Stability of the annular Poiseuille flow of a Newtonian liquid with slip along the walls

Abstract

The annular Poiseuille flow a Newtonian fluid is studied assuming that slip occurs along the walls. Different slip models relating the wall shear stress to the slip velocity are employed. In the case of non-monotonic slip models with a maximum followed by a minimum, there exist linearly unstable steady-state solutions with one or both the slip velocities along the inner and outer cylinders of the annulus corresponding to the (unstable) negative-slope branch of the slip equation. The resulting flow curve is non-monotonic with one or even two narrow unstable branches corresponding to the stick–slip instability regime. The sizes of these two unstable regimes are reduced as the radii ratio is reduced. It is demonstrated that the second unstable branch may not be observed at all due to the presence of stable steady-states. These results provide a partial explanation for the absence of the stick–slip instability in annular extrusion experiments.