# Numerical Analysis of Ultrasonic Nebulizer for Onset Amplitude of Vibration with Atomization Experimental Results

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Governing Equation

_{s}

^{2})]

^{1/3}

_{s}is the frequency of the capillary surface waves.

^{2})]

^{1/3}

_{s}from practical results.

_{cr}= 2ν [ρ/(Tω

_{s})]

^{1/3}

_{s}= (T k

^{3}/ρ + gk)

^{½}, ν is the kinematic viscosity of the fluid, k is the capillary wave number, and g is the gravity.

## 3. Finite-Element Analysis

_{e}× ω × sin (ωt).

^{3}is the homogeneous density, ω = 2πf is the angular frequency, $\mu $ = the dynamic viscosity, h

_{e}= the given amplitude, P = the equilibrium stress at the free fluid surface, and I = the 3 × 3 identity matrix.

_{a}is the atmospheric pressure of 1 atm. The full theoretical conduction can be found in the supplementary material.

^{3}), kinematic viscosity coefficient ν = 1.02 × 10

^{−6}(m²/s), and surface tension T = 7.2 × 10

^{−2}(N/m). The frequency range was plotted for the perception of harmonic frequency and the subharmonic frequency at 485 and 242.5 kHz individually (Figure 3). It shows that the beginning vibrational amplitude occurred at the assigned frequency of 485 kHz. Further, the wavelength of the capillary surface wave is 19.4 μm, as determined from Figure 4 by the peak-to-peak separation. It is fascinating that the simulated value of 19.4 μm and the theoretical value of 19.8 μm (i.e., given Equation (2)) for the wavelength of the capillary wave are comparable [31].

## 4. Experiments

^{3}times. As the greatest longitudinal vibration breaks the surface pressure of the liquid, a temperamental fluid capillary surface wave, in the long run, transforms into modest atomized droplets. The progress of the atomized droplets can be seen in Figure 5b–e.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Stability chart for the solutions of Mathieu’s equation. Reprinted from Benjamin and Ursell [18].

**Figure 2.**The modeling plot of the velocity in the Z-axis versus time at the nozzle tip of the silicon-based three-horn.

**Figure 3.**The calculated frequency spectrum at the tip of the silicon-based three-horn. The designated harmonic frequency from COMSOL Multiphysics 5.4 is 485 kHz. As expected, 242.5 kHz is the corresponding subharmonic frequency.

**Figure 4.**The vibrational velocity is propagated throughout the water surface on the tip of the silicon-based three-horn in the modeling. Inset: the 2D velocity profile at the corresponding position at 7.5505 × 10

^{−4}s simulation time. The red and blue colors present the displacement in the opposite directions.

**Figure 5.**(

**a**) Schematic presentation of a silicon-based three-horn ultrasonic nozzle. Optical images obtained from an atomization experiment after voltage was applied for (

**b**) 6.49 s, (

**c**) 6.50 s (

**d**) 43.91 s, and (

**e**) 63.59 s. The operating frequency was 484.5 kHz and the applied voltage was 7.9 V under 10 μL/min liquid flow.

**Figure 6.**Schematic diagram for measuring the longitudinal vibration at the nozzle tip [26].

**Figure 7.**Output signals of longitudinal vibration at the nozzle tip versus applied electrode voltage at the base of the silicon-based three-horn Fourier nozzle.

**Table 1.**Comparison of nozzle and atomization parameters. Vp shown is based on the best conditional atomization. Liquid flow rates were carefully adjusted to determine the potential operating conditions.

Nozzle Number | A1 | A2 | A3 | B1 | B2 | B3 | C1 | C2 | C3 | C4 | C5 |
---|---|---|---|---|---|---|---|---|---|---|---|

Atomization Frequency (kHz) | 484.5 | 486.5 | 485 | 486 | 484.5 | 485 | 488 | 489 | 489 | 489 | 489 |

Vp (V) | 7.9 | 6.5 | 8.7 | 7.9 | 6.9 | 6.5 | 7.1 | 6.5 | 6.6 | 6.5 | 6.8 |

Liquid Flow Rate (μL/min) | 10–20 | 10–30 | 10–230 | 10–30 | 10–20 | 10–20 | 10–30 | 10–100 | 10–100 | 10–100 | 10–50 |

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**MDPI and ACS Style**

Song, Y.-L.; Cheng, C.-H.; Reddy, M.K.
Numerical Analysis of Ultrasonic Nebulizer for Onset Amplitude of Vibration with Atomization Experimental Results. *Water* **2021**, *13*, 1972.
https://doi.org/10.3390/w13141972

**AMA Style**

Song Y-L, Cheng C-H, Reddy MK.
Numerical Analysis of Ultrasonic Nebulizer for Onset Amplitude of Vibration with Atomization Experimental Results. *Water*. 2021; 13(14):1972.
https://doi.org/10.3390/w13141972

**Chicago/Turabian Style**

Song, Yu-Lin, Chih-Hsiao Cheng, and Manoj Kumar Reddy.
2021. "Numerical Analysis of Ultrasonic Nebulizer for Onset Amplitude of Vibration with Atomization Experimental Results" *Water* 13, no. 14: 1972.
https://doi.org/10.3390/w13141972