Stability of the Annular Poiseuille Flow of a Newtonian Liquid with Slip along the Walls

摘要

The annular Poiseuille flow of a compressible Newtonian fluid is studied assuming that slip occurs along the wall. Different slip models relating the wall shear stress to the slip velocity are employed. In the case of linear slip, it is easily shown that the slip velocity along the inner cylinder is always greater than the slip velocity along the outer cylinder. In the case of a non-monotonic slip equation, there exist linearly unstable steady-state solutions corresponding to the negative-slope regime of the slip equation. As a result, the resulting flow curve is also non-monotonic with an intermediate unstable negative-slope branch which corresponds to the stick-slip extrusion instability regime. It is shown for small radii ratios = R1/R2, two stable steady-state solutions are possible in a certain range of the volumetric flow rate. As a consequence, the stick-slip instability regime is reduced in size and eventually disappears as is decreased. This provides an explanation for the fact that the stick-slip instability is not observed in annular extrusion experiments.