Remarks on the stability of viscometric flow

In flows of viscoelastic liquids, instabilities frequently arise at high shear rates. The explanation for these instabilities is still a largely unsolved problem. This paper discusses some consequences of a recent theory due to E. Becker and his coworkers at Darmstadt. This theory predicts instabilities if the first normal stress differences is sufficiently high. We show that this instability is associated with a change of type in the governing equation. The theory is based on a certain approximation. The justification for this approximation is also discussed and is found to be problematic.