To study viscoelastic materials, make a sandwich

When stretched or otherwise deformed, some substances, like rubber, respond elastically—that is, their response depends only on the extent of deformation. Other substances, like honey, have a viscous response that depends on the rate of deformation. Viscoelastic materials exhibit both responses. One way to mathematically describe the viscoelastic response is with the frequency-dependent bulk modulus and shear modulus. Those rheological properties can be expressed as complex values, with the imaginary part representing viscous dissipation. Gautier Lefebvre, Régis Wunenburger , and Tony Valier-Brasier of Sorbonne University in Paris present a new technique for determining a material’s complex moduli at ultrasound frequencies. Whereas current measurement approaches typically require that samples be thick and weakly absorbing, the new method—based on a Fabry–Pérot resonator geometry—can be used with thin samples and strongly attenuating materials. As sketched here, the team sandwiched the material (blue) between two identical, 60-mm-thick blocks (gray) of an aluminum–copper alloy; the blocks delay signals going to and from the ultrasound transducers (red). The sample thickness—from 40 µm to 1 mm—was set by a suitable choice of circular spacer (green). The researchers used one transducer to generate narrow pulses of longitudinal or transverse waves and measured the signals transmitted through the sample and reflected back to the originating transducer. From a spectral analysis of those signals the researchers could extract the sample’s reflection and transmission coefficients, which bear the telltale signature of constructive interference within the resonator. The coefficients could, in turn, be used to determine the sample’s complex moduli for frequencies between about 1 MHz and 5–8 MHz. In a demonstration of the technique, the researchers looked at a sample of an ultrasound coupling gel. Fitting the reflection and transmission coefficients to standard viscoelastic models for bulk and shear moduli, the researchers found quantitative agreement, from which they could obtain the gel’s rheological relaxation times. (G. Lefebvre, R. Wunenburger, T. Valier-Brasier, Appl. Phys. Lett. 112, 241906, 2018 .)