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3.3 Ultrasonic techniques

3.3.1 Classical absorption and background contribution

Sound fields constitute temporal and spatial oscillations of the local pressure, which prop- agate through the liquid medium adiabatically, with its amplitude decreasing exponen- tially along the direction of propagation z by:

where α is the attenuation coefficient, cs is the sound velocity in the liquid for compres- sional waves of frequency f, cs = λ · f, p is the sinusoidally oscillating sound pressure, p0 = p(z = 0) and i2 = −1. The attenuation coefficient α is usually considered in ultra- sonic spectroscopy. For our understanding of acoustical spectra, it is necessary to identify the physical mechanisms leading to sound attenuation in liquid systems. Oscillations of the liquid are coupled to the shear viscosity and other transport properties, which thus play an important role in compressional wave interactions. If the particle velocity is smaller than the sound velocity, the field in a viscous liquid is determined by the Navier-Stokes equations resulting in an acoustic absorption coefficient. An expression, which describes viscosity losses, is [52]:

with:

ηs : shear viscosity ηV : volume viscosity f : frequency with f = ω/2π ρ : density cs : sound velocity

The relation (3.28) is strongly dependent upon the properties of the medium and on the frequency. Here the properties of a medium are mainly defined by the shear and the vol- ume viscosity. Shear viscosity has the origin in Stokes friction. Additional losses result from the thermal conductivity, which has been fist shown in 1868 by Kirchhoff [53]:

with:

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