Helmut Nowotny

General one‐dimensional treatment of the layered piezoelectric resonator with two electrodes

A general transfer matrix description of arbitrarily oriented layered piezoelectric structures is presented. Except for the restriction to two electrodes, it is the most general one‐dimensional treatment possible. The description is derived as an exact solution of the fundamental differential equations and the boundary conditions at the terminating surfaces and at the electrical port. It allows the calculation of the electrical admittance appearing between the electrodes for any frequency, as well as the determination of the entire resonance frequency spectrum using only simple matrix multiplications. It covers the general case of multimode excitations and its coupling results. Thus it is not restricted to a single displacement direction and can be used for the rigorous analysis of layered structures containing, e.g., doubly rotated Y‐cut quartz crystals.

Ultrasonic separation of suspended particles

The forces on suspended particles in acoustic fields are reviewed briefly and the theoretical modelling of ultrasonic separators based on piezoelectrically excited layered resonators is described. Two flow-through resonator chamber concepts for ultrasonic particle (bio-cell) separation are investigated: (a) the coagulation or sedimentation approach, (b) the so-called h-shaped ultrasonic separator. The h-shaped ultrasonic separator is analysed by combining for the first time the mathematical modelling of the laminar flow with the acoustic force based velocity field of the particles relative to the suspension medium. This allows a complete modelling of the resonators particle separation performance. Examples for separation chamber designs optimized by use of the mathematical model are presented and the calculated particle traces in the h-resonator are shown and compared with experimental results. For direct comparison of different ultrasonic flow through separator concepts a separation performance figure is introduced and its value is given for the two investigated separator concepts for the sample suspensions of polystyrene spheres, yeast and spirulina cells in (salt) water. The presented results are of importance for the state of the art design of acoustic cell filters for perfusion type bioreactors, as recently launched at the biotechnology market, as well as for the ultrasonic separation of plant (algae) cells under low gravity conditions, where the sedimentation concept fails.

Layered piezoelectric resonators with an arbitrary number of electrodes (general one‐dimensional treatment)

A general transfer matrix description for one‐dimensional layered structures consisting of piezoelectric and nonpiezoelectric anisotropic layers of arbitrary number is used to calculate the electrical admittance matrix for such resonators with N electrodes. The calculation is done in detail for linearly stacked resonators with two free surfaces as well as for ring resonators with a closed acoustical path. Experimental and theoretical results are given and compared for a ring resonator with two piezoelectric layers excited by four electrodes. Such a configuration can be used to generate unidirectional resonant waves.

Viscosity sensor utilizing a piezoelectric thickness shear sandwich resonator

This paper describes a novel quartz crystal sensor for measurement of the density-viscosity product of Newtonian liquids. The sensor element consists of two piano-convex AT-cut quartz crystals vibrating in a thickness-shear mode with the liquid sample in between. This special set-up allows suppression of disturbing resonances in the liquid layer. Such resonances are generated in the common single-plate arrangements due to compressional waves caused by spurious out-of-plane displacements of the shear vibrating finite plate. The primary measurands of the sensor are the fundamental resonance frequency and the associated resonance Q-value, which are influenced by the viscously entrained liquid contacting the quartz surface. The sensor allows the measurement of samples with viscosities from almost zero (air!) up to 200 cP with a sample volume of 130 /spl mu/l.

Viscosity sensor based on a symmetric dual quartz thickness shear resonator

The paper describes a novel quartz crystal sensor for the measurement of the density-viscosity product of Newtonian liquids. The sensor element consists of two circular quartz crystal plates with an air-gap in between and the liquid sample in contact with the outer plate surfaces. Plano-convex AT-cut quartz crystals arranged in mirror symmetric crystallographic orientation and vibrating in an even-symmetric thickness-shear fundamental mode at 2.77 MHz are utilized. The two outer plane sides of the crystals are fully covered by gold electrodes, which are both connected to ground potential. This special mirror symmetric set-up allows the compensation of spurious displacements in the circular clamping zones of the two crystals. The measurement values of the sensor are the fundamental resonance frequency f and the associated resonance Q-value, which are analytically dependent on the density-viscosity product of the liquid in contact with the sensing surfaces. In contrast to an earlier report about a sandwich resonator sensor, which entrapped the liquid sample between two quartz plates, the immersible sensor presented here is not restricted to low viscosity samples. The sensor covers a viscosity range from almost zero (air!) up to 2000 Pa.s, and is not restricted to electrically insulating liquids.

Solving the cable problem between crystal sensor and electronics by use of a balanced bridge oscillator circuit

The balanced bridge oscillator circuit presented here perfectly compensates for the negative influence of the cable. The oscillator circuit is characterized by two almost equal bridge branches; the first one contains the sensor crystal connected via the sensor cable, the second one contains an identical cable terminated by a capacity equal to the resonators static capacity C/sub 0/. The cable compensation performance of the balanced bridge oscillator has been justified by a respective circuit analysis and by measurements of its key specifications in comparison with those of a conventional oscillator.

Viscosity sensor based upon an angular momentum compensated piezoelectric thickness shear sandwich resonator

The paper describes a novel quartz crystal sensor for measurement of the density-viscosity product of Newtonian liquids. The sensor element consists of two piano-convex AT-cut quartz crystals vibrating in a thickness-shear mode with the liquid sample in between. This special set-up allows suppression of disturbing resonances in the liquid layer. Such resonances are generated in the common single-plate arrangements due to compressional waves caused by spurious out-of-plane displacements of the shear vibrating finite plate. The primary measurands of the sensor are the fundamental resonance frequency and the associated resonance Q-value, which are influenced by the viscously entrained liquid contacting the quartz surface. The sensor allows the measurement of samples with viscosities from almost zero (air!) up to 200 cP with a sample volume of 130 /spl mu/l.

Three layer thickness extensional mode piezoelectric resonator for determining density and sound velocity of liquids

The principle of calculating two unknown physical parameters of a layered resonator out of two quasiharmonic series resonance frequencies is applied to the determination of density and sound velocity of liquids. The resonance frequencies are measured using a three layer sensor vibrating in thickness extensional resonance modes. The three layers are formed by two piezoelectric plates and the liquid sample in between. Knowing the behaviour of the two piezoelectric single resonators from measurements which have to be done first, we have calculated the sound velocity and the mass density of the liquid between these two plates out of two series resonance frequencies of the composite resonator.

Piezoelectric resonant sensor for sound velocity of liquids

The sensor consists of two circular piezoelectric plates with the liquid in between. Each piezoelectric plate is a bulk resonator with two electrodes driven in thickness extensional modes. The two resonator plates are electrically connected in parallel and the total admittance is measured in the vicinity of two quasiharmonic series resonance frequencies by a PC‐controlled electric admittance measurement system. The extensional thickness mode purity was checked directly by corresponding mode pattern measurements using a laser speckle vibration amplitude measurement system. The sensor element is mounted in a thermostated aluminum housing to avoid temperature effects and to obtain the sound velocity of the liquid at a defined temperature. Two quasiharmonic resonance frequencies are used to allow the elimination of the unknown density of the liquid. The sound velocity is calculated out of a rigorous one‐dimensional theoretical model of the three‐layer sensor arrangement. In addition to the determination of the sound velocity of the liquid, the mass density of the liquid can be obtained from the same primary measurements. However, at present the accuracy of the density value is one order of magnitude lower than that of the velocity (typically 0.1% for water, acetone, glycerin).

Vibration modes of piezoelectric plates with small spatial thickness variation

A general perturbation treatment is used to obtain the frequency spectrum and the modes of vibration for an electrically driven piezoelectric plate with small thickness variation in lateral direction. For all piezoelectric materials the coefficients of the differential equation for the displacement function are determined by the eigenvectors of the zero order solution without any assumptions about specific material properties, Considering in detail a plano-convex resonator, we obtain solutions of well known structure (quasiharmonic overtone modes described by harmonic oscillator functions). Frequency spectra calculated with the above method are in good agreement with measured and calculated spectra from literature.