Remarks on the stability of viscometric flow

Abstract

We study the stability of viscometric flow using the type of short memory introduced by Akbay, Becker, Krozer and Sponagel [1-71. The instability found by these researchers is recognized as a change of type leading to nonevolutionary character of the governing equations.We also address the question of justification for the short memory assumption and find that it cannot be justified for some of the more popular rheological models. AMS (MOs) SIGNIFICANCE AND EXPLANATIONIn 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 R. Decker 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.

Problems, Analysis, and Solutions of the Equations for Viscoelastic Flow

“…+ grad p -div ~ -P£, (1) and the conservation of mass div ! The equations we need are the balance of linear momentum p!…”

“…In this section we have only mentionedoa few mo~els and for extensive discussion and derivation of these and other models, we refer to books on this subject [2,3,1].…”