Thickness-shear mode quartz crystal resonators in viscoelastic fluid media

An extended Butterworth-Van Dyke (EBVD) model to characterize a thickness-s hear mode quartz crystal resonator in a semi-infinite viscoelastic medium i s derived by means of analysis of the lumped elements model described by Ce rnosek [R. W. Cernosek, S. J. Martin, A. R. Hillman, and H. L. Bandey, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 1399 (1998)]. The EBVD mod el parameters are related to the viscoelastic properties of the medium. A c apacitance added to the motional branch of the EBVD model has to be include d when the elastic properties of the fluid are considered. From this model, an explicit expression for the frequency shift of a quartz crystal sensor in viscoelastic media is obtained. By combining the expressions for shifts in the motional series resonant frequency and in the motional resistance, a simple equation that relates only one unknown (the loss factor of the flui d) to those measurable quantities, and two simple explicit expressions for determining the viscoelastic properties of semi-infinite fluid media have b een derived. The proposed expression for the parameter Delta f/Delta R is c ompared with the corresponding ratio obtained with data computed from the c omplete admittance model. Relative errors below 4.5%, 3%, and 1.2% (for the ratios of the load surface mechanical impedance to the quartz shear charac teristic impedance of 0.3, 0.25, and 0.1, respectively), are obtained in th e range of the cases analyzed. Experimental data from the literature are us ed to validate the model. (C) 2000 American Institute of Physics. [S0021-89 79(00)07020-1].