## 3 Results and Discussion
### Heat Transfer Coefficient Analysis  
Figure 12 presents the HTC and heat flux for the various surface structures studied in comparison to literature data. All surfaces showed a general increasing trend in HTC, particularly in the low heat flux region (\(\leq\)750 kW/m\({}^{2}\)). Consistent with the boiling curves (Figure 10), the HTC of the Large Lattice, Small Lattice, and Staggered surfaces was significantly higher than that of the Plain and Sintered Plain throughout the range of heat fluxes. The Sintered Plain surface exhibited an increasing HTC trend up to its maximum HTC of 43.34 kW/(m\({}^{2}\cdot\)K) corresponding to its CHF of 782 kW/m\({}^{2}\) at a wall superheat of 18.03 K. The Staggered surface showed a rapid increase in HTC at low heat fluxes, followed by a more gradual increase. Its peak HTC of 95.34 kW/(m\({}^{2}\cdot\)K) was achieved at a CHF of 2342.4 kW/m\({}^{2}\), with a wall superheat of 24.57 K.  
The Large Lattice and Small Lattice surfaces showed a rapid growth in HTC within the low to medium heat flux region, reaching their highest HTC values early in this range. The Small Lattice reached a peak HTC of 95.62 kW/(m\({}^{2}\cdot\)K) at a heat flux of 272.72 kW/m\({}^{2}\) and a corresponding wall superheat of 2.85 K. The initial rise and peak were followed by a steady decrease in HTC, with its final HTC at the maximum heat flux recorded being 65.3 kW/m\({}^{2}\) K at the maximum heat flux achieved of 2577. kW/m at a wall superheat of 39.5 K. Similarly, the Large Lattice reached its highest HTC of 133.41 kW/(m\({}^{2}\cdot\)K) at a heat flux of 513.97 kW/m\({}^{2}\) and a corresponding wall superheat of 3.85 K. However, the HTC decreased steadily to 43.14 kW/(m\({}^{2}\cdot\)K) at its maximum achieved heat flux of 2397.7 kW/m\({}^{2}\) at a wall superheat of 55.6 K.  
A notable trend for the Large Lattice and Small Lattice surfaces is an initial rise in HTC at lower heat fluxes, followed by a subsequent gradual decrease as the heat flux continues to increase. This behavior can be attributed to the evolving dominance of different heat transfer mechanisms at both low and high heat flux within the nucleate boiling regime. At lower heat fluxes, the Large and Small Lattice surfaces show a rapid increase in HTC, driven by enhanced nucleation site activation, efficient liquid replenishment facilitated by bubble dynamics, and the unique 3D architecture that ensures adequate liquid supply and vapor departure. High nucleation site density, along with grooves and cavities, promotes evaporation and vapor-liquid interaction, maximizing bubble-induced convection and overall heat transfer. As the heat flux increases, the HTC begins to decline despite the rising heat flux. This is attributed to a shift in the dominant boiling mechanism, transitioning from discrete bubble departure to a more complex regime of vapor flow and liquid rewetting. This is coupled with increased bubble interactions and coalescence, as well as vapor jet formation, which reduces the effective heat transfer area. While this activates more sites, dense bubble populations impede liquid motion, reducing convective efficiency and leading to greater vapor coverage on the surface, resulting in a gradual increase in thermal resistance. However, as discussed in Section 3.1 and further elaborated below, this did not trigger a boiling crisis or traditional CHF due to the optimized pore size and permeability of the lattice structures. These features enable efficient liquid replenishment and vapor escape, mitigating accelerated bubble crowding and allowing them to achieve peak HTC early with less severe declines. The structures effectively separate liquid and vapor pathways, delaying film boiling and dryout by facilitating rapid bubble departure and continuous liquid supply through connected pores, reflecting a trade-off between initial bubble-enhanced mixing and reduced liquid contact at higher densities.