Camille Perrot

Periodic unit cell reconstruction of porous media: Application to open-cell aluminum foams

In this article, the issue of reconstructing an idealized periodic unit cell (PUC) to represent a porous medium is examined by means of microcomputed tomography (μCT). Using μCT, three-dimensional images of open-cell foam are collected and used to characterize the representative parameters of its cellular morphology. These parameters are used in order to reconstruct the porous medium by means of an idealized PUC: a tetrakaidecahedron with ligaments of triangular cross sections, whose characteristic dimensions have been measured on the μCT images. The proposed reconstruction of the idealized PUC is applied to four aluminum foams. The averaged macroscopic properties of the foams (open porosity and thermal characteristic length) are deduced from their respective PUC model and compared to experimental measurements and literature data. Good correlations are obtained. For each of the foams, this provides a parameterized idealized periodic unit cell on which the partial differential equations governing sound dis...

Dynamic viscous permeability of an open-cell aluminum foam: Computations versus experiments

Is it possible to find a two-dimensional (2D) periodic unit cell representative of the dynamic viscous dissipation properties of a real porous media? This is a challenging question addressed in this paper through a review of tools and methods of experimental and computational micro(poro)mechanics. The combination of advanced experimental imaging and numerical homogenization techniques provides a unique opportunity to understand and assess the limits of two-dimensional models of microstructures, as a potential basis for the engineering prediction of macroscopic properties of acoustical materials. This is illustrated for a real sample of open-cell aluminum foam. The conclusion, based on this analysis, is that the 2D periodic foam model geometry provides a reliable estimate of the dynamic permeability, except in the low frequency range. This is not surprising because in the 2D periodic foam model geometry, ligaments are always perpendicular to the flow direction, thus decreasing artificially the static perme...

Microstructure based model for sound absorption predictions of perforated closed-cell metallic foams

Closed-cell metallic foams are known for their rigidity, lightness, thermal conductivity as well as their low production cost compared to open-cell metallic foams. However, they are also poor sound absorbers. Similarly to a rigid solid, a method to enhance their sound absorption is to perforate them. This method has shown good preliminary results but has not yet been analyzed from a microstructure point of view. The objective of this work is to better understand how perforations interact with closed-cell foam microstructure and how it modifies the sound absorption of the foam. A simple two-dimensional microstructural model of the perforated closed-cell metallic foam is presented and numerically solved. A rough three-dimensional conversion of the two-dimensional results is proposed. The results obtained with the calculation method show that the perforated closed-cell foam behaves similarly to a perforated solid; however, its sound absorption is modulated by the foam microstructure, and most particularly by the diameters of both perforation and pore. A comparison with measurements demonstrates that the proposed calculation method yields realistic trends. Some design guides are also proposed.

Solid films and transports in cellular foams

We show that critical path ideas lead to the identification of two local characteristic sizes for the long wavelength acoustic properties in cellular solids, the pore and throat sizes. Application of the model to real foam samples, which may contain solid films or membranes yields quantitative agreement between a finite-element numerical homogenization approach and experimental results. From three routinely available laboratory measurements: the open porosity ϕ, the static viscous permeability k0, and the average struts length Lm obtained from microscopy analysis; asymptotic transport parameters at high-frequencies and the normal incidence sound absorption coefficient are derived with no adjustable parameters.

A direct link between microstructure and acoustical macro-behavior of real double porosity foams

The acoustical macro-behavior of mineral open-cell foam samples is modeled from microstructure morphology using a three-dimensional idealized periodic unit-cell (3D-PUC). The 3D-PUC is based on a regular arrangement of spheres allowed to interpenetrate during the foaming process. Identification and sizing of the 3D-PUC is made from x-ray computed microtomography and manufacturing process information. In addition, the 3D-PUC used allows to account for two scales of porosity: The interconnected network of bubbles (meso-porosity) and the inter-crystalline porosity of a gypsum matrix (micro-porosity). Transport properties of the micro- and the meso-scales are calculated from first principles, and a hybrid micro-macro method is used to determine the frequency-dependent visco-thermal dissipation properties. Olny and Boutin found that the double porosity theory provides the visco-thermal coupling between the meso- and micro-scales [J. Acoust. Soc. Am. 114, 73-89 (2003)]. Finally, the results are successfully compared with experiments for two different mineral foam samples. The main originality of this work is to maintain a direct link between the microstructure morphology and the acoustical macro-behavior all along the multi-scale modeling process, without any adjusted parameter.

Identifying local characteristic lengths governing sound wave properties in solid foams

Identifying microscopic geometric properties and fluid flow through opened-cell and partially closed-cell solid structures is a challenge for material science, in particular, for the design of porous media used as sound absorbers in building and transportation industries. We revisit recent literature data to identify the local characteristic lengths dominating the transport properties and sound absorbing behavior of polyurethane foam samples by performing numerical homogenization simulations. To determine the characteristic sizes of the model, we need porosity and permeability measurements in conjunction with ligament lengths estimates from available scanning electron microscope images. We demonstrate that this description of the porous material, consistent with the critical path picture following from the percolation arguments, is widely applicable. This is an important step towards tuning sound proofing properties of complex materials.

On the dynamic viscous permeability tensor symmetry

Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and/or convergence assessment.

Computation of the dynamic thermal dissipation properties of porous media by Brownian motion simulation: Application to an open-cell aluminum foam

This paper reports simulation results of frequency dependent heat conduction through three-dimensional reconstructed unit cells of an open-cell aluminum foam under acoustic excitations. First, a three-dimensional random walk based algorithm is proposed to calculate the dynamic thermal permeability or dynamic bulk modulus of periodic complex porous geometries. Second, the error and convergence of the implemented calculation algorithm are quantified in terms of the random walk population, normalized trapping distance, and type of geometry. Finally, the algorithm is applied to the calculation of the dynamic bulk modulus of an aluminum foam and compared to laboratory measurements. Good agreement is obtained between simulations and measurements.

2–5 pyrochlore relaxor ferroelectric Cd2Nb2O7 and its Fe2+/Fe3+ modifications

The weak-field dielectric dispersion (100 Hz–1.8 GHz) studies both of pure and Fe2+/Fe3 modified Cd2Nb2O7 ceramics over the temperature range of 90–380 K are presented and discussed from the viewpoint of relaxor and glassy properties of the system. It is revealed that Cd2Nb2O7 pyrochlore is intolerant of the addition of 25 mol % Fe2+ or Fe3+ for Cd2+. From the x-ray diffraction analysis, pure Cd2Nb2O7 forms a single-phase pyrochlore, while the compositions Cd1.5Fe0.52+Nb2O7 and Cd1.5Fe0.53+Nb2O7 give CdNb2O6 columbite doped with Fe2+ or Fe3+ on the Cd sites (<8 and <2 mol %, respectively), except for minor amount of parasitic hematite. The novel CdNb2O6 type compounds are not ferroelectrics, unlike Cd2Nb2O7. In the latter, at TC=196 K the dielectric relaxation due to the motion of ferroelectric domain walls driven by an external ac electric field is observed. A polydispersive dielectric response of Cd2Nb2O7 around 188 K has characteristics of the relaxor ferroelectrics with glassy behavior (like PMN). Nea...

Linear elastic properties derivation from microstructures representative of transport parameters.

It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.