The current generated from the electrochemical reaction in a porous rotating disk electrode PRDE is modeled analytically where the reactant transport is dominated by either advection or diffusion. When advection dominates, the concentration field of the reactant is found by assuming each fluid element behaves as a batch reactor and tracking them along their streamlines, utilizing the solution of the flow field in an infinite porous rotating disk by Joseph. The current is expressed in a simple algebraic form involving a dimensionless reaction time. The model accurately depicts the universal curve found from previous experiments and numerical simulations when the ratio of height to radius of the disk is less than about 0.25. The diffusion-dominated regime is modeled utilizing a boundary layer theory. The current is found as a function of the rotation rate, reaction rate, permeability, diffusion coefficients, kinematic viscosity, and geometry of the disk. The model coincides with the Levich equation at low rotation rates and shows excellent agreement with simulations and experiments regardless of the geometry of the disk. Combined, the two analytic models accurately describe the PRDE for the full range of its operation when the disk is sufficiently thin that the infinite disk assumption holds.
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