# Effects of Atomization Injection on Nanoparticle Processing in Suspension Plasma Spray

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## Abstract

**:**

## 1. Introduction

## 2. Mathematic Model

#### 2.1. Modeling Liquid Primary Breakup to Estimate Droplet Mean Size

**Estimation of annular liquid sheath thickness:**To estimate the thickness of annular liquid sheath, a simple model is adopted. It is assumed that the annular two-phase flow within the discharge orifice is one-dimensional, in viscous and isothermal, with compressible ideal gas and small interface velocity slip ratio. The velocity of the gas flow, v

_{g}, satisfies the momentum equation as:

_{g}is the radius of gas flow, ρ

_{g}, the gas density, ${\dot{m}}_{l}$ is the mass flow rate of liquid and ALR is the air–liquid ratio by mass. The radius of gas flow can be written in terms of orifice radius, r

_{o}, using the definition of void fraction α as: ${r}_{g}=\sqrt{\mathsf{\alpha}}{r}_{o}$. According to Ishii [10], the interface velocity slip ratio “sr” under different flow rate can be expressed as:

_{g}, α and sr can be calculated for different operating conditions. The thickness of annular liquid sheath is then calculated as: $\mathsf{\delta}={r}_{o}-{r}_{g}$, which is also the diameter of the typical cylindrical ligament.

**Droplet mean size from primary breakup:**After obtaining the thickness of annular liquid sheath, we need to compute the length of a typical ligament fragment, i.e., the wavelength λ at which the disturbance grows most rapidly. Among the linear instability analysis theories, the one given by Weber is mostly widely used to determine λ [11]:

_{l}, ρ

_{l}, and σ

_{l}represent the liquid viscosity, density, and liquid surface tension, respectively. Here, we use the relative velocity difference of the gas and the liquid at the nozzle exit. The breakup wavelength λ is determined by the wave number k where the maximum growth rate ω occurs in the curve calculated by Equation (6). Assuming that each fragment stabilizes to one droplet, the Sauter Mean diameter of drop size can then be calculated from the conservation of mass:

#### 2.2. Eulerian/Lagrangian Model of Droplets or Particles in Plasma Jet

^{−4}, so the collisions between particles were neglected [13].

**Droplet secondary breakup modeling:**When the droplets with initial diameter estimated from Equation (7) were injected into the plasma jet, secondary atomization would continually breakup the droplets, especially near the orifice with strong aerodynamic interaction. To model the droplet secondary breakup, a cascade atomization and droplet breakup (CAB) model as shown in Figure 3 [14] has been utilized, which is determined by the gas aerodynamic force, the liquid viscosity, and the surface tension force.

_{bu}depends on the drop breakup regimes. As suggested by Reitz [16], three breakup regimes are classified with respect to increasing gas Weber number, bag breakup, stripping breakup regime, and catastrophic breakup regime. However, in this study, gas Weber number is mostly lower than 80, which falls into bag breakup regime, as shown in Figure 3. Here, Weber number provides the importance of inertia compared to surface tension. Breakup frequency ${K}_{bu}=0.05\mathsf{\omega}$ as suggested by O’Rourke and Amsden [15] is used in this study, and the drop oscillation frequency ω is given by

_{bu}is the breakup time, i.e., the time until the normalized deformation y(t) in the solution of Equation (8) exceeds the value of 1.

**Solvent evaporation of droplets:**The suspension droplets would evolve to agglomerates and nanoparticles due to solvent evaporation. As shown in Figure 4, the nano-sized solid particles were initially suspended in the micro-sized droplets, with small amount of particle aggregation, and uniform distribution. The aerodynamic interaction between the plasma gas and the droplet would further breakup the droplets into smaller pieces. At the same time, the hot plasma gas would also heat up and vaporize the solvent inside droplets. Once the solvent in droplets was totally vaporized out, the gas would blow away the solids to form individual nanoparticles. Otherwise, if the gas velocity is not large enough, the remaining solids would be sintered by the hot gas and the micro-size agglomerates would form thereafter. In this study, the nanoparticle size is larger than 1 nm but less than 1 μm, and the agglomerate is larger than or equal to 1 μm. These agglomerates or nanoparticles are simulated as new Lagrangian entities with their parent particle’s position, velocity and temperature.

_{d,}

_{0}, Q

_{d}, m

_{d}and c

_{p,d}are the initial droplet temperature, heat gain, mass, and the specific heat of the droplet, respectively. Q

_{d}can be calculated by Q

_{d}= Q

_{conv}− Q

_{rad}, where Q

_{conv}represents the convection heat, and Q

_{rad}is the radiation heat loss of particles. c

_{p,d}is calculated based on the average of the mass fraction of solid particle and solvent as: ${c}_{p,d}={c}_{p,p}\left(1-{\mathsf{\alpha}}_{sl}\right)+{c}_{p,sl}{\mathsf{\alpha}}_{sl}$.

**Particle acceleration and tracking model:**For particles in plasma jets, the forces imparted on the particles are mainly the drag force, Saffman lift force and Brownian force. For particles smaller than 100 μm, the drag force is prominent. For the particles near the jet edge and the substrate, where the flow shear stress is large, the Saffman lift force is significant. While for the sub-micron or nanoparticles, Brownian force is important. By accounting for these three forces, the particles acceleration rate could be expressed as,

_{g}is the gas velocity within the turbulent fluctuation calculated from the gas turbulence model. 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. C

_{D}is the drag force coefficient expressed by [19],

_{prop}represents the effects of variable plasma properties in the boundary layer surrounding the particle, and can be expressed as [20] ${f}_{prop}={\mathsf{\rho}}_{c}{\mathsf{\mu}}_{c}/{\mathsf{\rho}}_{w}{\mathsf{\mu}}_{w}$.${f}_{Kn}$ is the factor representing Knudsen effect, which can be expressed by:

_{w}, as well as the average molecular weight W of the gas mixture, and can be given as: ${v}_{w}={\left(8R{T}_{w}/\mathsf{\pi}W\right)}^{1/2}$. For nanoparticles, ${f}_{Kn}$ is in the range 0.005 to 0.1. For the agglomerates and micro-sized particles, ${f}_{Kn}$ changes from 0.994 to 0.996 [22].

_{c}= 2.594 is the constant in the Saffman lift force [23], d

_{ij}is the deformation tensor. In the expression of Brownian force, G

_{0}is a random number between −1 to 1, which is subjected to Gauss distribution. S

_{0}is the spectral intensity, which can be expressed as ${S}_{0}=\left(216{\mathsf{\mu}\mathsf{\sigma}}_{B}{T}_{\mathrm{g}}\right)/\left(32{\mathsf{\pi}}^{2}{r}_{p}^{5}{\mathsf{\rho}}_{p}^{2}{C}_{c}\right)$, Boltzman constant σ

_{B}= 1.38 × 10

^{−23}J/K.

**Heating and melting of particles:**A one-dimensional model was adopted for the particle heating and melting, in which the spherical shape of the particle was assumed. The internal convection within the molten part of the particle was not considered. The temperature distribution inside the particle was described as follows:

_{f}was defined as (T

_{s}+ T

_{g})/2, which is introduced to deal with the steep temperature gradient in the boundary layer around the particle. Only the radiation between the particle surface and the environment was considered in the case of optically thin plasma gas. The heat transfer coefficient, h

_{f}, can be calculated from [25]:

_{v}accounts for the effect of mass transfer due to evaporation, which can be found in reference [22]. Additional constraints of energy balance between the heat conduction and latent heat at the melting interface r

_{m}was also considered:

## 3. Experimental and Numerical Setup

_{2}nanoparticles were suspended in the alcohol solvent, as shown in Figure 4, with solid weight content of 10%. Gas mixtures of argon and hydrogen were ionized in plasma gun to form high temperature and high velocity plasma jet. The droplets and particles were accelerated and heated in the plasma gas. At last, the melting nanoparticles formed coatings on the substrate.

_{2}gas flow rates are 68 and 12 liters per minute, respectively. The electric power input of the plasma torch gun is 30 kW. The plasma flow field was solved using a three-dimensional cylindrical coordinate system. The radial distance was 6 cm with 57 grid points, the axial distance was 15 cm with 66 grid points, and the circular direction was 2$\mathsf{\pi}$ with 32 grid points. At the axis of the gas field, the symmetrical condition is applied. At the nozzle exit, the velocity and temperature could be expressed by the empirical formulae [26], v(r) = V

_{cl}[1 − (r/R

_{i})

^{1.2}], and T(r) = (T

_{cl}− T

_{w})[1 − (r/R

_{i})

^{6}] + T

_{w}, respectively. V

_{cl}and T

_{cl}are the velocity and temperature on the nozzle exit center line, respectively, which are calculated from the total amount of momentum and thermal energy transferred to the plasma jet. T

_{w}is the wall temperature with the initial value of 300 K, the velocity at the wall boundary is 0. The downstream of the jets flow is open.

## 4. Validation of Model Predictions

## 5. Discussion

#### 5.1. Flow Field of the Plasma Jet

#### 5.2. Effects of Droplet Diameter on Nanoparticle Release

#### 5.3. Effects of Atomization Injection Parameters on Nanoparticle Release

#### 5.4. Velocity, Temperature and Melting of Nanoparticles and Agglomerates

#### 5.5. Critical Agglomerate and Droplet Size

_{d,crit}and solid weight content of wt, experienced no secondary atomization and was sintered to one agglomerate with diameter of D

_{a,crit}, i.e., 50 μm in this case. Then, the critical suspension droplet size, D

_{d,crit}could be estimated as:

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomemclature

C_{D} | drag coefficient |

C_{p} | specific heat, J·kg^{−1}·K^{−1} |

D_{d} | droplet diameter, μm |

D_{a} | agglomerate diameter, μm |

d_{ij} | deformation tensor |

d_{p} | particle diameter, m |

f_{Kn} | factor ofKnudsen effect |

f_{prop} | factor to account property variation |

f_{v} | factor formass transfer |

G_{0} | zero-mean, unit-variance independent Gauss random number |

h | heat transfer coefficient, W·m^{−2}·K^{−1} or the half-thickness of sheath |

k | thermal conductivity, W·m^{−1}·K^{−1} or wave number |

K _{c} | constant coefficient in Saffman lift force |

Kn | Knudsen number |

L_{m} | latent heat of fusion, J·kg^{−1} |

L_{v} | latent heat of vaporization, J·kg^{−1} |

m_{p} | particle mass, kg |

${\dot{m}}_{v}$ | vaporization rate, kg·s^{−1} |

Nu | Nusselt number |

p | pressure, Pa |

Pr | Prandtl number, Pr = μC_{p}k^{−1} |

Q | heat flux, W·m^{−2} or the gas/liquid density ratio |

R | gas constant, J·mol^{−1}·K^{−1} |

r | radial coordinate for the particle, m |

${r}_{m}^{-}$ | inner radius of melting interface, m |

${r}_{m}^{+}$ | outer radius of melting interface, m |

r_{m} | position of particle melting interface, m |

r_{p} | particle radius, m |

S_{0} | spectral intensity |

SMD | Sauter mean diameter, μm |

T | temperature, K |

t | time, s |

T_{∞} | temperature outside boundary layer, K |

T_{d,0} | droplet initial temperature, K |

T_{m,d} | droplet melting point, K |

T_{s} | particle surface temperature, K |

T_{w} | gas temperature near particle surface, K |

v_{g} | gas velocity, m·s^{−1} |

V | velocity, m·s^{−1} |

v_{w} | mean molecular speed, m·s^{−1} |

W | molecular weight of thegas mixture, kg·mol^{−1} |

Weber | Weber number, dimensionless |

wt | solid weight content in suspension, dimensionless |

y | deformation parameter, dimensionless |

σ_{s} | Stefan-Boltzmann constant |

## Greek symbols

ρ | density, kg·m^{−3} |

μ | viscosity, kg·s^{−1}·m^{−1} |

γ_{w} | specific heat ratio of gas, dimensionless |

α | weight fraction or void fraction |

ε | surface emissivity coefficient |

δ | the thickness of annular liquid sheath |

σ | surface tension |

ω | the growth rate of surface disturbances |

## Subscript

d | suspension droplet embedded with nanoparticles |

f | film around the particle |

g | plasma gas |

p | solid nanoparticles or agglomerates |

sl | solvent |

## References

- Fauchais, P.; Montavon, G.; Lima, R.S.; Marple, B.R. Engineering a new class of thermal spray nano-based microstructures from agglomerated nanostructured particles, suspensions and solutions: An invited review. J. Phys. D
**2011**, 44. [Google Scholar] [CrossRef] [Green Version] - Ye, F.; Ohmori, A.; Li, C. New approach to enhance the photocatalytic activity of plasma sprayed TiO
_{2}coatings using p-n junctions. Surf. Coat. Technol.**2004**, 184, 233–238. [Google Scholar] [CrossRef] - Meillot, E.; Vincent, S.; Caruyer, C.; Damiani, D.; Caltagirone, J.P. Modelling the interactions between a thermal plasma flow and a continuous liquid jet in a suspension spraying process. J. Phys. D
**2013**, 46. [Google Scholar] [CrossRef] - Marchand, C.; Chazelas, C.; Mariaux, G.; Vardelle, A. Liquid precursor plasma spraying: Modeling the interactions between the transient plasma jet and the droplets. J. Ther. Spray Technol.
**2007**, 16, 705–712. [Google Scholar] [CrossRef] - Huang, P.C.; Heberlein, J.; Pfender, E. Particle behavior in a two-fluid turbulent plasma jet. Surf. Coat. Technol.
**1995**, 73, 142–151. [Google Scholar] [CrossRef] - Fazilleau, J.; Delbos, C.; Rat, V.; Coudert, J.F.; Fauchais, P.; Pateyron, B. Phenomena involved in suspension plasma spraying part 1: Suspension injection and behavior. Plasma Chem. Plasma Process.
**2006**, 26, 371–391. [Google Scholar] [CrossRef] - Ozturk, A.; Cetegen, B.M. Modeling of axially and transversely injected precursor droplets into a plasma environment. Int. J. Heat Mass Transf.
**2005**, 48, 4367–4383. [Google Scholar] [CrossRef] - Jabbari, F.; Jadidi, M.; Wuthrich, R.; Dolatabadi, A. A Numerical Study of Suspension Injection in Plasma-Spraying Process. J. Ther. Spray Technol.
**2014**, 23, 3–13. [Google Scholar] [CrossRef] - Lund, M.T.; Sojka, P.E.; Lefebvre, A.H.; Gosselin, P.G. Effervescent atomization at low mass flow rates. Part I: The influence of surface tension. Atom. Sprays
**1993**, 3, 77–89. [Google Scholar] [CrossRef] - Ishii, M. One-Dimensional Drift-Flux Model and Constitutive Equations for Relative Motion between Phases in Various Two-Phase Flow Regimes; Argonne National Laboratory: Argonne, IL, USA, 1977; pp. 47–77.
- Weber, C. Disintegration of liquid jets. Z. Angew. Math. Mech.
**1931**, 11, 136–159. [Google Scholar] [CrossRef] - Senecal, P.K.; Schmidt, D.P.; Nouar, I.; Rutland, C.J.; Reitz, R.D.; Corradini, M.L. Modeling high-speed viscous liquid sheet atomization. Int. J. Mult. Flow
**1999**, 25, 1073–1097. [Google Scholar] [CrossRef] - Xiong, H.B.; Zheng, L.L.; Sampath, S.; Williamson, R.L.; Fincke, J.R. Three-dimensional simulation of plasma spray: Effects of carrier gas flow and particle injection on plasma jet and entrained particle behavior. Int. J. Heat Mass Transf.
**2004**, 47, 5189–5200. [Google Scholar] [CrossRef] - Tanner, F.X. Development and validation of a cascade atomization and drop breakup model for high-velocity dense sprays. Atom. Sprays
**2004**, 14, 211–242. [Google Scholar] [CrossRef] - O’Rourke, P.J.; Amsden, A.A. The TAB Method for Numerical Calculation of Spray Droplet Breakup; No. 872089, SAE Technical Paper; SAE International: Warrendale, PA, USA, 1987. [Google Scholar]
- Reitz, R.D. Modeling atomization processes in high-pressure vaporizing sprays. Atom. Spray Technol.
**1987**, 3, 309–337. [Google Scholar] - Delbos, C.; Fazilleau, J.; Rat, V.; Coudert, J.F.; Fauchais, P.; Pateyron, B. Phenomena involved in suspension plasma spraying Part 2: Zirconia particle treatment and coating formation. Plasma Chem. Plasma Process.
**2006**, 26, 393–414. [Google Scholar] [CrossRef] - Fauchais, P.; Montavon, G. Latest developments in suspension and liquid precursor thermal spraying. J. Ther. Spray Technol.
**2010**, 19, 226–239. [Google Scholar] [CrossRef] - Chen, X.; Pfender, E. Behavior of small particles in a thermal plasma flow. Plasma Chem. Plasma Process.
**1983**, 3, 351–366. [Google Scholar] [CrossRef] - Lee, Y.C.; Hsu, K.C.; Pfender, E. Modeling of particles injected into a DC plasma jet. In Proceedings of the 5th International Symposium on Plasma Chemistry, Edinburgh, UK, 10–14 August 1981; Volume 2, p. 795.
- Chen, X.; Pfender, E. Effect of the Knudsen number on heat transfer to a particle immersed into a thermal plasma. Plasma Chem. Plasma Process.
**1983**, 3, 97–113. [Google Scholar] [CrossRef] - Xiong, H.B.; Lin, J.Z. Nanoparticles modeling in axially injection suspension plasma spray of zirconia and alumina ceramics. J. Ther. Spray Technol.
**2009**, 18, 887–895. [Google Scholar] [CrossRef] - Saffman, P.G.T. The lift on a small sphere in a slow shear flow. J. Fluid Mech.
**1965**, 22, 385–400. [Google Scholar] [CrossRef] - Wan, Y.P.; Prasad, V.; Wang, G.; Sampath, S.; Fincke, J.R. Model and powder particle heating, melting, resolidification, and evaporation in plasma spraying processes. J. Heat Transf.
**1999**, 121, 691–699. [Google Scholar] [CrossRef] - Chen, X.; Pfender, E. Heat transfer to a single particle exposed to a thermal plasma. Plasma Chem. Plasma Process.
**1982**, 2, 185–212. [Google Scholar] [CrossRef] - Ramshaw, J.D.; Chang, C.H. Computational fluid dynamics modeling of multicomponent thermal plasmas. Plasma Chem. Plasma Process.
**1992**, 12, 299–325. [Google Scholar] [CrossRef] - Brossa, M.; Pfender, E. Probe measurements in thermal plasma jets. Plasma Chem. Plasma Process.
**1988**, 8, 75–90. [Google Scholar] [CrossRef] - Fauchais, P.; Etchart-Salas, R.; Rat, V.; Coudert, J.F.; Caron, N.; Wittmann-Ténèze, K. Parameters controlling liquid plasma spraying: Solutions, sols, or suspensions. J. Ther. Spray Technol.
**2008**, 17, 31–59. [Google Scholar] [CrossRef]

**Figure 4.**Schematic of droplet injection, solvent evaporation and nanoparticle release. Reproduced with permission from [17]. Copyright Courtesy of Delbos, 2006.

**Figure 7.**Solvent evaporation position and nanoparticle release position for different droplet diameter.

Particle Diameter | Maximum of Melting Percentage | Mostly Melted Position |
---|---|---|

10–100 nm | 100% | 6 mm |

30 μm | 100% | 11 mm |

40 μm | 100% | 15 mm |

50 μm | 100% | 29 mm |

60 μm | 93.26% | 38 mm |

70 μm | 76.40% | 62 mm |

80 μm | 2.25% | 74 mm |

90 μm | 0 | None |

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**MDPI and ACS Style**

Xiong, H.-b.; Zhang, C.-y.; Zhang, K.; Shao, X.-m.
Effects of Atomization Injection on Nanoparticle Processing in Suspension Plasma Spray. *Nanomaterials* **2016**, *6*, 94.
https://doi.org/10.3390/nano6050094

**AMA Style**

Xiong H-b, Zhang C-y, Zhang K, Shao X-m.
Effects of Atomization Injection on Nanoparticle Processing in Suspension Plasma Spray. *Nanomaterials*. 2016; 6(5):94.
https://doi.org/10.3390/nano6050094

**Chicago/Turabian Style**

Xiong, Hong-bing, Cheng-yu Zhang, Kai Zhang, and Xue-ming Shao.
2016. "Effects of Atomization Injection on Nanoparticle Processing in Suspension Plasma Spray" *Nanomaterials* 6, no. 5: 94.
https://doi.org/10.3390/nano6050094