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

The viscometric functions ( η , N 1 and N 2 ) 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 ( η r = η / η 0 ) and the (positive) first normal stress difference N 1 showed increases with ϕ which were larger than the dilute suspension theory predictions of 1 + 2.5 ϕ , indicating semi-dilute suspension behaviour. The main interest centres on the second normal stress difference N 2 . The matrix fluid showed a zero second normal stress difference, and the measurements showed that N 2 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 N 2 . Possible causes for this result are discussed.