Motional resistance

Resistance to Motion—It has been demonstrated experimentally that Eq (2-3) represents fairly accurately the general law of resistance of bodies to motion. Resistance in the case of streamline or turbulent mo-... 

Letting = / 2 + allows the complex element Z to be represented by a real motional resistance R2 and inductance L2, as indicated in Figure 3.7b. From Equation 3.19, the motional impedance elements Lz and Rz can be related to the components of the surface mechanical impedance as [14]... 

The motional resistance, R2, represents power radiated into the contacting liquid by the oscillating device surface. It can be considered a shear-wave radiation resistance. This motional resistance leads to resonance damping. Muramatsu et al. [19] and Beck et al. [20] have shown experimentally that the motional resis-... 

Example 3.4 Calculate the liquid decay length S, motional resistance Rz, and change in series resonant frequency Af, caused by placing water in contact with one face of a 5 MHz TSM resonator having C =5 pF. For quartz [23] 7.74 X 10 , p, = 2.65... 

Solution From Equation 3.31, the liquid decay length in water at 5 MHz is 5 = 0.25 pm. From Equation 3.34b, the motional resistance is 290 ohms From Equation 3.35,... 

Abstract Oscillators are the standard interface circuits for quartz crystal resonator sensors. When applying these sensors in gases a large set of circuits is available, which can be adapted to particular applications. In liquid applications viscous damping accompanied by a significant loss in the Q factor of the resonator requires specific solutions. We summarize major design rules and discuss approved solutions. We especially address the series resonance frequency and motional resistance determination and parallel capacitance compensation. We furthermore introduce recent developments in network analysis and impulse excitation technique for more sophisticated applications. Impedance analysis especially allows a more complete characterization of the sensor and can nowadays be... 

Equivalent (motional) resistance of bare quartz crystal (acoustic load) Voltage ratio... 

The motional resistance, Ri (Sect. 6), is also used as a measure of dissipation. i i is an output parameter of some instriunents based on advanced oscillator circuits. However, experiments based on impedance analysis show that Ri usually is not strictly proportional to the bandwidth (although it should be, according to the Butterworth-van Dyke (BvD) circuit. Appendix A). Also, in absolute terms, Ry—being an electrical quantity and not a frequency— is affected by calibration problems much more than the bandwidth. In the author s opinion, P or D are better measures of dissipation than Ri. 

Fig. 14 Simplified Mason circuit (a) close to Fig. 13d. Since tan(fcqfiq) is large close to the resonance and, further, since this element is in parallel to the small load AZl, it may be neglected, b Close to resonance we have cot(fcqfiq 0) and the element - 2L4Zq cot(fcqfiq) can be approximated by a spring, a mass, and a dashpot. c Using the electromechanical analogy, the spring, the mass, and the dashpot may also be represented as a motional capacitance, Ci, a motional inductance, L, and a motional resistance, R ...

Figure 5.14 Changes in the series resonant frequency A/j (black) and motional resistance h.Rm (gray) following various modifications of the quartz crystal surface and interaction of the aptamer with thrombin. BF, buffer TH, thrombin. Experiments have been performed at 23 1°C. [Adapted from Hianik et al. (2008), with permission of Ben-tham Science Publishers.]...

Since the mid 1980s [11], it has been recognized that TSM resonators can also operate in fluid media if electronic oscillator drivers of suitable gain are employed to excite the resonator and to offset the losses due to damping of the resonator by the fluid. When immersed in water, the motional resistance of a 5 MHz TSM resonator increases to 360 ohms. For an infinite viscoelastic liquid in contact with the TSM, the frequency shift is ... 

Equation (14) is useful in estimating the thickness of compliant films at which deviations from the Sauerbrey equation are noticeable. Equation (15) is useful in interpreting motional resistance measurements of thin films. In the thin-film limit, the motional resistance change is proportional to the square of the film density, the cube of the film thickness, and the loss compliance of the film. For a 5 MHz QCM, typical values for q and Zq are 0.0402 Henry and 8.84 x 10 Pa s/m, respectively. 

The determination of shear storage and loss moduli of thin viscoelastic films with TSM resonators has been reviewed [20,37,38]. Even though the basic physics of damped TSM resonators is well understood, the effort to determine Gf and Gf from measurements of frequency shifts and motional resistance changes has been fraught with problems. For very thin, rigid films, the frequency shift contmns no information on either Gf or Gf because the Sauerbrey limit (equation (2)) is reached. For thicker and/or lossier films the fi equency shift and motional... 

Continuous measurement of motional resistance of the coated quartz crystal, a quantity that can be used to determine the loss compliance of the coating. 

The increased shift in frequency by a thin viscoelastic film may increase the frequency response to added mass as compared to eqn [1], thus acting as an acoustic amplifier. The change in motional resistance upon addition of a film with a thickness h, a density Pfj and a complex shear modulus G = G + iG" can be estimated as... 

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