Propagation of Ultrasonic Waves in Viscous Fluids

Abstract

Viscosity is a property of fluids which can have a great importance in many fields of science and industry. It can be measured by conventional viscometers or by ultrasonic methods (Hertz & Al, 1991). Ultrasonic methods are based either on the determination of the characteristics of propagation (velocity or attenuation) or by the measurement of reflection coefficient (Hertz & Al, 1991) (Malcom J.W Povey, 1997). In the ultrasound based experimental devices, the measurements of the propagation velocity and the attenuation during the propagation allow to determine the physical properties of the medium (He & Zheng, 2001). When an ultrasonic pulse is propagating into a viscous fluid, the pulse waveforms change because of the attenuation and the dispersion of the propagation medium. After its travelling through a medium, the transmitted is not a simply delayed and attenuated waveform copy of the pulse injected at the input. A modelling of the phenomenon of propagation is necessary for an adequate interpretation of the pulse waveforms. During the 20 to 30 last years, a special attention has been devoted to the modelling of the ultrasonic wave propagation in viscous media. In almost these models, the phenomenon of propagation is represented by a slightly dispersive linear system for which the phase is a linear function of frequency (Hertz & Al, 1991). Unfortunately the response of such systems is not causal (D.T, 1995). Hilbert transform or Fractional Calculus are some of the main mathematical tools which have been used to develop theoretical models respecting causality (Hertz & Al, 1991) (D.T, 1969) (He, 1999). In the case of viscous media for which the attenuation of the waves is proportional to the frequency squared, the methods based on Laplace transform allow the derivation of impulse responses respecting the causality (Thomas.L, 1995) (D.T, 1969) (Norton & Purrington, 2009).