Identifying micro- and macro- characteristic lengths governing sound wave properties in cellular foams

Abstract : Identifying microscopic geometric properties of 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. Firstly, we revisit recent literature data to identify the local characteristic lengths dominating the transport properties and sound absorbing behavior of real 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. Secondly, macro-characteristic lengths simulations were performed numerically in opened-cell and partially closed-cell polyurethane foams. Various representations were tried to bridge the micro- and macro- characteristic lengths. A successful one uses the curve of the viscous characteristic length over mean throat size as a function of membranes' closure rate. It was found to be close to one, meaning that the viscous characteristic length is a good indicator of the interconnection sizes.
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M. T. Hoang, Camille Perrot. Identifying micro- and macro- characteristic lengths governing sound wave properties in cellular foams. AIA-DAGA 2013 Conference on Acoustics, Mar 2013, Merano, Italy. ⟨10.1063/1.4793492⟩. ⟨hal-00812922⟩

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