Micro-Macro Acoustic Modeling of Heterogeneous Foams with Nucleation Perturbation

The properties of a polyurethane foam are greatly influenced by the addition of graphite particles during the manufacturing process, initially used as a fire retardant. These thin solid particles perturbate the nucleation process by generating bubbles in their immediate vicinity. A large body of work has focused on foams that are reasonably homogeneous. In this work, we propose a modeling approach for inhomogeneous foams that includes membrane effects and allows pore size distributions to be accounted for. The cellular structure of the foam is obtained through a random Laguerre tessellation optimized from experimental properties. The structure of real foam samples is analyzed using X-ray computed tomography and scanning electron microscopy, followed by image processing, to create three-dimensional, digital models of the samples. The corresponding effective material parameters, including the permeability, the tortuosity and the viscous characteristic length, are subsequently computed by applying a numerical homogenization approach. All the numerical data are presented, discussed and gauged against experimental results.