Assessment of errors induced by the anomalous dispersion of high frequency shear waves in rheometrical measurements on gelling systems

Abstract

The principal objectives of the work reported in this paper were two-fold. Firstly, to assess, by means of the numerical simulation of transverse wave propagation within a linear viscoelastic medium, the degree to which wavegroup propagation involving a finite frequency interval (2Δ ω) corresponds to an ‘ideal’ beat (i.e. one for which 2Δ ω → 0). Secondly, to compare the results of shear wave propagation measurements with predictions based on a rheometrical theory, which describes the gelation of materials in terms of their wave dispersion characteristics. The results of the numerical simulations indicate that for a sufficiently small value of the frequency interval Δ ω/ ω, the nodal and anti-nodal regions of the amplitude modulation envelope of wavegroups propagating within a critical-gel may be defined with sufficient accuracy to permit calculation of the corresponding value of the group velocity U. The results of high frequency shear wave dispersion measurements made on a system known to display critical-gel behaviour provide encouraging agreement with theory and the results of the simulations.