Viscometric functions of semi-dilute non-colloidal suspensions of spheres in a viscoelastic matrix

Abstract

The viscometric functions (η, N1 and N2) for non-colloidal suspensions of spheres in a Boger fluid matrix were measured. Volume fractions (ϕ) of 5%, 10% and 20% were investigated. The relative viscosity (ηr=η/η0) and the (positive) first normal stress difference N1 showed increases with ϕ which were larger than the dilute suspension theory predictions of 1+2.5ϕ, indicating semi-dilute suspension behaviour.The main interest centres on the second normal stress difference N2. The matrix fluid showed a zero second normal stress difference, and the measurements showed that N2 was always negative for the suspensions. This agrees with the dilute suspension prediction found using the Landau-Lifschitz averaging procedure, but not with the ensemble averaging method, which predicts a positive N2. Possible causes for this result are discussed.