Extension of anisotropic effective medium theory to account for an arbitrary number of inclusion types

The purpose of this work is to extend, to multi-components, a previously reported theory for calculating the effective conductivity of a two component mixture. The previously reported theory involved preferentially oriented spheroidal inclusions contained in a continuous matrix, with inclusions oriented relative to a principle axis. This approach was based on Bruggeman's unsymmetrical theory, and is extended to account for an arbitrary number of different inclusion types. The development begins from two well-known starting points; the Maxwell approach and the Maxwell-Garnett approach for dilute mixtures. It is shown that despite these two different starting points, the final Bruggeman type equation is the same. As a means of validating the developed expression, comparisons are made to several existing effective medium theories. It is shown that these existing theories coincide with the developed equations for the appropriate parameter set. Finally, a few example mixtures are considered to demonstrate the effect of multiple inclusions on the calculated effective property. Inclusion types of different conductivities, shapes, and orientations are considered and each of the aforementioned properties is shown to have a potentially significant impact on the calculated mixture property. (C) 2015 AIP Publishing LLC.