On the behavior of the porous rotating disk electrode
The flow, reactions and current in a porous rotating disk electrode (PRDE) is studied experimentally and theoretically. A PRDE is an electrochemically active porous disk mounted on a classic rotating disk electrode (RDE). For the oxidation of iodide, the measured current from a PRDE as a function of rotation rate shows much richer behavior than the flat RDE, including a sigmoidal dependence on the rotation rate that specifically depends on the geometry of the disk, its permeability, porosity and the fluid and reactant transport properties. It is found that when the complex behavior of the current is explained in terms of the ratio of the effective electrochemical reaction time to the residence time of the fluid in the porous disk all the data can be plotted onto a universal curve at high rotation rates. With this knowledge the PRDE is modeled analytically where the reactant transport is dominated by either advection or diffusion. When advection is dominant the current can be expressed in a simple algebraic form involving the dimensionless reaction time. 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. Combined with finite effects analysis, the two analytic models accurately describe the PRDE for the full range of its operation regardless of the geometry of the disk. Also, the dominant mass transfer mode transition point is identified. Additional experiments with ferrocenemethanol are carried out using PRDEs constructed by mounting various sized carbon fiber disks onto glassy carbon RDEs to complement previous experiments using iodide. The results validate the theories for the operation of the PRDE in the regimes of advection or diffusion dominated transport. A possible application of the PRDE system for measuring rock acidization and permeability is explored by developing analytic and numerical models for a nonconductive porous disk. This system exhibits regimes limited by different processes: diffusion, advection, and reaction. It is found that a one-dimensional analytic model incorporating the finite thickness of the porous disk and the surface reaction rate suffices to describe the system.