High-frequency tortuosity relaxation in open-cell foams

Propagation of ultrasounds through open-cell polymeric foams is studied using air-coupled ultrasound and Fourier spectral analysis (both phase and magnitude) in the frequency range 0.1 to 6 MHz. A detailed micrographic study is first performed to determine struts dimensions and cell geometry, hence, a unit cell model to describe these foams is proposed. Ultrasound phase velocity and transmission loss were then measured. Variation of these magnitudes with the frequency follows the shape of a sigmoid growth. This behavior of the phase velocity can be explained by introducing an apparent tortuosity with a relaxation-like behavior, which can be explained by considering a probabilistic tortuous walk, as it has recently been performed for other kind of foams. However and unlike in previous studies, the present one shows the whole transition of this sigmoid growth for all studied foams. This is achieved by a precise selection of the foam samples and by the fabrication of new air-coupled transducers that enlarge the experimental working frequency range to lower frequencies. The study of the measured sigmoid growth is used to determine the probability function, required by the probabilistic tortuous walk model, which best describes the variation of the apparent tortuosity.