## 4 Results and Discussion
### Analysis of Heat Transfer Process  
The heat transfer process of the bubble growth is analyzed in this section. As stated above, the quantity of heat in the bubble growth process mainly comes from the superheated fluid and the micro-layer. For the nano-structured surface, the evaporation of the wicked fluid cannot be neglected. Figure 17 shows the computed time histories of the heat transfer rates delivered to the bubble on the bared heater by the superheated fluid (\(P_{sl}\)), the micro-layer (\(P_{ml}\)). The total heat transfer rate (\(P_{tot}\)), and the proportion of \(P_{ml}\) in the \(P_{tot}\) are also indicated. Both \(P_{sl}\) and \(P_{ml}\) increased sharply at the beginning of the bubble growth, and they decreased when the bubble started to float. Figure 15: Comparison of the bubble diameter variation between numerical simulations and experiments on the 100 bilayer LDL heater. The micro-layer's variation of heat transfer rate was consistent with its variation of the radius and thickness discussed in Section 4.1. At the beginning of the bubble growth, the heat transfer rate delivered through the micro-layer was smaller due to the thicker thickness; however, the micro-layer's occupied area increased quickly during this period. Thus, the \(P_{ml}\) generally increased at the beginning. At the final stage of the bubble growth, although the micro-layer's thickness was thinner, the dry spot beneath the bubble was dominated, leading to the decrease of the \(P_{ml}\). For the superheated fluid heat transfer rate, the bubble grew inside the superheated layer, and as the liquid/vapor interface expanded, the \(P_{sl}\) increased. However, when the bubble grew into the bulk fluid, the temperature of the fluid decreased, leading to the fading of \(P_{sl}\). As indicated by the green dotted line in Figure 17, the peak value of the \(P_{ml}\)'s proportion in the \(P_{tot}\) was around 60% which means the micro-layer's evaporation was dominated at the beginning of the bubble growth. The time integral proportion of the \(P_{ml}\) in the whole bubble growth process was 40.55% in the \(\Delta T_{w}\) = 7.22 \({}^{\circ}\)C case and 32.23% in the  
Figure 16: Thickness distribution of micro-layers at different times on: (**a**) bared ITO heater at \(\Delta T_{w}\) = 7.22 \({}^{\circ}\)C; (**b**) bared ITO heater at \(\Delta T_{w}\) = 10.15 \({}^{\circ}\)C; (**c**) 100 bilayers Lbl. ITO heater at \(\Delta T_{w}\) = 22.69 \({}^{\circ}\)C.  
Figure 17: Heat transfer rates from different parts vary with time on: (**a**) bared ITO heater at \(\Delta T_{w}\) = 7.22 \({}^{\circ}\)C; (**b**) bared ITO heater at \(\Delta T_{w}\) = 10.15 \({}^{\circ}\)C.  
\(\Delta T_{w}\) = 10.15 \({}^{\circ}\)C case. The values were 62% and 52% in [PERSON]'s [29] and [PERSON]'s [58] studies, respectively. This difference may come from the different initial conditions. Moreover, the construction of the superheated layer was not included in their research, leading to a higher proportion of the micro-layer heat transfer rate. The bubble growth heat transfer analysis on the 100 bilayers LbL heater is demonstrated in Figure 18, and the heat transfer rate of the wicked fluid (\(P_{wick}\)) is indicated. Due to the higher wall superheat and the existence of the nano-structure, the total heat transfer rate, in this case, is larger than that in the above two cases. The \(P_{wick}\) increased quickly to its maximum value at the very beginning of the bubble growth and almost remained constant until the micro-layer dried up. The nano-structure provided a significant contribution. The \(P_{wick}\) was slightly lower than the \(P_{ml}\) at first and then it overtook the \(P_{ml}\) when the micro-layer gradually evaporated. The ratio of the time integral of \(P_{wick}\) and \(P_{ml}\) was 14:11 in the whole bubble growth process. The existence of the nano-structure is considered to directly enhance the evaporation beneath the bubble by feeding the micro-layer. The green dotted line in Figure 18 shows the proportion coupled \(P_{wick}\) and \(P_{ml}\).