Tobias equation

For the estimation of ( ), empirical relationships can be used. These include the Tobias equation [38], in which the conductivity ratio is related to the porosity by the relationship... 

TABLE 14.4 Olhmer— Tobias equation constants for (water + propionic acid + 1- octanol). 

Maxwell equation 37 Meredith-Tobias equation 38 Metal particles 12, 14, 16,18, 27 Metal-insulator threshold 102 Monte-Carlo simulation 107 Mossbauer measurement 118 Mott approach 107... 

Measurements of CuS04 molecular diffusivity by Cole and Gordon (C12a), referred to above, were carried out in diaphragm cells, mostly at 18°C. Their results were correlated by Fenech and Tobias (F3) using the Stokes-Einstein equation... 

Barkey, Tobias and Muller formulated the stability analysis for deposition from well-supported solution in the Tafel regime at constant current [48], They used dilute-solution theory to solve the transport equations in a Nernst diffusion layer of thickness S. The concentration and electrostatic potential are given in this approximation... 

Porous-Electrode Models. The porous-electrode models are based on the single-pore models above, except that, instead of a single pore, the exact geometric details are not considered. Euler and Nonnenmacher and Newman and Tobias were some of the first to describe porous-electrode theory. Newman and Tiedemann review porous-electrode theory for battery applications, wherein they had only solid and solution phases. The equations for when a gas phase also exists have been reviewed by Bockris and Srinivasan and DeVidts and White,and porous-electrode theory is also discussed by New-man in more detail. 

The tieline data of the system of Example 14.1 are plotted according to the groups of variables in the equations of Ishida, Hand, and Othmer and Tobias with these results ... 

W. G. Hoover, Molecular Dynamics, Springer-Verlag, New York, 1986 W. G. Hoover, Constant-Pressure Equations of Motion, Phys. Rev. A 34 (1986y) 2499-2500 D. J. Evans and G. P. Morriss, The Isothermal/Isobaric Molecular Dynamics Ensemble, Phys. Lett. 98A (1983) 433-436 G. J. Martyna, D. J. Tobias and M. L. Klein, Constant Pressure Molecular Dynamics Algorithms, J. Chem. Phys. 101 (1994) 4177-4189. 

A number of excellent compilations of dimensionless group correlations are available in the literature (see Levich [12], Selman and Tobias [14], and Poulson [17]). These compilations are not reproduced here, but the correlations for a number of common hydrodynamic geometries are listed in Table 1. Because these equations are empirical in nature, they are valid only for the employed ranges in Re and Sc. 

Maxwell s equation does not agree with the experimental results of De La Rue and Tobias (60), except for e - 1. 

Equation 60 is in agreement with the formation factor experiments of De La Rue and Tobias (60), Johnson et al. (62), and Wong et al. (63). The tortuosity is also discussed by Epstein (65) and Puncochar and Drahos (66). We conclude that for random packs and suspensions of e > 0.2, equation 60) should be used as the tortuosity of the system. 

Figure 8. Comparison of equations predicting the reduced conductivity dispersions of spheres of unequal sizes with data. Bruggemann Eq. (10), Meredith/Tobias Distribution Model Eq. (11). Also included are Maxwell Eq. (6) and Prager Eq. (8) for comparison.

Predictions of the Heterogeneous Conductivity of Simple Cubic Arrays, by Rayleigh s Corrected Equation (12), Meredith/Tobias/ and the Equation of Sangani and Acrivos (13)c... 

T. B. FOWLER, M. L. TOBIAS, and D. R. VONDT, EXTERMINATOR-II A FORTRAN IV Code for Solving Multigroup Neutron Diffusion Equation in Two Dimensions, ORNL-4078, Oak Ridge National Lab. (April 1967). 

Electrode polarization was considered by Tobias in terms of adopting a linear approximation to the Tafel equation. The influence of polarization, which is in essence a bubble-independent resistance, acts in series with the ohmic resistance, improving the uniformity of current distribution. 

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