Combined effects of compressibility and slip in flows of a Herschel–Bulkley fluid

In this work, the combined effects of compressibility and slip in Poiseuille flows of Herschel–Bulkley fluids are investigated. The density is assumed to obey a linear equation of state, and wall slip is assumed to follow Navier’s slip condition with zero slip yield stress. The flow is considered to be weakly compressible so that the transverse velocity component is zero and the pressure is a function of the axial coordinate. Approximate semi-analytical solutions of the steady, creeping, plane and axisymmetric Poiseuille flows are derived and the effects of compressibility, slip, and the Bingham number are discussed. In the case of incompressible flow, it is shown that the velocity may become plug at a finite critical value of the slip parameter which is inversely proportional to the yield stress. In compressible flow with slip, the velocity tends to become plug upstream, which justifies the use of one-dimensional models for viscoplastic flows in long tubes. The case of pressure-dependent slip is also investigated and discussed.

► The 1.5D results for compressible viscoplastic Poiseuille flow with Navier slip are derived.
► It is shown that the critical slip number for full slip is finite when the slip yield stress is zero.
► Solutions of viscoplastic Poiseuille flow with pressure-dependent slip are obtained.