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

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 s _r, 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.