We consider the existence of solutions for some models of non‐Newtonian fluid. We have found that Poiseuille and Taylor–Couette problems may have no usual solutions in a large class of Oldroyd models of viscoelastic fluids. That is, axisymmetric Couette‐like solutions and unidirectional Poiseuille‐like solutions fail to exist at sufficiently large Deborah numbers. We have observed that some of the flow features become universal and independent of model parameters in the critical case, i.e., on the boundary between existence and nonexistence regions. We have described a duality between unidirectional flows of the 4‐constant Oldroyd fluid and plane potential flows of an ideal fictitious gas. Based on this duality we have interpreted the nonexistence of solutions as a ‘‘block‐up’’ phenomenon, in the language of gas dynamics.
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November 1992
Research Article|
November 01 1992
Existence and nonexistence of solutions for some rheological models of viscoelastic liquids
M. A. Brutyan;
M. A. Brutyan
Central Aerohydrodynamic Institute, 140160 Zhukovsky‐3, Moscow region, Russia
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P. L. Krapivsky
P. L. Krapivsky
Central Aerohydrodynamic Institute, 140160 Zhukovsky‐3, Moscow region, Russia
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J. Rheol. 36, 1499–1514 (1992)
Article history
Received:
August 21 1991
Accepted:
July 23 1992
Citation
M. A. Brutyan, P. L. Krapivsky; Existence and nonexistence of solutions for some rheological models of viscoelastic liquids. J. Rheol. 1 November 1992; 36 (8): 1499–1514. https://doi.org/10.1122/1.550270
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