupled hierarchical structure with nano pore dimension of 80 nm. The detail of the deposition approach is given in the Experimental Methods. Once the coated decoupled hierarchical structure is developed, we examined heat transfer characteristics of this structure on the heating stage. These characteristics are shown in Figure 5a. Similar to the previous structures, we observed two regimes of phase-change. At low values of superheat, thin film evaporation at the mouth of the nano pores occurs and the phase-change characteristics are similar to the decoupled hierarchical structures without coated NPs (Supplementary Video 4). However, as we increase temperature, the nucleation sites on the surface are activated and we observe the transition to the thin-film evaporation/boiling regime (Supplementary Video 5). The phase-change on these structures is more chaotic as enhanced boiling on the nano membrane surface occurs. We continued these experiments to a temperature of 570 oC. No LFP was observed on these decoupled hierarchical structures. The characteristics curve of evaporation time of a water droplet on these surfaces is shown in Figure 5b. As shown, at high values of superheat the evaporation time on these surfaces is reduced by approximately two orders of magnitude. Nucleate boiling at the nano membrane surface and evaporation at the mouth of nano pores are responsible for this remarkable evaporation rate. Note that the developed structures are sintered at 600 oC, and conducting experiments at higher temperatures ( > 570 oC) affects the integrity of the structure. However, once higher temperature joining


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approach is implemented, these structures can be operated at higher temperatures. We compared heat transfer characteristics of the NPs coated decoupled hierarchical structure with other state-of-the-art surfaces as shown in Figure 6. One of the structures is a hierarchical structure74 in which Si micro-pillar structure is coated with SiO2 NPs through layer-by-layer deposition. The procedure for this deposition was initially proposed by Iler101 and further improved for aqueous solutions by Lee et al.102 The onset of film boiling in this structure is at a temperature of 250 oC, and the LFP occurs at a temperature of 453 oC. The other state-of-the art structure is a zirconium nanotube structure103, which is developed through anodic oxidation technique with hydrofluoric acid (0.5%). The onset of film boiling on this structure is close to 250 oC and LFP occurs at a temperature of 350 oC. LFP of around 400 oC is also reported by kwon et al.66 in Si hierarchical structures, but the characteristic curve of evaporation time was not reported. The Leidenfrost temperature on the decoupled hierarchical structures is suppressed up to temperature of 570 oC. Note that at low value of superheat, the existence of vapor layer adversely affect the heat dissipation capacity of decoupled hierarchical structures. However, at high value of superheat these surfaces outperform other state-of-the-art structures in heat dissipation. Furthermore, the heat flux by decoupled hierarchical structure and other state-of-theart structure are shown in Figure S5. The heat flux is determined through evaporation time and contact area of the droplet with the surface. As shown, the developed decoupled hierarchical structure in this work shows a distinct characteristic compared to the other structures. We should add that Vakarelski et al.67 used superhydrophobic structures to stabilize the film-boiling region on a hot object leading to low heat dissipation capacity. However, through decoupled hierarchical structures, one can keep high heat dissipation capacity at high temperatures through nucleate boiling and thin-film evaporation.


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Conclusions We present a new paradigm for heat dissipation at high temperatures through spray droplets and demonstrated the corresponding surface structure for suppression of Leidenfrost phenomenon. In these decoupled hierarchical structures, the de-wetting force by the vapor is governed by the microstructure while the capillary force is governed by the nano membrane. Through independent tuning of these forces, we suppressed the formation of a continuous vapor film underneath of a cooling droplet (Leidenfrost phenomenon). These novel structures show two orders of magnitude higher heat dissipation capacity compared to other state-of-the-art surfaces. These surfaces open a new path for thermal management of high power density systems and breakthroughs in power generation, chemical reactors, and aviation systems.


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a

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2000 (ms-1) 25

1600 y-coordinate (µm)

Cooling droplet

Capillary force Vapor flow

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10 Thin Film Evaporation/ Nucleate Boiling

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Film Boiling

0.5 0

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Figure 1. a) A schematic of decoupled hierarchical structure for suppression of Leidenfrost phenomenon is shown. The microstructure provides a path for generated vapor flow while the nano membrane keeps the cooling droplet attached to the structures. b) The velocity field in the microstructure is simulated at maximum measured heat flux of thin film evaporation (56.3 Wcm2

). The white squares represent the micro-pillars, while the small black dots denote the pores of

nano-membrane. The geometry of the nano-pores, dimension of microstructure, and the substrate temperature are the inputs to this model. The black line denotes the contact line of the cooling droplet. c) The de-wetting pressure field by the vapor flow is shown. This pressure should be lower than the capillary pressure by the nano-pores to keep the droplet attached to the structure. d) The ratio of de-wetting pressure to the capillary pressure as a function of temperature is


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shown. The onset of Leidenfrost phenomenon can be tuned with the dimension of nano-pores. For the pore radius of 80 nm, the Leidenfrost phenomenon is suppressed to more than 570 oC.

a

(i)

b

(ii)

c

(iii)

θ=3o Water droplet Nano AAO membrane

(iv)

d

Deep Si micro-pillars Nano AAO membrane

(v)

(vi)

Figure 2. a) A schematic of fabrication steps of decoupled hierarchical structure is shown. (i) The deep Si microstructure was fabricated in the first step. (ii) A layer of Au film with thickness of 500 nm was coated on the pillars through e-beam evaporation (Thermionics E-beam evaporator). Also, a thin layer of Au, 300 nm, was coated on the back-side of the nano membrane. The pores in the nano membrane were opened through etching with RIE180 from the front side after Au deposition. (iii) The nano membrane and the microstructure were assembled on top of each other. (iv) The structure was sintered at pressure of 2 MPa and temperature of 600 o

C for 3 hrs. (v) A sessile droplet was deposited on the surface. (vi) The nano membrane keeps

the droplet attached to the structure, while the microstructure provides a path for vapor flow. b) The structured of deep Si micro-pillar structures is shown. These micro pillars are developed through a custom-designed fabrication process. The height of pillars is 95 ± 2 µm. The microstructure is tilted 45o in the SEM sample holder to capture this picture. The scale bar is


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100 µm. c) The contact angle of a water droplet on the AAO nano membrane is measured. The membrane shows superhydrophilic characteristics. d) The developed decoupled hierarchical structure is shown. The deep Si micro-pillar structure provides a path for vapor flow, while the nano membrane keeps the cooling droplet attached to the substrate through the capillary force. The scale bar is 5 mm. Fluid dispensing system De-coupled hierarchical structure

High-speed camera

Water droplet

Heating Stage

Thermometer Heaters

Computer

PID controller

Figure 3. The experimental setup for measurement of phase-change characteristics on decoupled hierarchical structures is shown. A water droplet with volume of 30 µl is deposited on the surface. The characteristics of the droplet are visualized with a high-speed camera. The temperature of the surface is measured with two independent thermocouples. The temperature of the heating stage is controlled with a PID controller.


18

Page 19 of 34

T= 110 oC

0s

T= 330 oC

0s

T= 422 oC

0s

0s

0.2 s

50 s

100 s

b 40

0.2 s

0.2 s

0.2 s

6.5 s

4.3 s

3.5 s

20 s

19 s

Evaporation time of a water droplet (s)

a

T= 540 oC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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30 20

10 35 nm nano membrane 80 nm nano membrane

10.4 s

100

200

300

400 o

500

Temperature ( C)

Figure 4. a) The phase-change characteristics of a water droplet on smooth decoupled hierarchical structure are shown. The pore dimension in this nano membrane is 80 nm. At low value of superheat, only thin film evaporation at the nano pores dissipates heat. However, at high superheats, some nucleate boiling enhances the heat dissipation by the structure. Note that no LFP was observed even to temperature of 540 oC. b) The droplet evaporation time by two types of decoupled hierarchical structure is measured. The evaporation time is a decreasing function of temperature.


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T= 110 oC

0s

T= 200 oC

0s

T= 430 oC

0s

0s

4s

50 s

73 s

b 100

0.2 s

0.2 s

0.2 s

6s

2s

0.3 s

20.9 s

4.18 s


a

T= 570 oC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 34

10

1 80 nm nano membrane (80 nm nano membrane + SiO2 nano particles)

0.44 s

0.1

100

200

300

400

500

600

o

Temperature ( C)

Figure 5. a) The phase-change characteristics of a water droplet on NP coated decoupled hierarchical structure at four temperatures are shown. At low values of superheat, the heat is dissipated through thin film evaporation. At higher values of superheat both thin-film evaporation at the mouth of nano pores and nucleate boiling occurs. No LFP was observed on these decoupled hierarchical structures even up to 570 oC. The scale bar in the figures is 2 mm. b) The evaporation time of a water droplet on the decoupled hierarchical structure and NP coated one are compared. As noted, at high temperatures, the evaporation rate and consequently the heat dissipation by the NP coated decoupled hierarchical structure is two orders of magnitude higher than the other surface.


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LFP

LFP

10

1

0.1 100

De-coupled hierarchical structures Zirconium nanotubes structure [86] Nano-porous SiO2 hierarchical structure [64]

200

300

400

500

600

o

Temperature ( C) Figure 6. The phase-change characteristic on decoupled hierarchical structures is compared with state-of-the-art surfaces. On the other surfaces, Leidenfrost state occurs and limits heat dissipation capacity by these surfaces. The independent tuning of capillary pressure and the dewetting pressure of vapor allows suppression of LFP in decoupled hierarchical structures. These new surfaces offer two orders of magnitude higher heat dissipation capacity compared to the other surfaces at high temperature.


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Table 1: The convective cooling by the vapor flow MN (℃)

Re

PS ∗ Q

Nu

h (TUVP WVP )

MU (℃)

XN SXYZY

x= 200 2 400

21.39706

5.777206

3.61

866.4

233.6106

0.185333

450

30.57353

8.254853

4

960

255.8791

0.120904

500

37.76471

10.19647

4.2

1008

278.1475

0.071779

570

53.82353

14.53235

4.5

1080

309.3233

0.019227

x= 1 mm 400

119.1176

6.432353

3.7

888

233.6106

0.189954

450

167.6471

9.052941

4.1

984

255.8791

0.123927

500

225

12.15

4.3

1032

278.1475

0.073488

570

322.9412

17.43882

4.65

1116

309.3233

0.019867

x= 2 mm 400

198.5294

5.360294

4.25

1020

233.6106

0.21819

450

339.7059

9.172059

4.1

984

255.8791

0.123927

500

418.6765

11.30426

4.25

1020

278.1475

0.072633

570

538.6765

14.54426

4.5

1080

309.3233

0.019227


22

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ASSOCIATED CONTENT Supporting Information. The simulation of vapor flow in the deep microstructure, convective and radiative heat loss of decoupled hierarchical structure, approximate calculation of vapor pressure in microstructure. (PDF) Supplementary Videos 1-5. Liquid wicking in nano membrane and phase change characteristics on decoupled hierarchical structures. (AVI) AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Author Contributions H. G. conceived the idea. N. F. developed the decoupled structures and conducted the experiments. S. M. S. conducted the simulations. N. F. and P. I. analyzed the results. N. F. and H. G. wrote the manuscript and all the authors commented on the manuscript. H. G. directed the research. Notes

The authors declare no competing financial interest. ACKNOWLEDGMENT The authors gratefully acknowledge funding support from the Air Force Office of Scientific Research (AFOSR) under contract No. 110941 with Dr. Ali Sayir as program manager. The


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authors thank Drs. Long Chang and Jing Guo in the nanofabrication facility at University of Houston for their help on the development of microstructures. REFERENCES (1)

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