In press at Rheol. Acta
The Normal Stress Behaviour of Suspensions with Viscoelastic Matrix Fluids
April 25, 2001
Susanne E. Mall-Glei§le*(1), Wolfgang Glei§le(2), Gareth H. McKinley(3),
Hans Buggisch(2)
(1) Universitaet Karlsruhe (TH), Institut fuer Technische Thermodynamik und
Kaeltetechnik, Engler-Bunte-Ring 21, D-76131 Karlsruhe, DE
(2) Universitaet Karlsruhe (TH), Institut fuer Mechanische Verfahrenstechnik
und Mechanik, D-76128 Karlsruhe, DE
(3) Massachusetts Institute of Technology (MIT), Department of Mechanical
Engineering, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
* Corresponding author; e-mail:
susanne.mall-gleissle@ciw.uni-karlsruhe.de
Abstract
We investigate the variations in the shear stress and the first & second
normal stress differences of suspensions formulated with viscoelastic fluids
as the suspending medium. The test materials comprise two different silicone
oils for the matrix fluids and glass spheres of two different mean diameters
spanning a range of volume fractions between 5 and 25%. In agreement with
previous investigations, the shear-stress Ð shear-rate functions of the
viscoelastic suspensions were found to be of the same form as the
viscometric functions of their matrix fluids, but progressively shifted
along the shear rate axis to lower shear rates with increasing solid
fraction. The normal stress differences in all of the suspensions examined
can be conveniently represented as functions of the shear stress in the
fluid. When plotted in this form, the first normal stress difference, as
measured with a cone and plate rheometer, is positive in magnitude but
strongly decreases with increasing solid fraction. The contributions of the
first and the second normal stress differences are separated by using normal
force measurements with parallel plate fixtures in conjunction with the
cone-and-plate observations. In this way it is possible for the first time
to successfully quantify the variations in the second normal stress
difference of viscoelastic suspensions for solid fractions of up to 25
volume percent. In contrast to measurements of the first normal stress
difference, the second normal stress difference is negative with a magnitude
that increases with increasing solid content. The changes in the first and
second normal stress differences are also strongly correlated to each other:
The relative increase in the second normal stress difference is equal to the
relative decrease of the first normal stress difference at the same solid
fraction. The variations of the first as well as of the second normal stress
difference are represented by power law functions of the shear stress with
an unique power law exponent that is independent of the solid fraction. The
well known edge effects that arise in cone-and-plate as well as parallel
plate rheometry and limit the accessible measuring range in highly
viscoelastic materials to low shear rates could be partially suppressed by
utilizing a custom-designed guard-ring arrangement. A procedure to
correct the guard-ring influence on torque and normal force measurements is
also presented. |