  The distribution of fiber diameters plays a crucial role in the transport and
sound absorbing properties of a three-dimensional random fibrous (3D-RF)
composites. Conventionally, volume-weighted averaging of fiber diameters has
been utilized as an appropriate microstructural descriptor to predict the
static viscous permeability of 3D-RF composites. However, the long wavelength
acoustical properties of a 3D-RF composites are also sensitive to the smallest
fibers, this is particularly true in the high-frequency regime. In our recent
research, we demonstrated that an inverse volume-weighted averaging of fiber
diameters can effectively serve as a complementary microstructural descriptor
to capture the high-frequency behavior of polydisperse fibrous media. In the
present work, we review the identification of two representative volume
elements (RVEs) which relies on the reconstruction of 3D-RF composites having
volume-weighted and inverse-volume weighted averaged fiber diameters,
respectively in the low-frequency and high frequency regimes. We examine the
implication of such a weighting procedure on the transport and sound absorbing
properties of polydisperse fibrous media, highlighting their potential
advantages. Furthermore, we discuss the challenges associated with this
research field. Finally, we provide a brief perspective of the future
directions and opportunities for advancing this area of study, aiming to
overcome challenges and extend the benefits of employing polydispersity as a
new lever for the optimization of 3D-RF composites in sound-absorbing
materials.
