  The effect of wall slip on the apparent flow curves of viscoplastic materials
obtained using torsional parallel plate rheometers is analysed by considering
Herschel-Bulkley fluids and assuming that slip occurs above a critical wall
shear stress, the slip yield stress {\tau}_c, taken to be lower than the yield
stress, {\tau}_0. Thus, different flow regimes are encountered as the angular
velocity of the experiment is increased. When the rim shear stress {\tau}_R is
below the slip yield stress, the exerted torque is not sufficient to rotate the
disk and the material remains still. When {\tau}_c<{\tau}_R<{\tau}_0 the
material is still unyielded but exhibits wall slip and rotates as a solid at
half the angular velocity of the rotating disk. Finally, when
{\tau}_R>{\tau}_0, the material exhibits slip everywhere and yields only in the
annulus r_0<r<R, where r_0 is the critical radius at which the shear stress is
equal to the yield stress and R is the radius of the disks. In the general
case, the slip velocity, which varies with the radial distance, can be
calculated numerically and then all quantities of interest, such as the true
shear rate, and the two branches of the apparent flow curve can be computed by
means of closed form expressions. Analytical solutions have also been obtained
for certain values of the power-law exponent. In order to illustrate the effect
of wall slip on the apparent flow curve and on the torque, results have been
obtained for different gap sizes between the disks choosing the values of the
rheological and slip parameters to be similar to reported values for certain
colloidal suspensions. The computed apparent flow curves reproduce the patterns
observed in the experiments.
