A New Paradigm for Understanding and Enhancing the Critical Heat Flux (CHF) Limit

Nearly a century of research on enhancing critical heat flux (CHF) has focused on altering the boiling surface properties such as its nucleation site density, wettability, wickability and heat transfer area. But, a mechanism to manipulate dynamics of the vapor and liquid interactions above the boiling surface as a means of enhancing CHF has not been proposed. Here, a new approach is implemented to limit the vapor phase lateral expansion over the heat transfer surface and actively control the surface wetted area fraction, known to decline monotonically with increasing heat flux. This new degree of freedom has enabled reaching unprecedented CHF levels and revealed new details about the physics of CHF. The impact of wickability, effective heat transfer area, and liquid pressure on CHF is precisely quantified. Test results show that, when rewetting is facilitated, the CHF increases linearly with the effective surface heat transfer area. A maximum CHF of 1.8 kW/cm2 was achieved on a copper structure with the highest surface area among all tested surfaces. A model developed based on the experimental data suggests that the thermal conductivity of the surface structures ultimately limits the CHF; and a maximum CHF of 7–8 kW/cm2 may be achieved using diamond surface structures.

To ensure that boiling occurs only on the structured surface, the side walls of the liquid delivery channel were covered with a 200-µm-thick layer of epoxy, since a low thermal conductivity surface is shown to inhibit boiling 2 . The liquid supply line was initially machined with a 1.2  1.4 mm 2 cross-section. The channel was then filled with epoxy and cured for 6 hours. The supply channel was re-machined with a cross-section of 1.0  1.0 mm 2 within the epoxy, leaving a 200-µm-thick layer of epoxy covering all channel walls. The copper block used in this study is shown in Fig. s-3. The copper heat sink is brazed to a heating block which provides the required heat input and measures the temperature of the heated surface. The generation and accurate measurement of heat fluxes at the 1-5 kW/cm 2 level is a nontrivial task. In this study, we utilized copper blocks with imbedded cartridge heaters to produce the required heat flux. In the following, details of the heating and measurement platform used for the preliminary studies are described. The heating block consists of two 500 W cartridge heaters embedded in a copper block (cf. Fig. s-3). In this design, the heater block is attached to the test chip with a copper column. Three thermocouples are installed within the column to measure the temperature and calculate heat flux using the following equation. For testing at extremely high heat flux conditions, dimensions of the heater block must be optimized to maintain its maximum temperature below the melting point of the brazing materials which is 800°C to 900°C for majority of copper alloys 3 . Consequently, the heater block (cf. Fig. s-3 b) was designed to keep the maximum temperature below the melting point. A numerical simulation conducted to estimate the maximum temperature of the heater block showed that the maximum temperature could reach to ~750°C at a heat flux of 2 kW/cm 2 over a 7  7 mm 2 heat transfer area (cf . Fig s-4).

S2. Calculation of capillary pressure and permeability
There are numerous models available in the literature which can be used to estimate capillary pressure (ΔP) and and structure permeability ( = ) 4-8 . Ravi et al. 9 compared these models and showed that the best model for measuring liquid flow rate within the wicking arrays, and consequently liquid front velocity, can be achieved by combining the permeability model by Byon  In these equations, A^ represents the area of the meniscus, determined using the Surface Evolver algorithm 10 , and accounts for the surface roughness of the pillar wall. These models consider the effect of three-dimensional menisci on permeability and capillary pressure and can estimate the wickability of the microstructure with higher accuracy compared to other models 4-6 . The average difference between wicking values computed using the overall model and experimental data was about 18%.

S3. Effect of membrane permeability on CHF
In order to study the effect of membrane permeability on critical heat flux, we utilized three membranes with an order of magnitude change in permeability. Membrane permeability values are measured experimentally using Gurley method by the manufacturers and were reported in the membranes datasheets. It was shown in the manuscript that in the regions where membrane permeability limits the performance of microstructured surface (i.e. highlighted area in Fig. 3b) the ratio of critical heat flux to liquid pressure is relatively constant. This behavior can be elucidated by examining the relation between membrane mass transfer limit and critical heat flux: The ratio of the experimental values measured for q" ghi ΔP almost matches the ratio of membrane permeability of each membrane, which further proves our discussion. The heat transfer area ratio for the structure was the maximum (A j = 3.54), which corresponded to a maximum critical heat flux value of ~1760 W/cm 2 at wall superheat less than 36 ℃. The CHF value reached by this structure is an order of magnitude higher than values reported in the literature and clearly

S4. Maximum reported CHF
shows the importance of applied liquid pressure and heat transfer area on pushing the CHF limit.

S5. Calculation of effective surface area ratio
The enhanced area ratio A j introduced in the "Experimental Studies" section calculates the overall surface area of the microstructured surfaces; however, it does not reflect the effects of heat transfer on the effective surface area and therefore is not an accurate representation of the available heat transfer area. In order to consider the effects of surface geometry, heat transfer coefficient and also material thermal conductivity on added surface area, we introduced effective surface area ratio, defined as: l,@AA = where ε r denotes the effectiveness of microstructures and is calculated using the following equation: This result proves the applicability of A j,}rr for determining the effective surface area of each microstructure and also shows the significance of material thermal conductivity and geometrical dimensions on increasing the effective surface area.

S6. Effect of heat transfer area on CHF
As shown in the manuscript (cf. Eq. (1)), in order to consider the effects of enhanced heat transfer area on increasing CHF, q ghi " can be reformulated as follows: To check the validity of this hypothesis, we used equation (1) to compare the thermal performance of tested devices with similar wickability:  The uncertainty associated with heat dissipated through phase change process ( ") is due to uncertainty in the thermal conductivity and spacing measurements as well as temperature readings. Equation (s-18) provides the heat flux uncertainty. where ΔT = 3T ----4T / + T 1 and δΔT = 3δT / + 4δT / + δT / 4.12δT.