Sounding out Paper Pulp: Ultrasound Spectroscopy of Dilute Viscoelastic Fibre Suspensions

A model of attenuation of ultrasound in fibre suspensions is compared to a model of backscattering pressure from submersed cylinders subjected to a sound wave. This analysis is carried out in the region where the wavelength is of the same order as that of the diameter of the fibre. In addition we assume the cylinder scatterer to have no intrinsic attenuation and the longitudinal axis of the scatterer is assumed to be perpendicular to the direction of propagation of the incident wave. Peaks in the frequency response of both the backscattering pressure, expressed in the form of a form function, and the attenuation are shown to correspond. Similarities between the models are discussed. Since the peaks in the form function are due to resonance of the cylinder, we infer that the peaks in the attenuation are also due to resonance. The exact nature of the waves causing the resonance are still unclear however the first resonance peaks are related to the shear wave and hence the shear modulus of the material. The aim is to use the attenuation model for solving the inverse problem of calculating paper pulp material properties from attenuation measurements. The implications of these findings for paper pulp property estimation is that the supporting fluid could, if possible, be matched to density of that of pulp fibres and that the estimation of material properties should be improved by selecting a frequency range that in the region of the first resonance peaks.