Cessation of viscoplastic Poiseuille flow with wall slip

•A regularized slip equation with slip yield stress is proposed.•The cessation of the axisymmetric Poiseuille flow of Herschel-Bulkley fluids is solved numerically.•Different steady-state flow regimes are identified depending on relative values of the slip parameters.•In the case of zero slip yield stress, the velocity of viscoplastic fluids becomes and remains flat till complete cessation.•The stopping time of viscoplastic flow is finite only if the slip exponent is less than unity. We solve numerically the cessation of axisymmetric Poiseuille flow of a Herschel–Bulkley fluid under the assumption that slip occurs along the wall. The Papanastasiou regularization of the constitutive equation is employed. As for the slip equation, a power-law expression is used to relate the wall shear stress to the slip velocity, assuming that slip occurs only above a critical wall shear stress, known as the slip yield stress. It is shown that, when the latter is zero, the fluid slips at all times, the velocity becomes and remains uniform before complete cessation, and the stopping time is finite only when the slip exponent s1, the decay is much slower. Analytical expressions of the decay of the flat velocity for any value of s and of the stopping time for s