Frequency dependence of effective conductivity induced by spatial variance in isotropic heterogeneous media

It is an essential and challenging task to determine effective conductivity of heterogeneous media. Different from homogeneous media, heterogeneity causes the effective conductivity to behave as a function of frequency under an alternating current (AC). There have been few reports to quantify this function despite the wide applications of AC on heterogeneous media. This Letter derives the analytical form of the effective conductivity as a function of frequency caused by heterogeneity, where the local properties of the media are isotropic and independent of frequency. We use simulation and experiment data to validate our formulation and find that our form shows better agreement with the data than other models. This research provides a practical guidance on the interpretation and application of impedance and conductivity data.

Automated summary

Determining the effective conductivity of heterogeneous media is essential and challenging. This research derives the analytical form of the effective conductivity as a function of frequency caused by heterogeneity, and validates it using simulation and experiment data. The results show that this model has better agreement with the data than other models, and provides practical guidance on the interpretation and application of impedance and conductivity data.