Interpretation of Defect and Gas-Phase Fluxes through Mixed-Conducting Ceramics Using Nernst–Planck–Poisson and Integral Formulations

This paper derives and demonstrates two models to represent defect transport through mixed-conducting ceramic membranes. The Nernst–Planck–Poisson (NPP) model is more general, but requires the computational solution of a boundary-value problem on a mesh network. The Integral method relies on more assumptions, but defect fluxes can be evaluated analytically based upon material properties and gas-phase composition at the membrane surfaces. Using examples based upon yttrium-doped barium zirconate, the two approaches are compared quantitatively. Under many circumstances the models deliver quantitatively similar results, but for situations where the membrane is exposed to large and/or multiple partial-pressure gradients, the predicted fluxes can deviate. The variations are the result of different physical assumptions and mathematical simplifications that are being used in the two models.