High frequency poroelastic waves in hydrogels

Abstract

In this work a continuum model for high frequency poroelastic longitudinal waves in hydrogels is presented. A viscoelastic force describing the interaction between the polymer network and the bounded water present in such materials is introduced. The model is tested by means of ultrasound wave speed and attenuation measurements in polyvinylalcohol hydrogel samples. The theory and experiments show that ultrasound attenuation decreases linearly with the increase of the water volume fraction "{\beta}" of the hydrogel. The introduction of the viscoelastic force between the bounded water and the polymer network leads to a bi-phasic theory showing an ultrasonic fast wave attenuation that can vary as a function of the frequency with a non-integer exponent in agreement with the experimental data in literature. When {\beta} tends to 1 (100% of interstitial water) due to the presence of bounded water in the hydrogel, the ultrasound phase velocity acquires higher value than that of pure water. The ultrasound speed gap at {\beta} = 1 is confirmed by the experimental results that show that it increases in less cross-linked gel samples that own a higher concentration of bounded water.