# Investigation of Droplet Atomization and Evaporation in Solution Precursor Plasma Spray Coating

^{*}

## Abstract

**:**

## 1. Introduction

_{2}O

_{3}-stabilised ZrO

_{2}(YSZ).

## 2. Basic Description of the Problem

_{2}) mixtures, are ionized in a plasma gun to generate a high-temperature and high-velocity plasma jet. The YSZ material, usually zyrconyl nitrate and yttrium nitrate salts, is resolved in the solvent of water or ethanol to produce the liquid precursor. A needle-shaped injector, with diameter of 200 μm, is utilized to introduce the droplet from a pressurized liquid reservoir to the plasma jet. These droplets are accelerated and heated up by the plasma gas, then partially or fully atomized and vaporized, as illustrated in Figure 2. Finally, the pyrolysis salt YSZ material impacts the substrate to form the functional zirconia coatings.

## 3. Mathematical Model

#### 3.1. Droplets Tracking and Heating

_{p}is the particle mass and V

_{p}is velocity. During the particle tracking procedure, the turbulent dispersion of particles is calculated by integrating the trajectory equations for individual particles, using the instantaneous fluid velocity along the particle path. The particle temperature is also calculated with the given surrounding gas thermal conditions. It is assumed that there exists no heat conduction inside the particle, which describes the temperature of individual particle as follows (Equation (5)):

_{p}, C

_{p}, and Q

_{p}represents the droplet temperature, specific heat, and the heat flux at the surface, respectively. Detailed explanation of the above particle models for injected droplets can be found in our previous publications [19,20,21].

#### 3.2. Droplet Atomization

_{bu}is the breakup frequency, depending on the breakup regimes. As demonstrated by Reitz [23], three distinct breakup mechanisms dominated the fragmentation of drops with respect to the gas Weber number: bag breakup, stripping breakup, and catastrophic breakup regimes. The calculation of the Weber number can be found in [18,24]. In this study, the critical Weber number is below 80, which belongs to the bag breakup, as shown in Figure 2. Here, the critical Weber number reflects the importance of inertia to surface tension. ω

_{bu}here has the value of 0.05ω

_{os}as suggested by O’Rourke and Amsden [22] and, thus, the drop oscillation frequency ω

_{os}could be solved by Equation (8):

_{0}and r represent the radii of the parent and child droplets, respectively, and t

_{bu}is the characteristic breakup time, derived from Equation (6) when breakup occurs.

#### 3.3. Droplets Evaporation

_{net}. Taking both cases mentioned above into account, m

_{v}can be given as Equation (10):

_{g}, D

_{g}are the gas density and gas diffusion coefficient, respectively. Sh is the Sherwood number reflecting the convective heat transfer effect (Equation (11)):

_{p}is the particle Reynolds number. B is a mass transfer coefficient related to the local mass fraction of vapor in the gas phase Y

_{∞}and the vapor concentration surrounding the droplet surface is Y

_{*}, and can be given as Equation (12):

_{∞}is calculated in the plasma jet simulation, and Y

_{*}is calculated by Equation (13):

_{p}and W

_{0}are the molecular weight of the salts and gas, respectively. P

_{c}is the gas pressure and P

_{v}is the vapor pressure [25].

## 4. Numerical Treatment and Validation

#### 4.1. Geometry and Boundary Condition

#### 4.2. Validation of Numerical Model

## 5. Discussion

#### 5.1. Results of Plasma Gas Flow Field

#### 5.2. Acting Mechanism of Atomization and Evaporation

#### 5.3. Droplet Size Distribution

_{2}atmosphere. We noted that the number of smaller droplets (d ≤ 10 μm) usually outweigh those of the larger ones (d ≥ 20 μm), regardless of liquid or gas types.

#### 5.4. Effects of Liquid and Gas Types

_{2}plasma produces a smaller droplet size than Ar plasma, since the presence of hydrogen enlarges the gas heat capacity and, thus, more thermal heat can be transferred to the droplets. In the current study, the minimum droplet diameter obtained in Ar gas is 14 and 33 μm for water and ethanol, respectively. However, in Ar-H

_{2}gas, we could obtain much smaller minimum diameters as 2.5 and 20 μm, for water and ethanol, respectively. The shift from Ar to Ar-H

_{2}leads to the enhancement of the plasma dynamic velocity and thermal enthalpy, eventually boosting the fragmentation of droplets [9]. This is essential for water-based SPPS coatings: Only Ar-H

_{2}plasma could render the favorable occurrence of complete water disintegration.

_{2}plasma produces further decay of the solvent than Ar plasma, mainly because the Ar-H

_{2}atmosphere provides higher specific enthalpy, compared to pure Ar gas. Another reason is that the composite hydrogen in the plasma gas results in the higher velocity and dynamic pressure, which enlarges the shear rate of the gas and helps to break up the liquid into fine and desirable droplets downstream of the nozzle exit [7]. Therefore, it could be concluded that droplet evolution in SPPS prefer a solvent with low surface tension and a low boiling point in gas mixture with H

_{2}, which agrees with the previous observations in Section 5.3.

#### 5.5. Effects of Substrate Location

## 6. Conclusions

- Droplet size and distribution are the main factors impacting the microstructure of the coating surface. Fine droplets resulting from the complete atomization and vaporization contributed to the formation of smaller nanoparticles and a fully melting liquid nanoparticle with low liquid stock vapor is essentially decisive to constructing pure overlapped splats on the material surface.
- Droplet size largely depends on the atomization and evaporation consequences and goes through an instant decrease, corresponding to the axial position of the hot core region and the secondary breakup region. In these areas, atomized and vaporized actions exert inconsistent influences on the modification of droplet size. According to these features, operating parameters, such as types of solvent, could be adjusted from this aspect.
- Ethanol, used as a solvent, undergoes a speedy vaporizing process resulting in a sharp droplet size decrease near the nozzle exit. The evaporation of water or other non-volatility solvent highly depends on the plasma temperature and the length of hot core region. A higher enthalpy plasma gas and a longer length of the hot core region contribute to the effective evaporation. As for ethanol or other solvents with good volatility, the hot core region does not need to be that long; instead, the solvent with suitable atomization properties then become our principal care.
- In comparison with pure Ar gas, Ar-H
_{2}gas mixture reveals more superior performance with respect to the droplet atomizing and vaporizing as a result of the higher specific gas enthalpy, the enhancement of gas velocity, as well as better thermodynamic properties. - In order to procure an ideal, fine droplet size and uniform distribution near the torch exit, the substrate should be located where the droplet momentum has not yet fully diminished, and in this case it should be put somewhere before the standoff distance of 6 cm.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Different coating quality resulting from fully (

**a**), and not fully atomized and vaporized droplets (

**b**).

**Figure 6.**Ethanol droplet size distribution at different cross-sections at 15 mm (

**a**), and 40 mm (

**b**).

Case | Gas Mixture (Flow Rates, slm) | Specific Enthalpy (MJ/kg) | Solvent | Substrate |
---|---|---|---|---|

1 | Ar(33) | 9.16 | Ethanol | No |

2 | Ar-H_{2}(33-10) | 20.46 | Ethanol | No |

3 | Ar(33) | 9.16 | Water | No |

4 | Ar-H_{2}(33-10) | 20.46 | Water | No |

5 | Ar-H_{2}(33-10) | 20.46 | Ethanol | 40 mm |

6 | Ar-H_{2}(33-10) | 20.46 | Water | 40 mm |

7 | Ar-H_{2}(33-10) | 20.46 | Ethanol | 100 mm |

8 | Ar-H_{2}(33-10) | 20.46 | Water | 100 mm |

^{3}/s.

Parameter | Value |
---|---|

Solid density (kg∙m^{−3}) | 5.89 × 10^{3} |

Liquid density (kg∙m^{−3}) | 5.89 × 10^{3} |

Solid thermal conductivity (W∙m^{−1}∙K^{−1}) | 2.0 |

Liquid thermal conductivity (W∙m^{−1}∙K^{−1}) | 3.0 |

Solid specific heat (J∙kg^{−1}∙K^{−1}) | 580 |

Liquid specific heat (J∙kg^{−1}∙K^{−1}) | 713 |

Melting temperature (K) | 2950 |

Boiling temperature (K) | 5000 |

Latent heat of melting (J∙kg^{−1}) | 8 × 10^{5} |

Latent heat of vaporization (J∙kg^{−1}) | 6 × 10^{6} |

Parameter | Water | Ethanol |
---|---|---|

Molecular Weight (g∙mol^{−1}) | 18 | 46 |

Density (kg∙m^{−3}) | 1 × 10^{3} | 0.8 × 10^{3} |

Boiling Point at 1 atm (K) | 373 | 351 |

specific heat (J kg^{−1}∙K^{−1}) | 4200 | 2400 |

Critical Temperature (K) | 646 | 516 |

Critical Pressure (Mpa) | 22 | 6.38 |

Surface tension (10^{−3} J/m^{2}) | 72.9 | 22.3 |

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**MDPI and ACS Style**

Xiong, H.; Sun, W.
Investigation of Droplet Atomization and Evaporation in Solution Precursor Plasma Spray Coating. *Coatings* **2017**, *7*, 207.
https://doi.org/10.3390/coatings7110207

**AMA Style**

Xiong H, Sun W.
Investigation of Droplet Atomization and Evaporation in Solution Precursor Plasma Spray Coating. *Coatings*. 2017; 7(11):207.
https://doi.org/10.3390/coatings7110207

**Chicago/Turabian Style**

Xiong, Hongbing, and Weiqi Sun.
2017. "Investigation of Droplet Atomization and Evaporation in Solution Precursor Plasma Spray Coating" *Coatings* 7, no. 11: 207.
https://doi.org/10.3390/coatings7110207