## 3 Validation
### Pool Boiling on the Layer-by-Layer (LbL) Nano-Structured Surfaces  
This paper mainly focuses on simulating the pool boiling bubble growth on nano-structured surfaces fabricated by the LbL technique. The main idea of this technique is to dip a substrate into the cationic polymer and anionic nanoparticle solutions to create a nanoparticle bilayer. The different charge promotes nanoparticle adsorption onto the substrate, resulting in a uniform smooth porous layer. The thickness of the porous layer can be easily controlled by changing the number of bilayer dipping procedures. The detailed fabrication procedure was outlined in the study of [PERSON] et al. [40], and a brief schematic of the LbL dipping procedure can be also found in Figure 12.  
Table 1 summarizes the surface parameters of LbL nano-structured ITO heaters with different numbers of bilayers. These parameters were tested in the Microsystems Technology Laboratories (MTL) during the author's stay at MIT and were the input for the calculation of the nano-structure model.  
Before we conducted the bubble growth simulation on LbL heater, the interface height \(h_{c}\) shown in Equations (23) and (24) was first determined first. Taking the 100 bilayers LbL heater as an example, curves of Equations (18) and (21) were plotted in Figure 13, where the abscissa of the intersection point of two curves indicates that \(h_{c}=2.1\times 10^{-6}\) m when the nano-structure thickness is 2.76 \(\upmu\)m. Then, the nano-structure model shown in Equation (24) could be solved.  
Figure 11: Comparison of the bubble diameter variation between numerical simulations and experiments on the ITO heater.  
Figure 12: The LbL dipping procedure.  
Figure 14 demonstrates reasonable simulation results of the bubble growth on the 100 bilayers LBL heater. The wall superheat was 22.69 \({}^{\circ}\)C, the bulk temperature was 100 \({}^{\circ}\)C, the initial bubble diameter was 0.7 mm, the contact angle between the liquid and the heater was 5\({}^{\circ}\) due to the super hydrophilic LBL nano-structure, and the constant \(C_{0}\) in the micro-layer model was set to be 3.43 \(\times\) 10\({}^{-3}\). Compared with the experimental snapshots, the present method successfully describes the bubble growth behavior on the 100 bilayers LBL surfaces. The bubble's aspect ratio was larger than that on the bared surface due to the larger inertia force caused by the higher wall superheat and evaporation of the wicked fluid inside the nano-structure. The bubble departure time was 26.5 ms in the experiment, while it was 37.5 ms in the simulation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No. of Bilayers**} & \multirow{2}{*}{\
\begin{tabular}{c} **Size of** \\ **Nano-Particle/nm** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Thickness of the** \\ **Nano-Structure/um** \\ \end{tabular} } & \multirow{2}{*}{**Surface**} & \multirow{2}{*}{**Porosity/\%**} \\ \hline
0 & N/A & 0 & \(<\)10 & N/A \\
22 & \(20\pm 2\) & 0.50 \(\pm\) 0.02 & 26 \(\pm\) 3 & 63 \(\pm\) 1 \\
34 & \(20\pm 2\) & 0.93 \(\pm\) 0.04 & 45  
The comparison shown in Figure 15 also quantitatively proves the correctness and accuracy of the current method. The largest relative error between the experiment and simulation was less than 5%.