Determination of the shear impedance of viscoelastic liquids using cylindrical piezoceramic resonators.

In this paper, a new method for determining the rheological parameters of viscoelastic liquids is presented. To this end, we used the perturbation method applied to shear vibrations of cylindrical piezoceramic resonators. The resonator was viscoelastically loaded on the outer cylindrical surface. Due to this loading, the resonant frequency and quality factor of the resonator changed. According to the perturbation method, the change in the complex resonant frequency deltaomega = deltaomega(re) + jdeltaomega(im) is directly proportional to the specific acoustic impedance for cylindrical waves Zc of a viscoelastic liquid surrounding the resonator, i.e., deltaomega is approximately equal to jZc, where j = (-1)1/2. Hence, the measurement of the real and imaginary parts of the complex resonant frequency deltaomega determines the real part, Rc, and imaginary part, Xc, of the complex acoustic impedance for cylindrical waves Zc of an investigated liquid. Furthermore, the specific impedance ZL for plane waves was related to the specific impedance Zc for cylindrical waves. Using theoretical formulas established and the results of the experiments performed, the shear storage modulus mu and the viscosity eta for various liquids (e.g., epoxy resins) were determined. Moreover, the authors derived for cylindrical resonators a formula that relates the shift in resonant frequency to the viscosity of the liquid. This formula is analogous to the Kanazawa-Gordon formula that was derived for planar resonators and Newtonian liquids.