Minh Tan Hoang

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.

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.

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.

Multi-scale acoustics of partially open cell poroelastic foams

The present paper reports on the modeling of linear elastic properties of acoustically insulating foams with unit cells containing solid films or membranes at the junction between interconnected pores from a numerical homogenization technique. It combines fluid-flow induced microstructure identification with simulations of the effective Youngs modulus and Poisson ratio from a mixture of routinely available laboratory measurements (porosity, permeability, cell size) and finite element calculations when the boundary conditions of the periodic unit cell take particular symmetric forms. This combination results in microstructural determination of the macroscopic coefficients entering into the Biot-Allard theory of wave propagation and dissipation through porous media. Precise control over pore morphology and mechanical properties of the base material renders this multi-scale approach particularly suitable for various advanced applications.

An Overview of Microstructural Approaches for Modelling and Improving Sound Proofing Properties of Cellular Foams: Developments and Prospects

Significant advances have been made over the last 15 years in the field of modelling the acoustic properties of foams from the description of their microstructures. It entails a multidisciplinary work at the junction between physico-chemistry and mechanics of porous media, which involves a dialogue between different disciplines and requires the joint development of several techniques (imaging, upscaling, numerical computations, and experimental identification). It seems to be of timely interest to take stock of the methodological developments that have provided guidance on how to manufacture the new generation of foams with enhanced properties and to identify possible future methodological developments.

A Systematic Link between Microstructure and Acoustic Properties of Foams: A Detailed Study on the Effect of Membranes

In this study, we show how milli-fluidic tools can be used to elaborate polymer foams with tunable microstructural parameters, such as the size and the connectivity of the pores. We produce several samples having the same density and the same monodisperse pore size but different values of the closure rate of the windows separating the foam pores, which is estimated by measuring the proportion of closed cells and the size distribution of apertures for open-wall cells. This distribution is based on a distinction between the windows counting four or less edges from the windows counting more than four edges. Then a representative unit cell is reconstructed to mimic the main feature of microstructure information and serves as the basis to the computation of the sound absorbing parameter, using numerical homogenization techniques. Very good correspondences between numerical results and experimental measurements were observed. Our analysis reveals a significant dependence of membrane level on the sound absorption behavior of these foams.