LINEAR-STABILITY DIAGRAMS FOR THE SHEAR-FLOW OF AN OLDROYD-B FLUID WITH SLIP ALONG THE FIXED WALL

We consider the time-dependent shear flow of an Oldroyd-B fluid with s lip along the fixed wall. Slip is allowed by means of a generic slip e quation predicting that the shear stress is a non-monotonic function o f the velocity at the wall. The complete one-dimensional stability ana lysis to one-dimensional disturbances is carried out and the correspon ding neutral stability diagrams are constructed. Asymptotic results fo r large values of the elasticity number and finite element calculation s are also presented. The instability regimes are within or coincide w ith the negative-slope regime of the slip equation. The numerical calc ulations agree with the linear stability results when the size of the initial perturbation is small. Large perturbations may destabilize a l inearly stable steady state, leading to a periodic solution. The perio d and the amplitude of the periodic solutions increase with elasticity .