DYNAMICS OF COAXIAL TORSIONAL RESONATORS CONSISTING OR SEGMENTS WITH DIFFERENT RADII, MATERIAL PROPERTIES AND SURROUNDING MEDIA

High-Q torsional resonators constitute the most sensitive transducers for high frequency dynamic viscoelastic measurements of dilute polymer solutions. Most such resonators described in the literature are segme nted. Because of the need for torque and torsional displacement transd ucers the Q-value of the individual segments most often differ, but no rmally all segments have the same radius. A detailed analysis of the d ynamics of such resonators when both the radii, material properties an d surrounding media may be different for each segment, is presented. F or resonators where all segment lengths equal an integer multiple of a quarter of the torsional wavelength, we find that the Q-value of the resonator as a whole is mainly determined by the Q-value of the segmen t with the smallest radius. We further find that reduction of the radi us of the segment surrounded by polymer solution results in a stronger mechanical coupling between the resonator as a whole and the polymer solution. These findings suggest that the segment radii are important optimization parameters of segmented torsional resonators used to meas ure the high frequency dynamic viscoelastic properties of e.g. polymer solutions.