Viscosity of concentrated suspensions: An approach based on percolation theory

Abstract

A different approach to study the viscosity of concentrated suspensions is proposed. It is based on percolation theory. It is suggested that at the critical concentration of fillers, ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$ a macroscopic interconnected cluster (secondary structure) of fillers is formed. This cluster extends from one wall of the rheometer to the other. It is the properties of this macroscopic cluster which determine the viscosity for \ensuremath{\varphi}\ensuremath{\ge}${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$. An analytic formula is derived for ${\mathrm{\ensuremath{\eta}}}_{\mathit{r}}$(\ensuremath{\varphi}) above ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$, which is tested against a number of sets of experimental data.