Surfaces for high heat dissipation with no Leidenfrost limit

Evaporation and boiling are paramount components in a wide spectrum of fields ranging from power generation,^1–7 refrigeration and cooling,^8–10 water purification,^11,12 electronics/photonics cooling^13–21 to biosciences.^22–24 In boiling heat transfer, latent heat of liquid-vapor phase-change allows us to achieve a large dissipated heat flux. At low superheat values, direct contact of the liquid with the hot surface allows for efficient heat transfer. However, at high superheat values, a vapor film forms between the liquid medium and the hot surface and minimizes the heat transfer rate. The onset temperature of this phenomenon is denoted by the Leidenfrost point (LFP).^25–28 A range of surface structures are developed to tune the Leidenfrost point and consequently actuate the heat transfer rate including nanorough surfaces,²⁹ nanofibers,^30–32 micro/nano structures, and hierarchical structures.^33–36 Chemical modification of cooling medium³⁷ or active approaches (e.g., electrical fields^38,39) are also considered to tune LFP. Although these approaches have raised the limit, the limit still exists. Recently, a surface concept, decoupled hierarchical structures,⁴⁰ was developed that could eliminate the LFP. For water droplets, no LFP was observed on these surfaces even up to a temperature of 570 °C. In these structures, the capillary force for contact of a droplet to a hot surface and de-wetting force by the vapor phase are independently tuned to suppress LFP. These structures showed up to two orders of magnitude higher heat flux at high temperatures, but at low values of superheat, the heat dissipation capacity was inferior to other surfaces. Here, based on the same concept, we report a new metallic surface that shows no LFP and offers high heat dissipation capacity in all superheat ranges. These surfaces are developed through the one-step fabrication procedure with no required micro/nano fabrication and promise a cost-effective route for high heat dissipation capacity.

In Si decoupled hierarchical structures,⁴⁰ a nano-membrane keeps the droplet in contact with the surface through a capillary force, while high-aspect ratio micro-pillars provide a path for vapor flow. The capillary force, F_c, is a function of radius of nano-pores and the de-wetting force, F_v, by vapor is a function of dimension of micro-pillars. As these forces are independent, tuning of these forces allows us to satisfy the LFP suppression criterion (i.e., F_c/F_v ≥ 1).

The schematic of Cu decoupled hierarchical structures is shown in Fig. 1. In these structures, a stack of corrugated Cu meshes are used to provide a path for vapor flow (similar to micro-pillars) and multi-layers of Cu micro/nano particles are exploited to form a nano-porous surface (similar to the nano-membrane) to impose capillary forces on the liquid. The development procedure of Cu decoupled hierarchical structures is shown in Fig. 2. On a flat and smooth Cu substrate, corrugated Cu meshes (TWP Inc.) with two dimensions of 200 μm and 75 μm are vertically stacked. This dimension represents the opening dimension in meshes. Cu spherical particles with diameters of ≤ 425 μm (Sigma Aldrich), ≤75 μm (Sigma Aldrich), and 60–80 nm (SkySpring Nanomaterials) are obtained. To deposit Cu particles, particles of each size are mixed with isopropanol alcohol to form three homogenous dilute suspensions (30 wt. %). Initially, a layer of Cu particles with a dimension of ≤ 425 μm was deposited on the stack of Cu meshes through a dip coating process in the suspension. We continued the dip coating process three times to form a uniform layer of Cu particles. Next, Cu micro particles with a dimension of ≤75 μm were deposited through the dip coating method. Finally, the surface is furnished with Cu nanoparticles (60–80 nm). Once the nanoparticles are coated on the surface, the Cu decoupled hierarchical structure was placed in the furnace with an inert flow gas environment (Nitrogen). This gas environment was required to prevent oxidation of Cu in the sintering process. The structure was sintered at a temperature of 1050 °C for 1 h. The heating and cooling rate in the furnace was 6 °C per min. The final Cu decoupled hierarchical structure is shown in Fig. 2. The capillary force and de-wetting force by the vapor phase per unit area may be written as⁴⁰ 

and

where μ_v denotes the dynamic viscosity of the vapor phase, q the heat flux, L the length of vapor flow, ρ_v the density of the vapor phase, h_fg the enthalpy of liquid-vapor phase-change, d the characteristic diameter for vapor flow in corrugated mesh, γ_lv the surface tension of liquid-vapor, θ the contact angle of liquid and the surface, and ϱ the density of nano-pores on the surface. As the experiments had to be conducted at the ambient condition, the Cu structure could oxidize at high temperature (≥200 °C). Thus, we decided to examine these surfaces with non-aqueous liquids with a lower boiling point. One can apply a ceramic coating to the structure to minimize its oxidation at high temperatures. We chose Novec 7100 liquid (3M Co.) for these experiments. This liquid wets Cu substrates and has a boiling temperature of 75 °C, a surface tension of 13.6 N m⁻¹, a liquid density of 1510 kg m⁻³, a liquid dynamic viscosity of 0.58 mPa S, and an enthalpy of evaporation of 112 kJ kg⁻¹. At a maximum heat flux of 10⁷ W m⁻², for the corrugated mesh with the average opening of 200 μm, a vapor flow length of 1 m , a nano-porous surface with a pore density of 0.5, and a pore radius of 80 nm, the ratio of F_c/F_v is approximately 4. This suggests that even for extreme heat fluxes, the LFP could be suppressed on Cu decoupled hierarchical structures.

To examine heat transfer characteristics of Cu decoupled hierarchical structures, we studied phase-change characteristics of Novec 7100 liquid droplets on these surfaces. Initially, we studied the phase-change characteristics on a smooth Si wafer (Fig. S1 of the supplementary material) and micro-structured Si substrate (Fig. 3). The Si microstructure is a micro-pillar structure with a dimension of 95 μm in height, 40 μm in pillar width, and 60 μm in pillar spacing and is developed through the micro-fabrication procedure. This high aspect ratio pillars allow for low shear resistance for vapor flow. A Novec 7100 droplet with a volume of 30 μl was deposited on the substrate at various temperatures and phase-change characteristics were recorded with a high speed camera (Phantom V711, vision research). We reduced the distance between the dispensing needle and the surface to 6 mm to avoid the effect of droplet impact on LFP. The Weber number in all the experiments was 15.4. At low superheat values, the droplet undergoes the nucleate boiling process. However, at high superheat values, Leidenfrost state emerges and the heat transfer rate becomes minimal (i.e., heat transfer occurs through conduction in a thin vapor film underneath of the droplet). This slow heat transfer rate boosts the droplet evaporation time. The LFP for both Si and Si micro-structured surfaces is around 45 K superheat. Next, we examined phase-change characteristics of Novec 7100 droplets on a flat Cu substrate (Fig. S2 of the supplementary material) and Cu decoupled hierarchical structures (Fig. 4). For the Cu substrate, the similar transition to LFP at high superheat values occurs. However, for Cu decoupled hierarchical structures, no LFP state was observed even at a superheat value of 125 °C. As we conducted the experiments in the ambient condition, we did not continue the experiment at higher temperatures than 220 °C to avoid Cu oxidation. In the Cu decoupled hierarchical structure, LFP is suppressed and high heat dissipation capacity is achieved through nucleate boiling in all temperature ranges. As the dimension of the needle can affect the droplet evaporation time in the Leidenfrost state, we conducted an experiment with a smaller needle diameter on the Si micro-structured surface as shown in Fig. S3 of the supplementary material. The droplet evaporation time can change by approximately 0.56 s, but this evaporation time is two orders of magnitude larger than that of the nucleate boiling regime. Note that proper choices of dimension for both mesh and particles are required to develop a decoupled hierarchical structure and satisfy the condition of F_c/F_v ≥ 1. For the same Cu hierarchical structure, in the absence of micro particles with a dimension of ≤425 μm, the micro and nano particles fell in the mesh structure and block the path for vapor flow. We studied phase-change characteristics on this structure as shown in Fig. S4 of the supplementary material. As shown, LFP appears at a temperature of 110 °C.

To acquire an understanding of heat dissipation capacity of various substrates, we plotted droplet evaporation time as a function of temperature in Fig. 5. We also conducted similar experiments on Si decoupled hierarchical structures. As shown at low values of superheat, for Si, micro-structured Si, and Cu, the evaporation time is a decreasing function of temperature and reaches a minimum corresponding to maximum heat flux. Later, there is a transition regime in which the droplet evaporation time increases as a function of temperature reaching to LFP in which the heat transfer rate is minimal. For decoupled hierarchical structures, there is no LFP as also shown in the images of phase-change in Fig. 4(b). However, for Cu decoupled hierarchical structures, we observed an interesting trend. No LFP implies that the droplet evaporation time should monotonically decrease with time, which is consistent when the wall superheat value is more than 15 °C. However, at low superheat values, we observed an inverse trend in which droplet evaporation time increases with temperature. We also noted that at low value of superheat, micro-structured Si has higher heat dissipation capacity than the Cu decoupled hierarchical structure. The higher exposed surface area of the Si micro-structured surface for phase-change could explain the higher heat dissipation capacity. However, the opposite trend at low superheat values is a matter of question.

To understand this reverse trend, we probed the transient temperature of the Cu decoupled hierarchical structure underneath of the droplet. A k-type thermocouple with a diameter of 250 μm was placed at the surface of the Cu decoupled hierarchical structure where the liquid droplet lands. The transient temperature profile of the surface underneath of the droplet is shown in Fig. 6. The time scale starts at 1 s before the contact of the droplet on the surface. As shown, before the contact, the surface is isothermal. However, once the droplet touches the surface, a local cooling occurs underneath of the droplet and the temperature of the surface may fall below the phase-change temperature (75 °C). In this case, the droplet does not experience phase-change at the surface and wicks through the structure due to high capillary forces. The time scale for droplet penetration is determined by balance of the capillary force and viscous shear force of the liquid in the structure and is written as⁴¹ 

where μ_L denotes the viscosity of liquid, t the thickness of the Cu decoupled hierarchical structure, and r the characteristic pore dimension in the structure. For the thickness of 1 mm and characteristics pore dimension of 1 μm, the wicking time scale is approximately 85 ms. The wicking time is also shown in Multimedia view of Fig. 6 which is consistent with the predicted wicking time scale. This time scale is several times smaller than the phase-change time shown in Fig. 4(b) at low superheat values. That is, the droplet does not wick completely through the structure. While the fluid is wicking in the structure, it contacts higher temperatures regions and undergoes a phase-change process in the structure. This is schematically shown in the subset of Fig. 6. Since the phase-change process occurs inside the structure, the images do not show the actual phase-change time. That is, the phase-change time is higher than what is shown in Fig. 4. However, as temperature increases, the wicking length of the droplet will reduce, and the images provide the exact time of the droplet evaporation. Thus, local cooling underneath of the droplet clarifies the inverse trend observed in Fig. 5. We should add that since the mass heat capacity of the Si decoupled structure is higher than that of the Cu decoupled structure, no local cooling was observed in the Si decoupled structure.

We plotted the heat flux as a function of temperature for all the studied surfaces in Fig. 7. The heat flux is determined based on the droplet evaporation time and the contact area of the droplet on the surface (5.6 mm²). We omitted the data points of the Cu decoupled hierarchical structure in which local subcooling and partial wicking in the structure occurred. As shown, the Cu decoupled hierarchical structure shows a monotonic trend in heat flux as a function of temperature with no LFP. The heat transfer coefficient on this structure is approximately 20 kW m⁻²K⁻¹ in all temperature ranges.

In conclusion, we present a surface architecture that suppresses the Leidenfrost state and offers high heat dissipation capacity independent of temperature. These surfaces are developed in one-step fabrication with no required micro-nano structuring. Experimental studies on phase-change characteristics of these surfaces show nucleate boiling in all temperature ranges. At low superheat values, once the droplet touches the surface, local surface subcooling occurs that drops the surface temperature below the phase-change temperature. Thus, the liquid partially wicks in the structure before the phase-change. We envision that Cu decoupled hierarchical structures open a path for high heat dissipation in power generation systems, photonics/electronics, chemical reactors, and aviation systems.

See supplementary material for phase-change characteristics on smooth Si and Cu substrates, role of needle diameter on droplet evaporation time in the Leidenfrost state, and role of proper dimension of mesh and particles for development of decoupled hierarchical structures.

The authors gratefully acknowledge funding support from the Air Force Office of Scientific Research (AFOSR) for Grant No. FA9550-16-1-0248 with Dr. Ali Sayir as program manager and thank Professor Jakoah Brgoch, Dr. Martin Hermus, Ms. Anna Duke, and Mr. Fernando Rodriguez at the university of Houston for assistance in development of the structure.