Hanai-Bruggeman formula

The generalized Hanai-Bruggeman formula (11.7) for ellipsoidic inclusions and applied on a porous rock is ... 

There are a number of formulas for the determination of the effechve dielectric constant Maxwell Garneh (MG) formula, Bruggeman (BG) equation, Hanai-Bruggeman (HBG) formulas, empirical Lichtenecker mixture equahons, and so on. 

Boned and Pcyrclassc [95] extended the asymmetric integration technique used by Bruggeman and Hanai to randomly orientated ellipsoidal mixture and obtained the following formula ... 

Several authors have derived formula for dielectric permittivity of a two component mixture from differential analysis. Most of them considered the excess polarization due to a small sphere introduced to the effective medium where the volume of the sphere can become infinitesimal enabling establishment of a differential equation for the effective permittivity of the mixture [30], The particular solutions obtained for a 3D case by three of the most notable authors contain a fractional power of a third. These are Looyenga formula [31], Bruggeman [29] and Hanai formula [32] and formula by Sen et al. [33] given in equations 9.25, 9.26 and 9.27, respectively. 

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