A M is s in g M a s s M e t h o d t o M e a s u r e t h e O p e n P o r o s it y o f P o r o u s S o l id s (2004)

1. i n t r o d u c t i o n An air-saturated open cell porous material is a solid containing interconnected air cavities. In acoustics, one important physical property of such a material is indubitably its open porosity (0). The open porosity is defined as the fraction of the interconnected air volume to the total volume of a porous aggregate. Sound propagation models for porous solids use the open porosity to relate the effective properties of the saturating air to the effective properties of the porous aggregate [1]. Consequently, from the measurements of the effective properties on a porous aggregate [2], this scaling is required to go back to the effective properties of the interstitial air, hence the importance of the open porosity. In this paper, a non limitative method is proposed to evaluate the open porosity of air-saturated porous materials. The proposed method deduces the open porosity through the experimental determination of the volume of the solid phase of a porous aggregate. The method is based on the measurement of the apparent (in-air) and true (in-vacuum) masses of a porous aggregate, where an in-air “missing mass” is found and related to the volume of the solid phase through the Archimedes’ principle. The originality of the method lies in its predictable accuracy, the simplicity of the experimentation, and in the fact that no isothermal process needs to be assumed. 2. THEORY Let denote by Vs and Vf the volumes of the solid phase and interconnected air cavities, respectively, and by ps and pf the mass densities of the solid phase constituent and saturating air in a porous aggregate, respectively. While the mass density of the air may be determined from the ideal gas law, the mass density of the solid phase constituent as well as the solid phase and air-cavities volumes are usually unknown and not directly measurable. However, the total or bulk volume V, of a porous aggregate and its vacuum mass Mi are directly measurable with precision. The mass of solid per unit volume of porous aggregate is given by p i =(i-0)ps, where 0 is the open porosity defined as 0 = 1 -V s/ V t. Since the mass density of the solid phase constituent is usually unknown, the mass density pi can be deduced from the measurable parameters following: p i = Mi /V, , where Mi is measured with a balance under vacuum condition. Usually, a good estimate of Mi may be obtained using a balance in air. Nevertheless, in cases where a high precision is required, the measurement in air is not appropriate since the measured apparent mass Mi ’ underestimates the true value of Mi. This underestimate is due to the Archimedes’ principle [3] on the buoyancy. In air, the buoyancy is very small yet not negligible for the purpose of this work. Consequently, the difference Mi - Mi ’ between the in­ vacuum and in-air masses gives the “missing mass” error relative to any measurements performed on a balance in air. Following the Archimedes’s principle, the “missing mass” of the porous aggregate measured in air is M = pfVs , since the volume of air displaced by the solid phase of the aggregate is equal to Vs. Following this observation, one can deduce a simple method for the measurement of the open porosity 0 of the porous aggregate. This yields