Wagner’s equation

Other forms of vapor pressure equations, such as Cox equation (Osborn and Douslin 1974, Chao et al. 1983), Chebyshev polynomial (Ambrose 1981), Wagner s equation (Ambrose 1986), have also been widely used. Although... 

Equation (3.103) (which is also known as Wagner s equation) may be transformed into the formula for steady-state oxygen permeation under conditions when the surface exchange limitations are negligible ... 

The VLE relationship that applies under these conditions is Raoult s law. The vapor pressure of the two components P.) is related to temperature through Wagner s equation (Reid et al., 1987)... 

For an oxygen permeable membrane with oxide-ion and electronic conductivities of (T, (S/cm) and ffg (S/cm), respectively, its theoretical oxygen flux density, 7O2 (mol/ cm s), under a given oxygen partial pressure difference between / (O2) and PiOj)" can be calculated by Wagner s equation ... 

With respect to 7O2 obtained for the tape-cast membrane at 1000 °C, note that the value was enhanced only 50% compared to those for the bulk specimen, although the membrane thickness was reduced by a factor of about one-half. This implies that the oxygen-permeation flux was limited by surface exchange kinetics rather than ambi-polar diffusion process in ceramics. If this is the case, the Wagner s equation can be modified by including a characteristic thickness of dc as follows (Bouwmeester, Kruidhof, Burggraaf, 1994) ... 

Given that the electrical conductivity of CSO-15MFO is given by Eqn (17.13), the Wagner s equation can be modified ... 

Wagner s equation for the oxidation rate of a metal, forming the oxide MaOb, can in one form be written... 

The strains and at which the maxima occur in the shear stress and first normal stress difference are sometimes used as empirical measures of nonlinearity. Using the exponential damping function (Eq. 10.31) in Wagner s equation (Eq. 10.10) Osaki etal. [42] derived the following relationships ... 

Figure 10.14 Recoverable shear for steady simple shear for an LDPE. Also shown is the shear-rate dependent recoverable shear 2 aiy), the predictions of the rubberlike liquid model (straight line.fromEq. 10.5) and Wagner s equation (solid curve,from Eq. 10.10).FromLaun...

When the flux is governed by bulk oxygen diffusion, it is generally described by Wagner s equation (Chen et al, 1997),... 

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