Compound piezoelectric cylindrical resonators as sensors of the rheological parameters of viscoelastic media

The electro-elastic behavior of a viscoelastically loaded layered cylindrical resonator (sensor) comprising two coupled hollow cylinders is presented. The inner cylinder is a piezoelectric ceramic tube. The outer cylinder is a non-piezoelectric (passive) metallic cylinder. An analytical formula for the electrical admittance of a compound layered cylindrical resonator loaded with a viscoelastic liquid is established. Admittance (conductance) diagrams were obtained using a continuum electromechanical model. The established analytical formulas enable the determination of the influence of the liquid viscosity, material, and geometrical parameters of a compound cylindrical resonator on the response characteristics of the compound sensor. In the paper, the sensor implications resulting from the performed analysis are described. Moreover, the algorithm of the method developed by the authors to evaluate the rheological parameters of a viscoelastic liquid is presented. Good agreement between the theoretical results and experimental data is shown. The analysis presented in this paper can be utilized for the design and construction of cylindrical piezoelectric viscosity sensors, annular accelerometers, filters, transducers, and multilayer resonators.     

Solidly mounted ZnO shear mode film bulk acoustic resonators for sensing applications in liquids

Solidly mounted film bulk acoustic resonators (FBAR) operating at 850 MHz in the shear vibration mode have been fabricated. C-axis inclined zinc oxide (ZnO) thin films realized by modified reactive magnetron sputtering were used: Coupling factors k2 of 1.7% and Q-factors of 312 were determined in air. Q-factors of 192 were measured in water, making these devices attractive for sensing applications in liquids, e.g., biosensing.     

Nonspecific binding removal from protein microarrays using thickness shear mode resonators

Nonspecific binding is a universal problem that reduces bioassay sensitivity and specificity. We demonstrate that ultrasonic waves, generated by 5-MHz quartz crystal resonators, accelerate nonspecifically bound protein desorption from sensing and nonsensing areas of micropatterned protein arrays, controllably and nondestructively cleaning the micropatterns. Nonsensing area fluorescent intensity values dropped by more than 85% and sensing area fluorescent intensity dropped 77% due to nonspecific binding removal at an input power of 14 W. After patterning, antibody films were many layers thick with nonspecifically bound protein, and aggregates obscured patterns. Quartz crystal resonators removed excess antibody layers and aggregates leaving highly uniform films, as evidenced by smaller spatial variations in fluorescent intensity and atomic force microscope surface roughness values. Fluorescent intensity values obtained after 14-W QCR operation were more repeatable and uniform.     

Doubly rotated resonators for sensing the properties of liquids

When a doubly rotated resonator is operated in a liquid, the displacement of the surface is partly out of the plane of the plate of the resonator. The out-of-plane component of the displacement propagates a damped compressional wave into the liquid, and the in-plane component propagates a damped shear wave. In this paper, we report the measurements of the series resonant frequency and the motional arm resistance of doubly rotated quartz resonators (theta approximately 35 degrees and phi = 7 degrees) in liquids to compare with singly rotated AT-cut resonators (theta approximately 35 degrees and phi = 0 degrees). A modified Butterworth-Van Dyke (BVD) equivalent circuit model is suggested to analyze doubly rotated cut resonators under liquid loading.     

The analog of the Kanazawa-Gordon formula for cylindrical resonators

In this paper, a formula relating the shift in the resonant frequency of a shear piezoceramic cylindrical resonator to the viscosity of a Newtonian liquid that loads the resonator surface was established. This formula is analogous to the classical Kanazawa-Gordon formula that describes the change in the resonant frequency of a shear planar resonator loaded with a Newtonian liquid. To this end, the author applied the perturbation method to analyze the behavior of the piezoceramic cylindrical resonators vibrating in a shear mode and loaded with a viscous liquid. The shift in resonant frequency obtained using the perturbation method (mechanical model) was compared to an exact value of the shift in resonant frequency obtained from the complete electromechanical model (admittance diagrams) that describes shear vibrations of a piezoceramic cylindrical resonator loaded with a viscous liquid. Good conformity between the two types of results obtained can prove the correctness of the analytical formulas established in this paper. The results of this work can be applied for the design and construction of viscosity sensors.     

Determination of the properties of viscoelastic materials using spherical nanoindentation

The article is devoted to determining the properties of linearly viscoelastic isotropic materials from the experiment on the introduction of a spherical indenter at a constant-rate displacement in a viscoelastic sample. The results are based on the Lee–Radok (J. Appl. Mech. 27:438–444, 1960) solution of the viscoelastic contact problem. An exact formula is obtained for calculation of the relaxation function using indentation load–displacement data. To illustrate the application of this formula, it is used to find the relaxation function of polymethyl methacrylate (PMMA). The relaxation function found in the article is compared with data measured in a conventional test to evaluate the suitability of the proposed method.     

Recent advances in the continuum mechanics of viscoelastic liquids

The kinematics of viscoelastic fluid flows, the development of constitutive relations and their use in viscometric and nonviscometric flows is given. Experimental data in viscometric flows, extensional flows and the eccentric rotating disk motion along with oscillatory shear flows are presented and compared with theoretical predictions. The flow classification scheme for the selection of the appropriate constitutive equation, the perturbation schemes applicable to fixed and variable domains are described. These are applied to review the literature on particle motions, lubrication problems and rotating flows. Stability of the flows is discussed along with some recent work on existence, uniqueness and the use of dynamical system and hyperbolic theory in connection with propagating singular surfaces.     

Determination of the parameters of piezoceramic elements from amplitude measurements

A new method of measuring the parameters of a piezoceramic element is proposed, the basis of which is the maximum values of the amplitudes of the conductance and its derivative. The method only requires simple automated instruments.     

Motion of viscoelastic liquids in a porous medium

Nonlinear effects occurring in filtration of viscoelastic liquids are considered. The qualitative differences between one-dimensional and planar cases and between motion in homogeneous and inhomogeneous porous media are demonstrated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 52, No. 5, pp. 751–756, May, 1987.     

Real-time detection of organic compounds in liquid environments using polymer-coated thickness shear mode quartz resonators

The selection of sensitive coatings is a critical task in the design and implementation of chemical sensors using coated thickness shear mode quartz crystal resonators (QCRs) for detection in liquid environments. This design or selection is performed through a study of the sorption process in terms of the partition coefficients of the analytes in the coatings. The partition coefficient, which is controlled by the chemical and physical properties of the coating materials, determines the inherent selectivity and sensitivity toward analyte molecules. The selection of the coatings is logically determined by the interactions between coating and target analyte molecules, but can also be made through a systematic variation of the coating's properties. The determination of the partition coefficients is only accurate if all contributions to the total measured frequency shifts, deltafs, of the coated QCR can be established. While mass loading is often assumed to be the dominant factor used in determining partition coefficients, viscoelastic effects may also contribute to deltafs. Both the effect of viscoelastic properties and the effect of mass loading on the sensor responses are investigated by using a network analyzer and oscillator circuit and by characterizing the total mechanical impedance of the loaded sensor. Different types of coatings including rubbery and glassy polymers are investigated, and the targeted analytes include classes of polar compounds (methanol), nonpolar compounds (toluene, xylenes), and chlorinated hydrocarbons (trichloroethylene, tetrachloroethylene, etc). It is seen that changes in viscoelastic properties due to analyte sorption may be significant enough to place the sensor in the nongravimetric regime. However, for most applications involving the detection of relatively low concentrations of organic compounds and the use of acoustically thin films, changes in the complex shear modulus of the coatings contribute less than 5% of the total shift in the series resonant frequency, depending on the coating. In that case, the measured deltafs and, hence, the calculated approximate classification and selection of the coatings for operation in a complex solution of water/analyte molecules.     

Viscoelastic properties of low-viscosity liquids studied with thickness-shear mode resonators

The network analysis method was applied to AT cut quartz blanks (f(0) = 10 MHz), which were loaded with liquids of low and medium viscosity (water, methanol, ethanol, 1-propanol, 1-butanol, glycerol solutions). The shift of the resonance frequency Δf could be separated into a term due to rigidly coupled mass Δf(rig) and a term due to viscous damping Δf - Δf(rig). From the difference Δf - Δf(rig) and the broadening of the resonance curve, the complex shear modulus G = G' + iωη(L) was calculated. The viscosity coefficients η(L) are in good agreement with literature data. As G' > 0, it can be concluded that the examined fluids also reveal elasticity at shear frequencies in the MHz range. For the low-viscosity liquids, elastic contributions resulting from collective interactions of molecules are measurable but small and neglectable in most applications. The medium viscous liquid glycerol (98%) begins to exhibit considerable elasticity, resulting from the relaxation of separate molecules.     

Determination of ZnO temperature coefficients using thin film bulk acoustic wave resonators

Thin film bulk acoustic wave (BAW) resonators have been the subject of research in RF microelectronics for some time. Much of the interest lay in utilizing the resonators to design filters for wireless applications. Some of the major advantages BAW devices present over other filter technologies in use today include size reduction and the possibility of on-chip integration. As the technology matures, the necessity to more fully characterize the performance of the devices and to develop more accurate models describing their behavior is apparent. In this investigation, the effects that temperature variations have on 1.8-2.0 GHz zinc oxide (ZnO)-based solidly mounted BAW resonators (SMRs) are studied. The average temperature coefficients of the series and parallel resonant frequencies of the fabricated devices are found to be -31.5 ppm//spl deg/C and -35.3 ppm//spl deg/C, respectively. The slight decrease in separation between the two resonant frequencies with temperature implies there is slightly less effective coupling with increased temperature. No definite trend is found describing the behavior of the quality factor (Q) of the resonator with temperature variations. With little temperature coefficient data for thin film ZnO available in the literature, the importance of an accurate model is evident. The resonator device performance is simulated using Ballato's electronic circuit model for acoustic devices on a SPICE-based platform. By virtue of the comparison between the predicted and measured device response, various material parameters are extracted.     

The behavior of angle-ply laminated cylindrical shells with viscoelastic interfaces in cylindrical bending

The behavior of a simply supported angle-ply laminated cylindrical shell in cylindrical bending with viscoelastic interfaces is studied. The Kelvin–Voigt model is adopted to represent the character of interfaces. State-space formulations are developed based on the exact elasticity equations, and in particular, a variable substitution technique is used to derive the state equations with constant coefficients. Since the behavior of this structure under static loading is time-dependent, the power series expansion technique is used to approximate the variations of physical variables with time. The response for a laminated shell with viscous interfaces is also investigated as a particular case. Results show that the displacements as well as the maximum stresses in the panel increase rapidly with time. Thus, the imperfect bonding properties should be considered carefully in the design of laminated structures.     

Dynamic nonlinear properties of viscoelastic liquids from the rheological flow curve

A method is developed for prediction and calculation of nonlinear properties of viscoelastic liquids solely by measurement of tangent stresses during flow in a rheometer.Translated from Inzhenerno-Fizicheskii Zhurnal. Vol. 57, No. 5, pp. 786–788, November, 1989.     

Analysis of piezoelectric bulk-acoustic-wave resonators as detectors in viscous conductive liquids

An analytical solution for the resonance condition of a piezoelectric quartz resonator with one surface in contact with a viscous conductive liquid is presented. The characteristic equation that describes the resonance condition and accounts for all interactions including acoustoelectric interactions with ions and dipoles in the solution is obtained in terms of the crystal and liquid parameters. A simple expression for the change in the resonance frequency is obtained. For viscous nonconductive solutions, the frequency change is reduced to a relationship in terms of the liquid density and viscosity. For dilute conductive liquid, the change in frequency is derived in terms of the solution conductivity and dielectric constant. The boundary conditions for the problem are defined with and without the electrical effects of electrodes. Experiments were conducted with various viscous and conductive chemical liquids using a fabricated miniature liquid flow cell containing an AT-cut quartz crystal resonator. The results, which show good agreement with the theory, on the use of quartz crystal resonators as conductivity and/or viscosity sensors are reported.     

Thermal effects on the bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory

Summary. The static thermo-viscoelastic responses of fiber-reinforced composite plates are investigated by the use of a refined shear deformation theory. In this theory, trigonometric terms are used for the displacements in addition to the initial terms of a power series through the thickness. The form of the assumed displacements of this theory is simplified by enforcing traction-free boundary conditions at the plate faces. No transverse shear correction factors are needed because a correct representation of the transverse shear strain is given. Using the method of effective moduli solves the equations governing the bending of simply supported fiber-reinforced viscoelastic composite plates. An exact closed-form solution is presented for plates subjected to nonuniform distributions of temperature. The validity of the present theory is demonstrated by comparison with solutions available in the literature. A wide variety of results are presented for the bending response of viscoelastic rectangular plates under thermal loads. The influences of plate aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and constitutive and volume fraction parameters on the thermally induced response are studied.