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Heat and Mass Transfer Within an Evaporating Solution Droplet in a Plasma Jet

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Abstract

Solution precursors have been injected into the plasma gases to produce finely structured ceramic coatings with nano- and sub-micrometric features. The trajectory history and heat and mass transfer within individual solution droplets play a very important role in determining the coating microstructure. A mathematical model is developed to analyse the thermal behavior of individual precursor droplets travelling in the high temperature plasma jet. This model involves the motion and evaporation of the precursor droplet in a DC plasma jet and the heat and mass transfer within the evaporating droplet. The influence of Stefan flow, as well as the variable thermo-physical properties of the solution and the plasma gas, is considered. The internal circulation due to the relative velocity between the droplet and the plasma jet, which may be approximated by the Hill vortex, is considered as well. The trajectory, temporal droplet surface temperature, and radius variation are predicted. The temporal temperature and concentration distributions within the evaporating droplet are presented for different injection parameters.

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Abbreviations

A r :

averaging parameter

B T, B M :

Spalding heat and mass transfer numbers

C D :

droplet drag coefficient

C P :

specific heat (J/kg·°C)

D :

mass diffusivity of the vapor into the plasma (m2/s)

L :

latent heat of vaporization (J/kg)

\( {\dot{\text{m}}} \) :

vaporization rate (kg/s)

m v :

mass fractions of vapor

M :

molecular weight (kg/kmol)

Nu :

Nusselt number

P :

pressure (Pa)

Pe:

Peclet number

Pr:

Prandtl number

Q g :

heat transfer from the plasma gas to drop surface (J/s)

Q i :

heat conduction from droplet surface into its interior (J/s)

r :

radius (m)

Re :

Reynolds number

Sh :

Sherwood number

T :

temperature (K)

t :

time (s)

U :

velocity in axial direction (m/s)

V :

velocity in radial direction (m/s)

ρ:

density (kg/m3)

λ:

thermal conductivity (w/m·k)

μ:

dynamic viscosity (kg/m·s)

g:

gas mixture

l:

liquid

s:

surface

v:

vapor

∞:

far from the droplet

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Acknowledgments

The financial support of the National Natural Science Foundation of China (Project 50706027), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, and Shanghai Leading Academic Discipline Project (Project J50501) are gratefully acknowledged.

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Authors and Affiliations

  1. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai, China

    Yanguang Shan & Yuan Hu

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  1. Yanguang Shan
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  2. Yuan Hu
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Correspondence to Yanguang Shan.

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Shan, Y., Hu, Y. Heat and Mass Transfer Within an Evaporating Solution Droplet in a Plasma Jet. J Therm Spray Tech 21, 676–688 (2012). https://doi.org/10.1007/s11666-011-9726-x

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  • DOI: https://doi.org/10.1007/s11666-011-9726-x

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