Viscoplastic Couette Flow in the Presence of Wall Slip with Non-Zero Slip Yield Stress

The steady-state Couette flow of a yield-stress material obeying the Bingham-plastic constitutive equation is analyzed assuming that slip occurs when the wall shear stress exceeds a threshold value, the slip (or sliding) yield stress. The case of Navier slip (zero slip yield stress) is studied first in order to facilitate the analysis and the discussion of the results. The different flow regimes that arise depending on the relative values of the yield stress and the slip yield stress are identified and the various critical angular velocities defining those regimes are determined. Analytical solutions for all the regimes are presented and the implications for this important rheometric flow are discussed.