Viscoelastic Wave Dispersion In Gelling Systems:A Theoretical And Experimental Study

Abstract

At the gel point (GP), a material undergoes change from short range connectivity to 3D sample spanning structural self similarity (the critical gel, CG). The linear stress relaxation modulus, G(r), at the gel point is characterised by the Gel Equation; G(i)=St~, where a is the viscoelastic stress relaxation exponent (0<s a «sl) and S is the strength of the 3D gel structure. This provides a basis for GP determination by oscillatory shear measurements, as at the gel point the dynamic moduli are related (via the gel equation) as G'(w)=G(u))/ tan(ctJt/2). The problems associated with this method (strain sensitivity, mechanical weakness and non-equilibrium nature of critical gels) can be overcome by using highfrequency wave propagation measurements. Here, the conjunction of viscoelasticity and wave propagation results in viscoelastic wave dispersion. Viscoelastic wave dispersion is shown herein (using self-similar networks, known as 'ladder models') to characterise the gel-like properties of systems (where 0<s a «sl) prior to the GP, in terms of the gel equation, with measurements at any single frequency. Modified Gross-Marvin models allow simulation of preGP wave dispersion characteristics and facilitates comparison between system wave dispersion and CG wave dispersion during network growth for 0<s a 1. This indicates that 'gel-like' behaviour can be observed, via wave dispersion measurements, prior to the development of a frequency independent loss tangent. Wave dispersion measurements on the thermoreversible sol-gel transition of aqueous gelatin solutions are reported, using a virtual gap rheometer. Experimental results are in close agreement with the developed theory, indicating the suitability of wave dispersion measurements for studying gelling systems. Transactions on Modelling and Simulation vol 21, © 1999 WIT Press, www.witpress.com, ISSN 1743-355X