Effective Relative Permittivity in Effective Media and Mixtures
Three methods are available to compute the averaged electrical conductivity of the mixture.
Volume Average, Permittivity
If the relative permittivity of the two materials is not so different from each other, the effective relative permittivity εr is calculated by simple volume average:
where εi is the relative permeability of the material i.
If the permittivity is defined by second-order tensors (such as for anisotropic materials), the volume average is applied element by element.
Volume Average, Reciprocal Permittivity
The second method is the volume average of the inverse of the permittivities:
If the permittivity is defined by a second-order tensor, the inverse of the tensor is used.
Power Law
A power law gives the following expression for the equivalent permittivity:
The effective permeability calculated by Volume Average, Permittivity is the upper bound, the effective permeability calculated by Volume Average, Reciprocal Permittivity is the lower bound, and the Power Law average gives a value somewhere between these two.