## 4 Simulation of Direct Vapor Generation
### Multiple Pores Scenario  
In the previous part, the case of a single evaporating pore is mainly studied. It is shown that the pore size plays a crucial role in the overall efficiency. Note that the thin-film evaporating region is more efficient in vapor generation compared with the bulk region. Efficiency can thus be further improved if we increase the portion of the thin-film evaporating region. To this end, scenarios with multiple pores are considered in the following part. Specifically, the total pore size is fixed (fixed thermal concentration), while the pore number varies. In other words, more pores imply a smaller size  
Figure 12: The normalized overall efficiency vs. thermal concentration: red squares are experimental data reported from [48]; black solid line represents simulation results; efficiency is normalized for comparison, specifically, \(\eta^{*}=1\) corresponds to \(C_{\text{th}}=53\), and \(\eta^{*}=0\) corresponds to \(C_{\text{th}}=486\). for each one. We still focus on the two-dimensional model. Let \(L\) be the width of the absorber, and \(C\) as the thermal concentration. Then the total pore size is \(L/C\). In the case that \(n\) identical pores are considered, the width for each pore is \(L/(Cn)\). Similar to the single pore scenario case, \(L\) is chosen as \(2\times 10^{4}\)\(\Delta x\). For example, the thermal concentration is 50, i.e., the width is 400 \(\Delta x\) when \(n=1\). In order to investigate how the pore number affects the overall efficiency, a consistent heat flux boundary condition is considered in the simulations of different scenarios. The overall efficiency is given by  
\[\eta=n\frac{m_{n}h_{fg}}{Q_{a}}, \tag{46}\]  
where \(m_{n}\) is the mass flow rate of the vapor generated in each pore. The results are shown in Figure 13. When the number of pores increases, the overall efficiency will increase first and then decrease. In other words, maximum efficiency exists which corresponds to a moderate number of pores. For more distributed scenarios, the area of thin-film evaporating region is larger, though the total pore area is the same. As a result, the overall efficiency increases. When the number of pores keeps increasing, the pore size becomes very small. Although the thin-film evaporating region still increases, the water supplement could be slugged due to the suppressed viscosity, which reduces the evaporating mass flow rate. This phenomenon was reported in [49], where it is mentioned that, pores with diameters less that 300 nm can hinder water evaporation. Conditions with various incident power are also shown in Figure 13, specifically, \(q_{\text{in}}=1\times 10^{-4}\) and \(q_{\text{in}}=1.2\times 10^{-4}\) are demonstrated. It is revealed that when the incident power is larger, the overall efficiency is also higher. The difference is more obvious for scenarios with more distributed pores. However, it is also noticed that the peak position keeps the same, specifically, \(n=11\) renders the maximum efficiency in our simulations. Another factor that may affect the overall efficiency of vapor generation is the wettability of solid walls. The pores discussed above have purely hydrophilic solid walls. The most efficient region of TFE is the thin-film evaporating region, the formation of which relies on the hydrophilicity of the wall. Beyond this region, specifically, near the vapor outlet, the liquid film becomes even thinner, the liquid there can hardly transfer to vapor through evaporation. A section of hydrophobic solid wall can be employed at the vapor outlet, the length of which is \(50\Delta x\) in our simulations. Hence, pore walls have heterogeneous hydrophobicities.