Diffusion-reaction in mixed ionic-electronic solid oxide membranes with porous electrodes

Abstract

We solve the transport equation for diffusion-reaction in the limit of small pressure gradient in a mixed ionic-electronic conductor (MIEC) solid oxide membrane consisting of a porous anode and cathode separated by a thin dense layer. The maximum enhancement in the ion current in the porous membrane, compared to the non-porous membrane, is L dS(1−θ) τ s +θ where L d = D IE/ K is the length scale that determines the transition from diffusion limited to surface exchange limited transport in the non-porous membrane, K is the surface exchange coefficient, D IE the effective ionic diffusion coefficient, S the pore surface area per unit volume, φ the porosity and τ s the tortuosity of the solid phase. Maximum enhancement is achieved when the thickness of the membrane L⪢ L p, and when L g⪢ L p, where L p= L d(1−θ) Sτ s is the width of the active region of the membrane and L g is the length scale for variation of the chemical potential of the gas in the pores of the membrane.