Acoustic shear waves

If an electric held of the proper frequency is applied across the quartz crystal, the crystal wiU oscillate in a mechanically resonant mode. These condihons correspond to the creation of a standing acoustic shear wave that has a node midpoint between the two faces of the crystal and two antinodes at both faces of the disk. This is depicted schematically in Eig. 21.20b. In an EQCM experiment the crystals are operated at the fundamental resonant frequency that is a function of the thickness of the crystal. A crystal with a thickness of 330pm has a resonant frequency of 5 MHz. Crystals with these characteristics are commercially available. In an EQCM experiment, an alternating electric field of 5 MHz is applied to excite the quartz crystal into... 

V. Dutt, R. R. Kinnick, R. Muthupillai, T. E. Oliphant, R. L. Ehman and J. F. Greenleaf, Acoustic shear-wave imaging using echo ultrasound compared to magnetic resonance elastography, Ultrasound Med. Biol., 2000, 26, 397 103. 

Hook F, Ray A, Norden B, Kasemo B (2001) Characterization of PNA and DNA immobilization and subsequent hybridization with DNA using acoustic-shear-wave attenuation measurements. Langmuir 17 8305-8312... 

Duncan-Hewitt, W. C. Thompson, M., Four-layer theory for the acoustic shear wave sensor in liquids incorporating interfacial slip and liquid structure, Anal. Chem. 1992, 64, 94-105. 

Quartz Crystal Microbalance (QCM) sensors detect changes in mass adsorption at an interface and may represent an alternative sensor technology for the study of biospecific interactions in real-time [78], The operating principle of these sensors is based on changes of frequency in acoustic shear waves in the substrate of the sensor. When the QCM system is used in piezoelectric detection mode, the resulting frequency will shift in direct proportion to molecular mass adsorbed at the surface of the sensor [79]. 

Cavic, B. A., Thompson, M. (2002). Interfacial nucleic acid chemistry studied by acoustic shear wave propagation. Anal ChimActa 469, 101-113. 

Fig. 3 Schematic diagram of the propagation of an acoustic shear wave launched by a TSM resonator loaded with a viscoelastic overlayer and exposed to a fluid. Note the progressive zero, significant, and dramatic attenuations of the wave on moving from the rigid layer (electrode plus surface feature-entrapped material) to the viscoelastic solid to the fluid. The acoustic decay lengths in these three regions are, respectively, infinity, [2C/ 1 — C7C ] / /(ft)ypf), and t A[G"//(o in the latter two instances, typical values are 2 and 0.2 pm.

Equations (14.11b) and (14.11c) represent acoustic shear waves whose particle displacements are completely orthogonal to the direction of wave propagation. Equation (14.11b) describes polarization along the y axis, and equation (14.11c) polarization along the z axis. These two waves are degenerate because they have the same wave vector. As a consequence, the two waves can be combined arbitrarily to obtain any type of polarization desired. 

Acoustic shear waves and shear-wave resonators, in particular, have a long tradition in interfacial sensing. Typically one infers the thickness and softness of an adsorbate layer from the shifts of resonant frequency and bandwidth. Laterally heterogeneous samples (vesicles, cells, adsorbed particles) can be modeled numerically. The shifts of frequency and bandwidth are proportional to the stress-velocity ratio (the "load impedance") at the interface, and this load impedance can be calculated by (for instance) the finite element method (FEM). 

The chapter is organized as follows. Section 8.2 provides a short reminder of what acoustic shear waves can and cannot do. Shear waves have distinct advantages (compared to other surface anal3Ttical techniques like optical reflectometry or atomic force microscopy [AFM]), but there are also some caveats to be kept in mind. Section 8.3 briefly summarizes some predictions from simple planar models of slip. An experimental result, which stands as an example for an experience in the authors laboratory, is presented in section 8.4. Section 8.5 provides the results from FEM calculations. Section 8.6 discusses nonlinear phenomena and acoustic streaming, in particular. 

Third, slip can imply interfacial sliding between a simple liquid and a solid (see chapter 2). Generally speaking, slip in this sense is the exception rather than the rule. The interactions between small molecules and a solid wall are expected to be at least as strong as the interactions between the molecules in the bulk. The effective viscosity at the interface therefore should be similar to (or larger than) the bulk viscosity. Still, there is experimental evidence in favor of slip even in simple liquids. Acoustic shear waves should be a well-suited tool of investigation. " ... 

This work highlights the peculiar behavior of soft matter in acoustic shear fields. It also shows how FEM calculations help in the interpretation of experimental findings. The authors are convinced that acoustic shear waves and the related phenomena are of broad... 

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