A phase transition approach to elucidate the propagation of shear waves in viscoelastic materials

Abstract

In the field of acoustics, a medium has traditionally been considered a liquid if shear waves cannot propagate. For more complex liquids, such as those containing polymer chains or surfactant aggregates, this definition begins to be unclear. By adopting a rheological model-independent approach, this work investigated by means of dynamic elastography, the liquid–solid phase transitions in viscoelastic liquid media. When the storage shear modulus G′ dominated the loss shear modulus G″, a minimal shear wave attenuation frequency region was defined and the medium was considered solid. When G″ dominated G′, the shear waves were strongly attenuated and the medium was considered liquid. The investigated medium, an aqueous solution of xanthan gum, behaved as a bandpass filter with transition bands, showing liquid–solid–liquid behavior from low to high frequency. During these transitions bands, shear waves still propagated but highly attenuated. The limiting values where shear waves were no longer observed were identified as the low and high cutoff frequencies. Finally, the ability of various rheological models to predict the phase transition frequencies and describe the dispersion curves was tested. A three-element rheological model, the Jeffreys model, was required to accurately fit the experimental response of the medium at different concentrations over the entire frequency range. Shear wave propagation methods can overcome the technical limitations of traditional rheometry and explore higher frequencies, rarely investigated in viscoelastic liquids.