This paper is devoted to the determination of the acoustic characteristics of a porous medium saturated by air[ The analysis of sound propagation in such a medium is performed using an homogenization technique[ This theory is suitable since acoustic wavelengths are much greater than the usual pore size[ The macroscopic descriptions involve the e}ects of air viscosity\ inertial forces and heat transfer[ The _rst part of the paper deals with single porosity materials[ Two cases are investigated ] "i# a medium with large pores in which thermal exchanges are negligible ^ "ii# a medium with smaller pores for which thermal exchanges must be accounted for[ The second part is concerned with dual porosity media\ i[e[ when the grains themselves are also porous[ Neglecting heat transfer _rst yields a simpli_ed macroscopic description[ This simply dual porosity model is then improved by considering thermal e}ects[ These results show that new porous materials could be evolved by introducing a microporosity structure that would give enhanced absorption properties over a wide range of frequencies[ Þ 0887 Elsevier Science Ltd[ All rights reserved[
This work is concerned with deriving a macroscopic ®ltration law for describing transient linear viscoelastic ¯uid ¯ow in porous media. This is performed using a homogenisation technique, i.e. by upscaling the heterogeneity scale description. The macroscopic ®ltration law is expressed in Fourier space as a generalised Darcy's law with a dynamic permeability tensor. This model is valid at low Reynolds and Deborah numbers. Analytical results are determined in the particular case of the ¯ow of an Oldroyd ¯uid in a bundle of capillary tubes and are compared to those obtained by a corresponding phenomenological model.
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