Uhlig model

In addition, the phenomenon of potential attenuation has been theoretically included as a cmde approximation as predicted by the Charge Disk and Uhlig models. Both models exhibit similar potential profiles. RnaUy, sets of formulae used in cathodic protection are given as mathematical recipes for practical purposes in the field of corrosion prevention. 

In earlier attempts of the rationalization of gas solubilities in molten salts Blander et al. [292] used the Uhlig model, according to which the solubility depends on the work required for the production of the cavity in the molten salt in which the gas molecule is to reside. This, in turn, depends on the surface tension of the salt melt and the van der Waals surface area of the gas molecules. This approach, however, under-estimates the actual solubilities [289, 290]. 

On the assumption that = 2, the theoretical values of the ion solvation energy were shown to agree well with the experimental values for univalent cations and anions in various solvents (e.g., 1,1- and 1,2-dichloroethane, tetrahydrofuran, 1,2-dimethoxyethane, ammonia, acetone, acetonitrile, nitromethane, 1-propanol, ethanol, methanol, and water). Abraham et al. [16,17] proposed an extended model in which the local solvent layer was further divided into two layers of different dielectric constants. The nonlocal electrostatic theory [9,11,12] was also presented, in which the permittivity of a medium was assumed to change continuously with the electric field around an ion. Combined with the above-mentioned Uhlig formula, it was successfully employed to elucidate the ion transfer energy at the nitrobenzene-water and 1,2-dichloroethane-water interfaces. 

Here we make use of Uhlig s model, writing eq. [5.5.14] as the energy required to create a molecular-sized eavity in the solvent. 

Lautenschliiger I, Dombrowsky H, Frerichs I, Kuchenbecker S-C, Bade S, Schultz H, Zabel P, Scholz J, Weiler N, Uhlig S (2010) A model of the isolated perfused rat small intestine. Am J Physiol Gastrointest Liver Physiol 298 G304-G313... 

In pursuing the mathematical details peculiar to Uhlig s model, when the current is defined as Jx = Ai, while the cross sectional area of the pipe is A = 2Trrx, the current gradient in the x-direction is... 

Now, the overpotentials are approximated sis t = j. - E, rfo = (f>o Eeorr o due to Eeorr 0 sincc the pipeline is designed against corrosion. Thus, these assumptions lead to the cathodic protection attenuation equation known as Uhlig s equation for an infinite pipeline which is compared with the disk model equation in mathematical and graphical form (Figure 8.13)... 

Figure 4.75 Schematic of simple model for corrosion enhanced crack nucleation at emerging slip step. (From Duquette, D.J. and Uhlig, H.H. (1969). Trans. ASM, 62,839. Reproduced by kind permission of ASM, Metals Park, Ohio, USA)...

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