## 2 Experimental Methods
### Capillary Wicking Measurement  
The capillary wicking capability of the 3D-printed porous surfaces (Large Lattice, Small Lattice, and Staggered) was quantitatively evaluated by measuring their respective liquid suction speeds. The experimental procedure was adapted from the capillary-wicking test presented by [PERSON] et al. [24]. For these measurements, a Pyrex glass capillary tube with an inner diameter of \(1\) mm was utilized. All measurements were conducted at room temperature using ethanol as the working fluid. A high-speed camera (Nova S16, Photron, Tokyo, Japan) was employed to record the wicking process at a speed of 16,000 frames per second (fps). The results are presented in Figure 4.  
Figure 4: Capillary absorption performance of three porous surface structures (Small Lattice, Large Lattice, and Staggered).  
Figure 3: Movable range of liquid and vapor in porous surface structures.  
Each structure's absorption rate is a direct indicator of its capillary force strength. The Small Lattice structure demonstrates the highest absorption rate at 37.381 mm/s, signifying the most robust capillary action. This rapid movement is facilitated by its smaller pore spacing and highly interconnected pathways, which are critical for quickly replenishing liquid and rewetting surfaces during boiling, ultimately improving heat transfer efficiency.  
Conversely, the Large Lattice and Staggered structures exhibit significantly slower absorption rates (18.772 mm/s and 19.324 mm/s, respectively)--roughly half that of the Small Lattice. This reduced speed is attributed to weaker capillary forces, as their larger pore spacing diminishes capillary pressure and slows liquid ascent.  
These findings highlight a clear relationship between capillary absorption and the geometric design of porous surfaces. Our experimental measurements of liquid suction speeds align perfectly with theoretical expectations for capillary phenomena: smaller pores inherently produce stronger capillary forces, leading to faster fluid rise. This principle is vital for effectively rewetting nucleation sites during boiling, emphasizing the fundamental link between pore geometry, fluid properties, and capillary-driven transport in 3D-printed thermal surfaces. The complex dynamics of liquid within porous media are primarily controlled by capillary forces, where capillary pressure (\(\Delta P\)), which drives liquid into small pores, is defined by the Young-Laplace equation.  
\[\Delta P=\frac{2\gamma\cos\theta}{r} \tag{1}\]  
where \(\Delta P\) is the capillary pressure, \(\gamma\) is the surface tension, \(\theta\) is the contact angle of the liquid on the solid surface, and \(r\) is the effective pore radius. This equation clearly indicates that smaller pore radii directly result in proportionally higher capillary pressures. Our designed porous structures directly leverage this principle: the Small Lattice features nominal square pore dimensions of 0.5 mm \(\times\) 0.5 mm, resulting in a smaller effective pore radius compared to the Large Lattice, which has nominal square pores of 0.65 mm \(\times\) 0.65 mm. This intrinsic difference in pore geometry dictates their respective capillary strengths and fluid-wicking capabilities.  
Furthermore, the dynamics of liquid penetration into porous structures due to capillary action can be approximated by the Lucas-Washburn equation, particularly for initial wicking:  
\[L^{2}=\frac{\gamma\ r\cso\theta}{2\mu}\ t \tag{2}\]  
where \(L\) is the penetration length, \(\mu\) is the dynamic viscosity of the fluid, and \(t\) is the time. This equation provides a theoretical framework for understanding observed liquid suction speeds, demonstrating that faster liquid penetration (higher suction speed) is favored by smaller pore radii, higher surface tension, lower viscosity, and better wettability.