Effects of radial diffusion on the efficiency of porous flow-through electrodes

A model is proposed to evaluate the effect of radial diffusion on the efficiency of porous flow-through electrodes. The model includes the electrode parameters of porosity (), thickness (L) and equivalent pore radius (R), the superficial flow speed of the electrolyte (v) and the molecular diffusivity of the reactant in the electrolyte (D). The effects of these variables are incorporated in a dimensionless group(L) =vR ²/2DL which controls the conversion efficiency of the electrode. Satisfactory agreement was found between the model predictions and the experimental results of several authors on different electrode-electrolyte systems over a wide range of conditions. Implications of this work for design purposes are outlined. The effect of radial diffusion limitations on the voltage efficiency of the electrode is also discussed. It is shown that radial diffusion effects predominate under conditions of large values of pore radius, polarization and exchange current density, and small values of diffusivity.List of symbols b RT/F(V) - c ⁰ Feed reactant concentration, (mol cm^–3) - c _s Reactant concentration at the electrode surface - c(x) Average or mixing-cup concentration of reactant atx - c _m(x) Reactant concentration at the centre of the pore - c _w(x) Reactant concentrations at the wall of the pore - d Equivalent pore diameter (cm), Equation 2 - D Diffusion coefficient of reactant (cm² s^–1) - f Conversion efficiency of the electrode - i _L Maximum obtainable limiting current, (A cm^–2) Equation 1 - i ₀ Exchange current density based on bulk concentration,c ⁰ - i ₀ Normalized exchange current densityi ₀ SL/i_L - L Electrode thickness (cm) - n Number of electrons - q Tortuosity factor - R Equivalent pore radius (cm) - (Re) Reynolds number (Re) =/sv - S Specific surface area of the porous medium (cm^–1) - (Sh) Sherwood numberK _md/Dd - superficial flow speed (cm s^–1) - x Distance, see Fig. 3. - Transfer coefficient - (x) Polarization at distancex - Porosity - (x) Dimensionless group, see Equation 6 - v Kinematic viscosity (cm² s^–1)