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David C. Silverman |
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The equations shown in the table of correlations in the section Mass Transfer Correlations were derived from mass transfer data under conditions in which the electrode itself was not attacked by the environment. Any variation in surface roughness should arise only from the type of preconditioning or sanding of the electrode. Some of the variation in the equations could have been caused by varying degrees of initial surface roughness. But, for all practical purposes, the electrodes could be considered hydraulically smooth. Corrosion studies by their very nature involve surfaces that have interacted, often detrimentally, with the environment. A corrosion study using the rotating cylinder electrode should be no different. Oxygen reduction could drive anodic dissolution of the metal non-uniformly across the surface. Limited solubility of the metal ion released could result in deposition of a non-uniform salt film. Deposits could develop on the electrode surface resulting in localized metal loss. In all cases, metal dissolution is involved and the surface would become non-uniformly roughened. The effect of surface roughness on mass transfer is not well-defined quantitatively. When the roughness is great enough to interfere with the hydrodynamic boundary layer, such roughness could alter the Sherwood number vs. Reynolds number relationship from those shown. The consequence is to make the quantitative correlation of the corrosion rate versus rotation rate and the subsequent identification of a mass transfer influenced corrosion mechanism more difficult to establish. Relationships between the Sherwood number and the Reynolds number are not as well known for roughened surfaces. In fact, the relationships seem to depend not only on the amount of roughness but also on the geometry of the roughness. The following brief discussion provides a summary of variation in dependencies. In several early studies (Theodorsen, T. and Regier, A., "Experiments on Drag of Revolving Disks, Cylinders, and Streamline Rods at High Speeds", Nat. Advisory Comm. Aeronaut., p. 367, Report No. 793, U.S. Government Printing Office, Washington, D.C., 1945 and Makrides, A. C. and Hackerman, N., J. Electrochem. Soc. 105(3), 156 (1958)), the friction factor of rough electrodes was found to vary with the relative roughness in terms of the height of the irregularities by an equation of the form:  (5)where "A" and "B" are constants. Note that though the friction factor may become independent of Reynolds number, equation (4) indicates that the Sherwood number (mass transfer coefficient) would still increase with Reynolds number and would be greater than that for a smooth cylinder operated under the same conditions. The important point is that surface roughness would affect the Sherwood number vs. Reynolds number relationship both through equations (4) and (5) and by the fact that as the surface roughness increases, the projected surface area would deviate by a greater amount from the actual surface area normally used for the calculation. Later, enhanced mass transfer resulting from roughening of the electrode surface was examined for several types of roughness (Gabe, D. R. and Walsh, F. C., J. Appl. Electrochem. 14, 555 (1984), Gabe, D. R. and Walsh, F. C., J. Appl. Electrochem. 14, 565 (1984), Gabe, D. R. and Makanjuola, P. A., J. Appl. Electrochem., 17, 370 (1987)). The following table shows how the Sherwood number vs. Reynolds number relationship can vary as a function of type of roughness. The 0.356 exponent has been assumed to be unchanged.
What is most telling is how the mass transfer coefficient can be enhanced by surface roughness. This figure )
shows the effect. Extreme surface roughness can enhance the
mass transfer coefficient by several orders of magnitude.
The above discussion assumes mass transfer control is between the interface and the solution with no other diffusion processes occurring. But, the build-up of scale on the electrode surface can creates an additional diffusion resistance. If corrosion occurs at the scale interface with the metal surface, the species driving the corrosion process must migrate through the scale and then enter the environment. Corrosion of steel in water in the near neutral range is a good example of a process that can result in such a phenomenon. In this process, the corrosion rate is driven by the mass transport of oxygen to the iron surface. But while the corrosion layer roughness possibly increases oxygen mass transfer to the fluid-solid interface the corrosion layer thickness can impede oxygen mass transport through itself to the iron under the scale layer where it would react with iron. This latter diffusion process can become slower as this layer becomes thicker. The resulting mass transfer coefficient would depend on time of exposure sometimes resulting in a decrease in mass transfer coefficient and Sherwood number over a fairly long time period (Mahato, B. K., Cha, C. Y., Shemilt, L. W., Corros. Sci., 20, 421 (1980)). This complication implies that using the rotating cylinder electrode to model another geometry requires that for some corrosion processes, both total exposure time and the time to make an individual measurement may be important variables. Measurements may have to be taken at constant rotation rate over periods of several days to even a week to ensure that steady state is reached or the trend to steady state is understood. This discussion implies that the relationship among friction factor, mass transfer coefficient, surface roughness, and hydrodynamics is not simple. Care must be taken when assuming that any of the equations mentioned in the section Mass Transfer Correlations apply to a corroding cylinder. When corrosion occurs and the cylinder surface becomes roughened, measurements should be made to ensure that the proper Sherwood number vs. Reynolds number relationship is used. CYLEXPERT does not consider the effect of surface roughness in its estimate but does ask if surface roughness has been observed. Possibly, a plot of the limiting current vs. logarithm of the Reynolds number would suffice to show the exponent on the Reynolds numbers. In a system suffering corrosion or developing deposits, deviation from the Sherwood number vs. Reynolds number relationship for smooth cylinders should not be attributed only to normal experimental error especially if they fall far outside of the equation band discussed above. Additional information can be found in D. C. Silverman, "The Rotating Cylinder Electrode for Examining Velocity-Sensitive Corrosion - A Review", Corrosion, Vol.60, No.11, p. 1003, 2004. 1  (1560k)
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David C. Silverman, Ph.D. - Primary Consultant |
