Innovative Approaches on the Estimation of the Effective Permittivity of Fibrous Media

Estimating the effective permittivity of anisotropic fibrous media is critical for advancing electromagnetic applications, requiring detailed microstructural and orientation analyses. This study introduces innovative approaches for disclosing the orientation and microstructure of fibers, leading to mixing relations. It particularly focuses on two specific fiber configurations: 1. wave-curved fibers and 2. a collection of interconnected fibers. The first approach uses sinusoidal wave fibers, considering their curvature and direction. Conversely, the approach for the interconnected fibers operates on the principle of representing fibers as a collection of straight segments. Investigations on fibrous media for both approaches were performed using numerical calculations at the microwave frequency of 2.45 GHz. Each fibrous medium was treated as an effective medium by using fibers significantly smaller than the microwave wavelength. A thorough comparison was made between the proposed mixing relations, numerical data, and state-of-the-art mixing relations to assess their consistency and validity. The comparison of the proposed approaches with traditional models shows an improved accuracy of up to 70% and 8% for the real and imaginary components of the permittivity, respectively. Additionally, the root-mean-square errors were determined as 0.001 + <i>j</i>0.003 and 0.001 - <i>j</i>0.007 for the sinusoidal and interconnected straight fibers approaches, respectively. In addition, a woven alumina fabric was used to compare the experimental resonance frequency with that from simulations using the permittivity of the fabric estimated by the interconnected straight fibers approach. These findings advance the predictive accuracy of permittivity estimation in fibrous media, providing a robust foundation for engineering applications.