A calculation of the flow resistivity in intermediate flow regime

Abstract

Many of the acoustic properties of fibrous materials can be modeled and predicted with the aid of appropriate empirical formulas. Among the input parameters that are required by such types of macroscopic models, the flow resistivity is a very well-established quantity in the literature, as usually this parameter is measured in steady Poiseuille flow conditions, i.e., at comparatively low flow speeds. One major concern with respect to such a parameter is the question of its possible frequency dependence. From a theoretical point of view, we have examined to which extent the capilar pore approximation can be utilized in intermediate flow regimes. The tendency towards lower values of flow resistivity for increasing acoustic Reynolds number also appears in all samples studied. And only the greater density samples, for the tested frequencies, were found in the flow regime of Poiseuille. However, if we want to obtain the value of the flow resistivity, for any sample, the employed experimental procedure makes it possible by a relationship between the experimental values and those of the Biot function. The value of the flow resistivity in different dynamical flow regimes to that of Poiseuille can be obtained.