Bruggeman relation

Dielectric saturation produces "irrotational bounding of the solvent molecules surroimding the ion and hence yields solvation numbers. Pottel et al.25,58 use the empirical Bruggeman relation for the estimation of the "effective" volume fraction of the solvent. Comparision with its "analytical" value yields solvation numbeiTS Zp. Lestrade et al.30 39 use the Kirkwood Frohlich equation with the Kirkwood parameter assumed independent of electrolyte concentration, to calculate solvation numbers Zl Ly means of the number of molecules per unit volume required to explain the limiting slope of the permittivity depression. A siu vey of solvation numbers Zp and obtained from these methods and their critical discussion is given in Ref. 14. 

The second term on the right side accounts for concentration overpotential. In porous media, the conductivity is corrected by the Bruggeman relation, k= where Koo is the conductivity of the bulk electrolyte. 

The effective medium theory consists in considering the real medium, which is quite complex, as a fictitious model medium (the effective medium) of identical properties. Bruggeman [29] had proposed a relation linking the dielectric permittivity of the medium to the volumetric proportions of each component of the medium, including the air through the porosity of the powder mixture. This formula has been rearranged under a symmetrical form by Landauer (see Eq. (8), where e, is the permittivity of powder / at a dense state, em is the permittivity of the mixture and Pi the volumetric proportion of powder / ) and cited by Guillot [30] as one of the most powerful model. 

A comparison of these expressions is given in Table I. This table shows the increase in the mixture resistance due to the presence of nonconducting particles or droplets, - Rj, divided by the fluid resistance as a function of the dispersed-phase concentration. R and Rj are the mixture and fluid resistances, respectively. Maxwell s (68) and Bruggeman s (74) relations give... 

Calibration. Various methods were used to calibrate the probe. These studies were conducted to find the relation between voltage (e) and solids concentration and to compare the experimental measurements with the predictions of the Maxwell and Bruggeman relationships. It was also necessary to establish an efficient probe calibration procedure. 

A Bruggeman-type relation has been reported by Yeo and Yeager [52] to approximate the dependence of ionic conductivity on water content in a Nafion membrane ... 

The bubbles in the inter-electrode gap (bubble diffusion region and bulk region) increase the inter-electrode resistance, as they affect the electrical conductivity of the electrolyte. The parameter describing this increase is the gas void fraction e, defined as the fraction between the volume of gas and the total volume of liquid and gas. Several relations are used in the electrochemical literature to quantify this effect. The most widely used are the relations from Bruggeman [16] ... 

To account for effects given by porous structures an effective factorisation for a macroscopic view is necessary. Thus, transport parameters like diffusion coefficients and conductivities are scaled with the volume fraction of the related phase. Based on an empirical expression by Bruggeman [15] a sufficient approximation can be achieved by assuming... 

Ritter, F. J., Bruggeman-Rotgans, I. E. M., Verweil, P. E. J., Persoons, C. J. and Tal-man, E. (1977) Trail pheromones of the Pharaoh s ant, Monomorium pharaonis isolation and identification of faranal, a terpenoid related to juvenile hormone II. Tetrahedron Letters, 2617-18. 

The effective solid phase conductivity, is related to the respective active material volume fractions, eg, in the anode and cathode electrodes, which is expressed in terms of Bruggeman correction for tortuosity and often with a value... 

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