## 5 Results and Discussion  
Figure 9 shows the atomization rate results measured with an interval of 2 kHz within the frequency range of 100-150 kHz at driving voltages of 100 V, 120 V, and 140 V, respectively. The liquid used in the experiment was pure water at room temperature (25 \({}^{\circ}\)C), and the pore diameter of the micro-tapered aperture was 12 \(\upmu\)m. It can be observed that the atomization rate had a total of four peak points located at \(f_{1}=106\) kHz,\(f_{2}=116\) kHz,\(f_{3}=122\) kHz and \(f_{4}=148\) kHz, respectively. Table 2 shows the atomization rates at different resonance frequencies, when the driving voltage was set at 120 V. The atomization rates at the three driving voltages reached a peak when the driving frequency was \(f=122\) kHz. The atomization rate was 2.48 mL/min, 3.06 mL/min, and 3.18 mL/min, respectively. Figure 8: The equipment used for the measurement of the atomization rate. Figure 7: The morphology of the atomizing film. (**a**) Schematic diagram of the atomizing film structure; (**b**) front view of the atomizing film; (**c**) back view of the atomizing film [31]. According to the comparisons among the vibration modes of several different resonance points, during the progress of driving frequency at 121.1 kHz, the micro-tapered aperture volume had the highest variation rate. This gives rise to a higher variation rate of the tapered angle and a greater difference between the forward and reverse flow resistance, and further leads to a higher atomization rate. Furthermore, in combination with the data recorded in Figure 5, it can be seen that there were some deviations between the four resonance frequencies obtained in the frequency sweep and the four peak frequencies in the atomization. This is because the atomizer was in a no-load state during the frequency sweep experiment. Additionally, during the atomization experiment, due to the action of the liquid on the piezoelectric vibrator, the resonance frequency experienced some variations, and thus resulted in some deviations in the resonance points and the optimal atomization frequency. Figure 10 shows the relationship between the atomization rate and voltage at different resonance frequencies. The liquid used in the experiment was pure water at room temperature (25 \({}^{\circ}\)C), and the pore diameter of the micro-tapered aperture was 12 \(\upmu\)m. It can be observed that obvious atomization started to emerge when the driving voltage reached 60 V. All of the atomization rates at these four resonance frequencies increased with the increase in driving voltage. Table 3 shows the atomization rates at different driving voltages, when the driving frequency was set as 122 kHz. This can be explained by the fact that as the applied voltage increased, the variation of the micro-tapered aperture volume also increased, leading to the increase of the aperture angle variation; as a result, the difference between the forward and reverse flow resistance of the micro-tapered aperture also increased, thus exerting a more obvious pumping effect. According to Equation (4), a micro-tapered aperture produces a higher atomization rate in this case. Figure 11 shows the outlet diameters of micro-tapered apertures used in this experiment. Figure 12 exhibits the relationship between the atomization rate and the micro-tapered aperture size under the same working condition. The liquid used in the experiment was pure water at room temperature (25 \({}^{\circ}\)C), and the working frequency was 122 kHz. Under the same working conditions, the larger the outlet diameter of the micro-tapered aperture, the higher the atomization rate will be. Table 4 shows the atomization rate of different micro-tapered aperture sizes under the same conditions. The micro-tapered apertures basically had a constant inlet diameter. When the outlet diameter increased, the aperture