The debye rigorous equivalent of the Maxwell-Garnett mixing rule for effective modeling of carbon suspensions under MW irradiation

This paper responds to the recent needs of the industrial microwave power community for homogenized models of bi-phased mixtures, compatible with the FDTD electromagnetic simulation method. We propose an explicit transformation of the Maxwell-Garnett mixing rule to the Debye relaxation formula. For that purpose, both models are rearranged into rational functions, and the conditions for their equivalence are derived. These explicitly provide the Debye parameters as a function of the polynomial coefficients of the Maxwell-Garnett formula. Computational examples show the accuracy of our approach, its advantages over alternative Debye-approximation methods based on curve-fitting algorithms, and its contribution to the developments of the FDTD modeling for microwave power applications.