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Journal of Materials Science

, Volume 29, Issue 23, pp 6104–6114 | Cite as

Oxygen mass transfer at liquid-metal-vapour interfaces under a low total pressure

  • P. Castello
  • E. Ricci
  • A. Passerone
  • P. Costa
Article

Abstract

The problem of oxygen exchange at the interface between a gas and a liquid metal is treated for systems under a “vacuum” (Knudsen regime, pressures lower than 1 Pa), where, due to the large mean free path of gas molecules in a vacuum, transport processes in the gas phase have no influence on the total interphase mass exchange, which is controlled by interface phenomena and by oxygen partition equilibrium inside the liquid. Owing to the double contribution of molecular O2 and volatile oxides to the oxygen flux from the surface, non-equilibrium steady-state conditions can be established, in which no variations in the composition of the two phases occur with time, as the result of opposite oxygen exchanges. The total oxygen and metal evaporation rates are evaluated as a function of the overall thermodynamic driving forces, and an account of the transport kinetics is given by using appropriate coefficients. A steady-state saturation degree sr, is defined which relates the oxygen activity in the liquid metal to the O2 pressure imposed and to the vapour pressures of volatile oxides. When metals able to form volatile oxides are considered, pressures of molecular O2 higher than those defined under equilibrium conditions have to be imposed in the experimental set-up in order to obtain a certain saturation degree, as a consequence of the condensation of the oxide vapours on the reactor walls. Effective oxidation parameters are determined, which define the conditions leading the liquid to a definite steady-state composition under a “vacuum” when it is out of equilibrium. The effective value of the oxygen pressure which corresponds to the complete oxygen saturation of the metal, \(P_{O_{2,} s}^E \), is evaluated at different temperatures for the systems Si-O and Al-O. The results are represented as curves of \(P_{O_{2,} s}^E \) against T, which separate different oxidation regimes; these results agree well with the experimental data found in the literature.

Keywords

Oxygen Exchange Oxygen Flux Saturation Degree Oxygen Mass Transfer Volatile Oxide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

aη

activity of the component η in the liquid phase

kη

partial-transport coefficients for the mass transfer of the component η (mol s g−1 cm−1)

Kη

global-transport coefficients for the mass transfer of the component η (mol s g−1 cm−1)

Mη

molecular weight of the species η (g mol−1)

NMtot

global metal flux between the gas and the condensed phase (mol cm−2 s−1)

\(N_{O_2 }^{tot} \)

global oxygen flux between the gas and the condensed phase (mol cm−2 s−1)

Pj

partial pressure of the jth oxide (Pa)

PM

vapour pressure of the pure metal (Pa)

\(P_{O_2 } \)

partial pressure of molecular O2 (Pa)

Ptot

total pressure (Pa)

PME

effective metal-vapour pressure (Pa)

\(P_{O_2 }^E \)

effective oxidation pressure (Pa)

RE

effective evaporation ratio

s

actual value of the bulk-saturation degree

sr

value of the bulk-saturation degree in steady-state (regime) conditions

T

temperature in the system, far from the container wall (K)

Tw

temperature of the container wall (K)

xη

molar fraction of the component η in the liquid phase

αη

condensation coefficient of the species η (cm−3/2)

Subscripts

l

a quantity evaluated for a liquid below the saturation point

liq

quantity in the bulk liquid

s

a quantity evaluated in conditions where the liquid metal is saturated with oxygen

I

a quantity in the interfacial liquid layer

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Copyright information

© Chapman & Hall 1994

Authors and Affiliations

  • P. Castello
    • 1
  • E. Ricci
    • 1
  • A. Passerone
    • 1
  • P. Costa
    • 2
  1. 1.Istituto di Chimica Fisica Applicata del Materiali del C.N.R.GenovaItaly
  2. 2.Istituto di Scienza e Tecnologie ChimicheFacoltà di Ingegneria dell'Università di GenovaGenovaItaly

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