Effect of the microstructure closed pore content on the acoustic behavior of polyurethane foams

Abstract

The present paper proposes to investigate the links between the microstructure of polyurethane foams and their sound absorbing efficiency, and more specifically the effect of membranes closing the cells. This study is based on the complete characterization of 15 polyurethane foam with various cell sizes and reticulation rates (i.e., open pore content): (i) characterization of the microstructure properties (cell size C s , strut thickness t, reticulation rate R w …) from SEM pictures, (ii) characterization of nonacoustic parameters (porosity U, airflow resistivity r, tortuosity a 1 …) from direct and indirect methods. Existing analytical links between microstructure properties and nonacoustic parameters are first applied to fully reticulated materials. Then, they are improved empirically to account for the presence of the closed pore content. The proposed expressions associated to the Johnson-Champoux-Allard porous model allow a good estimation of the sound absorbing behavior of all polyurethane foams, fully reticulated or not. This paper also demonstrates the important effect of the presence of cell membranes: increase of the airflow resistivity, tortuosity, and the ratio between the thermal and viscous characteristic lengths while decreasing these two characteristic lengths. Thus, the sound absorption efficiency at low frequencies is improved but can be worsened in some higher frequency bands.

A semi-phenomenological model to predict the acoustic behavior of fully and partially reticulated polyurethane foams

“…12 and in this paper depict an anisotropy in the reticulation rate: i.e., a different reticulation rate is observed in the longitudinal direction (SEM pictures taken in the plane perpendicular to the wave propagation) and in the transverse direction (SEM pictures taken in the plane parallel to the wave propagation). The reticulation rate considered in this work is the one measured in the longitudinal direction since it characterizes the foam microstructure in the plane impinged by the acoustic wave.…”

“…It is a simplification of the 3-parameter model presented by the author in Ref. 12. It only requires measurements of the cell size C s and reticulation rate R w assuming that the geometric ratio between strut length l and strut thickness t is known.…”

“…[7][8][9][10][11] A detailed description of these approaches has been recently given by a) the authors. 12 A combination of empirical and analytical methods was also presented in Ref. 12 to link microstructure properties of highly porous isotropic PU foams with nonacoustic macroscopic parameters required in the JCA model.…”

“…12 A combination of empirical and analytical methods was also presented in Ref. 12 to link microstructure properties of highly porous isotropic PU foams with nonacoustic macroscopic parameters required in the JCA model. The presented semi-phenomenological (or semi-empirical) model was based on existing scaling laws, validated for fully reticulated PU foams, and improved using both geometrical and empirical approaches to account for the presence of membrane closing the pores.…”

“…The geometric ratio B ¼ l/t, which is related to foam porosity and density, is set constant and is determined from the 15 highly porous PU foams previously investigated in Ref. 12 and having an open porosity ranging from 96.8% and 99% and a frame density from 21.5 kg Á m À3 to 29.5 kg Á m…”