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.