Porous Rotating Disk Electrode (PRDE)
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Bomi Nam |
The rotating disk electrode (RDE) is a highly valuable tool in analytical chemistry for measuring electrochemical reactions and mass-transfer rates. Its strength lies in the firm understanding of the flow field through von Karman's solution and the analytic Levich and Koutetskii-Levich equations [1] that relate the current to the rotation rate as a function of various chemical and physical parameters. The porous rotating disk electrode (PRDE) has great potential due to the characteristics of the additional porous material, such as increased sensitivity from much higher surface area. However it is not yet well understood.
Figure 1. Schematic of the rotating disk electrode (RDE) and the porous rotating disk electrode (PRDE). Electrode is mounted on non-conducting material such as Teflon and steadily rotated in fluid containing the reactant at some rate Ω. The PRDE has a conducting porous disk attached to the flat electrode surface.
Experiments [2] indicate that the PRDE exhibits a richer behavior compared to the RDE. Understanding of such a system will allow the PRDE itself to become a useful analytical tool and it will have broad applications to analytical chemistry, industrial electrochemical reactors, environmental applications as in removal of contaminants of low concentrations, fuel cells and batteries. The focus of this research is the thorough understanding of the interactions of the flow, reaction, and transport in the porous media and the development of simplified models and analytical formulas.
The current from the classic rotating disk electrode increases linearly with the square root of the rotation rate, according to the Levich equation. In comparison, experimental measurements of the current for a PRDE exhibit much more complex behavior, as shown in Figure 2. The current undergoes two transitions resulting in a sigmoidal curve that depends on the porosity and geometry of the disk and the rotation rate.
Figure 2. Current density versus the square root of the rotation rate for porous disks of radius 2 mm and various heights mounted on a flat electrode. Inset shows the carbon disks used with porosity of 78%. Orange line shows the response of an RDE.
To understand the behavior of the porous rotating disk electrode, a commercial partial differential equation solver (COMSOL Multiphysics) was employed to model the system. The hydrodynamics of the system is modeled by solving the Navier-Stokes equation in the ambient fluid and a modified form of Darcy's law that includes force terms induced by the rotation in the porous media. The species transport problem is modeled by solving the convection-diffusion equation with a reaction term utilizing the hydrodynamics solution. System is axisymmetric and the cross section of the porous disk is shown in Figure 3 for three different rotation rates. The total current produced by the electrochemical reaction in the porous disk can be directly calculated from the solution to the species transport problem.
Figure 3. Typical streamlines and concentration field for the three regimes in the porous disk and its vicinity. From top to bottom: below the lower critical rotation rate, transition region, and above the upper critical rotation rate.
Simulation results [3] indicate that the physics of the PRDE can be characterized by a single dimensionless parameter Tr , essentially a ratio of the reaction time to the residence time plus a correction for the geometry of the disk.
Based on understandings from the simulations, analytic models are developed to predict the current depending on the dominant mode of reactant transport, which for the PRDE are either advective or diffusive transport. Combined, the two models accurately describe the PRDE for its full range of operation [4].
When advection dominates, the concentration field of the reactant is found by assuming each fluid element behaves as a batch reactor and tracking it along its streamline. The solution of the flow field in an infinite porous rotating disk by Joseph [5] is utilized. The normalized current is expressed in a simple algebraic form involving a dimensionless reaction time. As shown in Figure 4, the model accurately depicts the universal curve when the height to radius ratio of the disk is less than about 0.25.
Figure 4. Normalized current versus the dimensionless reaction time for results from ten sets of simulations in color and seven sets of experiments in black compared to the analytic model. Dotted lines are the two critical reaction times. Below the first critical point diffusion effects cause scatter in the data.
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 of the ambient fluid and porous media, kinematic viscosity, and geometry of the disk. The model coincides with Levich equation at low rotation rates and shows excellent agreement with simulations and experiments regardless of the geometry of the disk.
Currently additional experiments using a different reaction system are carried out to verify that indeed the behavior of the PRDE is universal as suggested by the simulations and analytic models.
References
- Y. A. Koutetskii and V. G. Levich, "An application of a rotating disc electrode to the study of kinetics and catalytic processes in electrochemistry." Dokl. Akad. Nauk SSSR, 117, 441 (1957).
- R. T. Bonnecaze, N. Mano, B. Nam, and A. Heller, "On the behavior of the porous rotating disk electrode." J. Electrochem. Soc., 154, F44 (2007).
- B. Nam and R. T. Bonnecaze, "Flow and reaction in a porous rotating disc electrode." to be published (2008).
- B. Nam and R. T. Bonnecaze, "Analytic models of the infinite porous rotating disk electrode." J. Electrochem. Soc., 154, F191 (2007).
- D. D. Joseph, Q. "Note on steady flow induced by rotation of a naturally permeable disk." J. Mech. Appl. Math., 18, 325 (1965).