Abstract
The Knudsen effect on mass transfer between a plasma gas and a small particle is investigated. A predictive model is developed by incorporating the Z-potential approach into the jump theory. The predictions of the model are explored through a case study. The results indicate that the Knudsen effect is significant and depends strongly on the particle size and the surface conditions. The plasma and the particle surface temperatures are also found to be determining factors. Under certain conditions, it is observed that the Knudsen effect can enhance the plasma-particle mass transfer, contrary to the predictions of the previous near-isothermal models.
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Abbreviations
- C :
-
concentration (kmol m−3)
- C p :
-
specific heat capacity (J kg−1 k−1)
- d :
-
particle diameter (m)
- D :
-
molecular diffusivity (m2 s−1)
- H :
-
specific enthalpy (J kg−1)
- I :
-
heat conduction potential (J s−1 m−1)
- Kn:
-
Knudsen number
- Kn*:
-
effective Knudsen number
- l :
-
mean free path of gas molecules (m)
- M :
-
molecular weight of the gas
- N :
-
mass flux (kmol m−2s−1)
- P :
-
capacitance variable defined by Eq. (2)
- Pr:
-
Prandtl number
- Q :
-
heat flux (J m−2 s−1)
- r :
-
radial position (m)
- R :
-
gas constant (J kmol−1 K−1)
- Sc:
-
Schmidt number
- Sc*:
-
modified Schmidt number
- T :
-
temperature (K)
- v :
-
mean molecular speed (m s−1)
- V :
-
transport variable defined by Eq. (2)
- Y :
-
mole fraction
- Z :
-
Z-potential (J kmol−1)
- γ :
-
specific heat ratio,C p /C v
- λ :
-
thermal conductivity (J m−1 K−1 s−1)
- μ :
-
gas viscosity (kg m−1 s−1)
- ρ :
-
gas density (kg m−3)
- η :
-
transport coefficient defined by Eq. (2)
- θ :
-
surface accomodation coefficient
- θ h :
-
thermal accomodation coefficient
- θ m :
-
mass accomodation coefficient
- O:
-
in the gas phase in the immediate particle vicinity
- c :
-
using the continuum approach
- r :
-
reference state
- s :
-
at the particle surface
- ∞:
-
in the bulk of the plasma gas
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Joshi, S.V., Park, J.Y., Taylor, P.R. et al. Knudsen effect on plasma-particle mass transfer. I. Formulation and application to self-diffusion. Plasma Chem Plasma Process 6, 281–298 (1986). https://doi.org/10.1007/BF00575133
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DOI: https://doi.org/10.1007/BF00575133