Airflow resistivity calculation of compressed fibrous materials through indirect determination of an equivalent fiber radius

Several numerical models exist in the literature to calculate the air flow resistivity of fibrous materials as a function of their density. A first category of models is based on empirical relationships obtained using regression fit of experimental data on specific types of fibers; a second category is based on the knowledge of the structure of the fibers, and in particular of their radius and their orientation; for real materials, the determination of these parameters can be very complex and difficult to represent with single values or with a statistical distribution. Finally, a third category of models is based on the experimental values measured on a material density and an analytical model that allow to calculate the value of airflow resistivity for different compression rates. In the present research experimental measurements of air flow resistivity have been carried out on different types of fibrous materials and at different compression rates, and various literature formulas have been tested to verify their applicability. In particular, an indirect approach is proposed for the determination of an equivalent hydraulic fiber radius starting from an experimental measurement on a material density, and the subsequent calculation for different degrees of compression of the flow resistivity with the use of well-established models which depend on such parameter. A discussion on the comparisons between experimental data and numerical models will illustrate the advantages and limitations of the proposed approach. Moreover, a critical analysis of the equivalent hydraulic radius compared with measured radii distribution using a standard SEM analysis will be presented and discussed