## 3 Results and Discussion  
### Heat Flux-Wall Superheat Relationship  
#### 3.1.1 Boiling Curve Analysis  
Figure 10 illustrates the pool boiling performance (Heat Flux vs. Wall Superheat) of the Sintered Plain, Large Lattice, Small Lattice, and Staggered surfaces in de-ionized and de-gassed water at atmospheric pressure, as represented by the boiling curves.  
The Plain and Sintered Plain surfaces exhibit similar trends in wall superheat with respect to heat flux, indicating that the metal sintering process does not introduce additional thermal adverse effects. The Staggered surface and the Plain surface both showed an increase in wall superheat with increasing heat flux, with the trend for the Staggered surface being more suppressed, resulting in a steeper slope in the boiling curve. Sintered Plain and Staggered surfaces reached their critical heat flux (CHF) at 782 kW/m\({}^{2}\) and 2342 kW/m\({}^{2}\) respectively.  
In contrast, the Large Lattice and Small Lattice exhibit continuously rising heat flux with increasing wall superheat up to the experimental limit, without exhibiting a traditional CHF phenomenon. The highest heat flux recorded for the Large Lattice and Small Lattice surfaces was 2398 kW/m\({}^{2}\) and 2577 kW/m\({}^{2}\), respectively. The wall superheat continued to rise while maintaining a stable temperature gradient.  
However, as noted in Section 2.7, based on Figure 7b, the experiment was terminated once the temperature near the cartridge heaters approached the melting point of copper, indicating a system-level thermal limit rather than a boiling crisis on the surface. Throughout this period of extremely high heat fluxes, there was no visible evidence of a stable blanket vapor film forming on the heating surface, nor any indication of thermal instability or overshoot in wall superheat. This suggests that a dynamic and robust balance between liquid supply to the heating surface and vapor bubble departure was maintained.  
As illustrated in Figure 3, lattice structures allow for liquid supply and vapor departure in all three spatial directions. Furthermore, under high heat flux conditions where vapor growth rates are significant, the 3D dispersion provided by the lattice structure was highly effective in preventing vapor bubble coalescence on the heating surface. This extraordinary and sustained high-performance behavior results directly from the lattice structure's exceptional design and geometry. The surface maintains active rewetting and  
Figure 10: Boiling curves for various 3D-printed geometric structures in comparison to plain surface.  
efficient heat transfer despite increasing wall superheat, fundamentally delaying the boiling crisis mechanism.  
Notably, the Small Lattice showed the steepest slope on the graph, meaning that the rise in wall superheat with increasing heat flux was the most suppressed. Additionally, for the Small Lattice near 750 kW/m\({}^{2}\), and the Large Lattice near 1000 kW/m\({}^{2}\), an increased rate of wall superheat rise was observed, suggesting that the vapor bubble departure diameter may be changing in response to the square pore size of each structure.  
While all the BJ3 DP structured surfaces significantly improve boiling heat transfer, the Large Lattice and Small Lattice designs demonstrate a higher degree of robustness against the boiling crisis, effectively extending the nucleate boiling regime beyond the traditional CHF point observed for the Staggered surface.