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