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.
We consider the problem of steady fast flow of a family of Oldroyd fluids into a hole, and show that the field of flow is partitioned into elliptic (subcritical) and hyperbolic (supercritical) regions. We analyse the characteristics and show that the vorticity changes type as in the experiments of Metzner, Uebler & Fong (1969).
His research interests include undergraduate engineering education, internal combustion engines and emissions, gas-phase particle synthesis, and instrumentation.
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.
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