Bruggeman equation

The bulk conductivity of a fully dense cermet, oh, can be estimated from the effective conductivity, oe, and the porosity,, of a porous cermet anode using the Bruggeman equation [12]... 

Of the numerous equations proposed [84] to describe the conductivity of suspensions (k), one is cited here for illustration. The Bruggeman equation gives,... 

Meredith and Tobias49 noted that Bruggeman s equation overcorrects in the concentrated ranges and devised another approach called the Distribution Model by considering only two size fractions. As in the Bruggeman equation, the smaller size fraction is added first and then is considered as part of a continuous medium having its own bulk conductivity when the larger size fraction of bubbles is added ... 

In the aggregate topology the ESU are two spheres (Figure 7.1b). These two spheres are submerged into the effective medium, and their relative concentrations are/and 1 -/, where/is a volume fraction of the constituent A. Using the dipolar approximation of 5(0) for a sphere [12] leads to the Bruggeman equation ... 

Remarkably, the thermal conductivities of the composites filled with BP40 and BP80 are much higher than the prediction of Bruggeman equation. This demonstrates that the brush-like AlN particles enhance the thermal conductivity of the polymer matrix significantly. The intrinsic reason can be explored by Agari model [16], which considers the effect of dispersion state by introducing factors Cj and Cj ... 

The evolution of a gas during an electrolytic reaction produces a dispersion of bubbles in the electrolyte. Since the bubbles have virtually zero electrical conductivity the current flow path becomes restricted and ohmic voltage losses become greater than those for the electrolyte. The usual way to deal with bubbles is to assign to the electrolyte an effective conductivity which is typically correlated as a function of gas voidage There are a number of correlations of this type one of the most reliable is the so-called Bruggeman equation ... 

The Maxwell equation as written in Eq. (8.32) has been used by many researchers to describe the behavior of MMMs. It was however later suggested that the Maxwell equation is applicable for the low loading level of dispersed phase since it was assumed that the streamline around the dispersed articles were not affected. Instead the Bruggeman model was recommended in which the effect of the particles added to the dilute suspension is considered. The Bruggeman equation is given by... 

D is the multi-component diffusion coefficient of the material of gas diffusion layer given by the Bruggeman equation... 

Bruggeman equation for different exponents L. The curve for Z,=0.33 is the same as for the CRIM equation (see Section 8.7.4.3). (Turves are compared with experimental data for water-saturated sandstone. Pooley et al. (1978). 

Coutanceau-Monteil and Jacquin (1993) investigated the permittivity of sedimentary rock samples in the frequency range from 20 to 1000 MHz. A comparison of model equations and experimental results shows that the GRIM model fits the data for water-saturated quarry limestones, whereas the Hanai-Bruggeman equation fits the data for water-saturated Fontainebleau sandstones fairly well. 

Thus, the GRIM equation is identical with the generalized Lichtenecker and Rother (1931) equation with a = 0.5 and with the Hanai-Bruggeman equation for L = 033. 

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