## 4 Results and Discussion
### Effects of Defect Size on Gas Chamber Pressure and PDR  
Before evaluating membranes with controlled defects, a series of pressure decay tests over a range of feed pressures were first conducted using a nondefective membrane. It was found that the pressure value of the gas chamber did not obviously decline. For example, with the conditions of water depth 30 mm, gas chamber volume 365.59 mL, and original applied pressure 95.48 kPa, the pressure declined from 95.48 kPa to 94.60 kPa after 100 s. This pressure decay can be mainly attributed to gas diffusion through intact pores [20], proving that the experimental system was intact, airtight, and sealed hermetically. Figure 4 shows the time dependence of gas chamber pressure and PDR of different needle sizes (0.20 mm, 0.22 mm, 0.30 mm, and 0.35 mm). Here, the following experimental conditions were used: water depth 30 mm, gas chamber volume 365.59 mL, and original applied pressure 80 kPa. The equivalent diameters of different defects size were evaluated to be 0.185 mm, 0.189 mm, 0.276 mm,  
Figure 3: The effect of applied pressure on equivalent diameters (water depth 30 mm, gas chamber volume 365.59 mL, original defect size 0.35 mm). and 0.352 mm, respectively. As can be seen from the figure, the measured pressures in the gas chamber declined with time. Taking 0.185 mm defect as an example, the measured pressure decreased from 79.17 kPa to 1.86 kPa after 157.0 s. The pressure can be described as a quadratic function of time and may be presented by the following relationship:  
\[P=75.5607-0.7391t+0.0018t^{2},\ R^{2}=0.9999 \tag{16}\]  
In addition, it was found that the measured PDR was the highest compared with other values at the beginning. The measured PDR also decreased from 1.03 kPa/s to 0.02 kPa/s after 157.5 s. Using Equations (7) and (8), it was found that the values of the chamber pressure and PDR changed with time, although they followed different trends. Moreover, along with the increasing defect size, the required time for the measured pressure to decrease to zero became increasingly shorter:, 157.0 s, 150.0 s, 70.0 s, and 43.3 s, respectively. Similarly, the required time for the measured PDR to decrease to zero also became increasingly shorter: 157.5 s, 150.5 s, 70.5 s, and 43.5 s, respectively. In contrast, the PDR values in the initial stages got larger: 1.03 kPa/s, 1.12 kPa/s, 2.28 kPa/s, and 4.22 kPa/s, respectively. This may be because the mass flow rate increased due to the increasing defect size, resulting in a reduction in the required time and an increase in the initial PDR value. Furthermore, there was a good agreement between the trend of the model predictions, in which there were no adjustable parameters, and the measured data of pressure and PDR. The measured data was in close agreement with the simulated values in varying degrees. The correlation between the two curves of simulated results and experimental data of pressure and PDR are given in Table 1. Values of Pearson's correlation coefficient \(r\) (more than 0.950) indicated a high consistency between the two curves. The significance (less than 0.001) showed the prediction model was valid for the  
Figure 4: The effect of defect size on the pressure decay and the pressure decay rate (PDR). (**a**) \(d_{OR}\) = 0.185 mm; (**b**) \(d_{OR}\) = 0.189 mm; (**c**) \(d_{OR}\) = 0.276 mm; (**d**) \(d_{OR}\) = 0.352 mm. Reaction conditions: water depth = 30 mm, gas chamber initial pressure = 80 kPa, and gas chamber volume = 365.59 mL. present study. Moreover, the differences between the measured data and simulated value changed with time. Although the initial measured pressures were approximately equal to the initial calculated pressures, the model underestimated the pressure in most cases. As for the PDR, the difference between the measured PDR and the calculated PDR changed with time, and it was relatively small in the middle of the pressure decay time. The differences corresponded to the selection parameters in the model.