Dynamic behaviour of porous media saturated by a viscoelastic fluid. Application to bituminous concretes

International audienceThis paper deals with the acoustics of porous media saturated by an incompressible viscous or viscoelastic fluid. By using the homogenization method for periodic structures, we determine the macroscopically equivalent medium. We show that the heterogeneous material displays three types of behaviour: biphasic, elastic, viscoelastic, according to the contrast of the mechanical properties of the constituants. This contrast is measured by the small parameter ε, ratio of the dimension of the pores to the macroscopic wave length. Therefore the macroscopic behaviour depends also on the excitation. The calculations of the effective macroscopic coefficients are performed for a one-dimensional geometry. The results applied to a porous media saturated by an Newtonian fluid show that the type of behaviour changes with the frequency. We treat the case of a saturation by a viscoelastic fluid by considering bituminous concretes. We investigate how this material behaves according to the temperature and the excitation frequency. The applicability of a time-temperature equivalency is studied and a comparison between experimental results and the 1D model is presented

Deformable porous media with double porosity. Quasi-statics. I: Coupling effects

International audienceWe investigate the macroscopic quasi-static description of a deformable porous medium with a double porosity constituted by pores and fractures. For this purpose, we use an homogenization technique which gives the macroscopic modelling from the description at the pore and fracture levels. It appears that the macroscopic description is sensitive to the ratios between the different scales, l/l′ and l′/l″, wherel, l′ l″ are characteristic lengths of the pores, the fractures and the macroscopic medium, respectively. In the first paper we investigate the case l′/l″=(l/l′)^2, which exhibits a coupling between the flows through the pores and the fractures. The macroscopic description is shown to depend on a single pressure field and exhibits a broken symmetry. Other situations will be examined in a subsequent paper. Large spectra of pore and fracture sizes are also evoked

Deformable porous media with double porosity III: Acoustics

International audienceWe investigate the acoustics of saturated porous media with a double porosity constituted by pores and fractures. This work is the direct extension of earlier papers by Auriault and Boutin, where the quasi-static behaviour was studied. The different macroscopic descriptions of the acoustics are shown to be the quasi-static ones, completed by classical inertial terms and with a generalized seepage law for the fractures. Therefore, when the three scales, i.e. the pore, the fracture and the macroscopic scales are equally separated, the medium exhibits memory effects. Finally, we investigate the interpretation of laboratory experiments on single porosity medium under an acoustic excitation. It is shown that the viscoelastic effects which are observed when the frequency is about a few kHz have their origins in the same phenomenon. But the macroscopic description now depends on the size and the shape of the sample, and therefore it is nonspecific for the porous medium

Deformable porous media with double porosity, quasi-statics. II: Memory effects

International audienceAs in our previous paper, we investigate the macroscopic quasi-static description of a porous medium with a double porosity constituted by pores and fractures. For this purpose, we use a homogenization technique. As expected, the macroscopic description is sensitive to the ratios between the different scales,l/l′ andl/l′ wherel, l′, l″ are characteristic lengths of the pores, the fractures, and the macroscopic medium, respectively. In the first paper, we investigated the case l′/l″=O(l^2/l′^2)≪1 (case 1) which exhibits a coupling between the flows through the pores and the fractures. In the present paper, we deal with the other homogenizable cases. The case 3 where l/l′=O(l′^2/l″^2)≪1 gives a macroscopic description similar to that of a single porosity medium. The main result, however, is the case 2, where l/l′=O(l′/l″)≪1, which exhibits memory effects. These are due to the seepage through the micropores

Rayleigh scattering in elastic composite materials

International audienceThis paper is devoted to long wave propagation in heterogeneous media. More specifically, we deal with Rayleigh diffraction in elastic materials with a periodic microstructure whose heterogeneities are in finite concentration or show great contrasts in properties. This study is based on the homogenization method but contrary to the usual procedure in which only the first significant terms are used, the developments are established up to the third order. We demonstrate that the terms of a superior order successively introduce effects of polarization, of celerity dispersion and of attenuation and we thus bring to the fore a characteristic distance of mode conversion. Finally we demonstrate that the effect of dispersion alone appears in macroscopically isotropic materials

Nonlocal boundary conditions for corrugated acoustic metasurface with strong near field interactions

The propagation of long-wavelength sound in the presence of a metasurface made by arranging acoustic resonators periodically upon or slightly above an impervious substrate is studied. The method of two-scale asymptotic homogenization is used to derive effective boundary conditions, which account for both the surface corrugation and the low-frequency resonance. This method is applied to periodic arrays of resonators of any shape operating in the long-wavelength regime. The approach relies on the existence of a locally periodic boundary layer developed in the vicinity of the metasurface, where strong near-field interactions of the resonators with each other and with the substrate take place. These local effects give rise to an effective surface admittance supplemented by nonlocal contributions from the simple and double gradients of the pressure at the surface. These phenomena are illustrated for the periodic array of cylindrical Helmholtz resonators with an extended inner duct. Effects of the centre-to-centre spacing and orientation of the resonators' opening on the nonlocality and apparent resonance frequency are studied. The model could be used to design metasurfaces with specific effective boundary conditions required for particular applications

Analysis of coupled heat and moisture transfer in masonry structures

Evaluation of effective or macroscopic coefficients of thermal conductivity under coupled heat and moisture transfer is presented. The paper first gives a detailed summary on the solution of a simple steady state heat conduction problem with an emphasis on various types of boundary conditions applied to the representative volume element -- a periodic unit cell. Since the results essentially suggest no superiority of any type of boundary conditions, the paper proceeds with the coupled nonlinear heat and moisture problem subjecting the selected representative volume element to the prescribed macroscopically uniform heat flux. This allows for a direct use of the academic or commercially available codes. Here, the presented results are derived with the help of the SIFEL (SIimple Finite Elements) system.Comment: 23 pages, 11 figure

Acoustics of multiscale sorptive porous materials

This paper investigates sound propagation in multiscale rigid-frame porous materials that support mass transfer processes, such as sorption and different types of diffusion, in addition to the usual visco-thermo-inertial interactions. The two-scale asymptotic method of homogenization for periodic media is successively used to derive the macroscopic equations describing sound propagation through the material. This allowed us to conclude that the macroscopic mass balance is significantly modified by sorption, inter-scale (micro- to/from nanopore scales) mass diffusion, and inter-scale (pore to/from micro- and nanopore scales) pressure diffusion. This modification is accounted for by the dynamic compressibility of the effective saturating fluid that presents atypical properties that lead to slower speed of sound and higher sound attenuation, particularly at low frequencies. In contrast, it is shown that the physical processes occurring at the micro-nano-scale do not affect the macroscopic fluid flow through the material. The developed theory is exemplified by introducing an analytical model for multiscale sorptive granular materials, which is experimentally validated by comparing its predictions with acoustic measurements on granular activated carbons. Furthermore, we provide empirical evidence supporting an alternative method for measuring sorption and mass diffusion properties of multiscale sorptive materials using sound waves

Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works