Torsional parallel plate flow of Herschel-Bulkley fluids with wall slip

Abstract

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.