A general model of the viscosity of complex-shaped particle dispersions is developed based on an exact virial expansion about the low concentration limit and a mathematical analogy between the hydrodynamics of concentrated particle suspensions and the problem of calculating the conductivity of a suspension of insulating particles in a conductive matrix. This transport property relation indicates that the viscosity of concentrated dispersions is governed by percolation exponents and that the critical concentration where the polymer viscosity diverges defines a particle shape dependent viscosity percolation threshold. Utilizing the hypothesis of universality we deduce general scaling curves for the suspension viscosity which are applicable to general shaped particles suspended in Newtonian fluids at arbitrary concentrations. The dependence of the maximum packing density, percolation threshold of overlapping particles, and the viscosity percolation threshold are investigated as a function of particle shape. A viscosity-conductivity analogy is also developed to estimate the leading concentration viscosity virial coefficient of arbitrarily-shaped particles, the intrinsic viscosity, for arbitrarily-shaped particles utilizing a random walk path averaging method. Complications in modeling the viscosity of suspensions arising from particle aggregation, shear thinning arising from particle alignment and the non-Newtonian polymer matrix are also considered and modeled phenomenologically.
Citation: Journal of Macromolecular Science-Polymer Reviews
Pub Type: Journals
clay, conductivity, fillers, percolation theory, polymers, rheology, viscosity