Instability and nonuniqueness of quasisteady flows of a viscoelastic liquid.

*(English. Russian original)*Zbl 0888.76004
Fluid Dyn. 31, No. 6, 819-827 (1996); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza. 1996, No. 6, 29-39 (1996).

Summary: Within the framework of the four-constant Oldroyd model, unidirectional steady-state and quasisteady flow of a viscoelastic liquid is considered. A new explanation, not based on the assumption of slip, is given for the well-known effect of a sharp increase in the fluid flow rates at shear velocities higher than a certain critical value. It is shown, analytically and numerically, that the phenomenon of hysteresis is closely related to this effect. The relation between the problem of stability of the flow in question and the problems of nonuniqueness of the steady-state solution is also noted. A modification of the standard Oldroyd model is proposed and the corresponding integral conditions removing the singularities related with the nonexistence and nonuniqueness of the steady-state solution are determined.

##### MSC:

76A10 | Viscoelastic fluids |

##### Keywords:

sharp increase in flow rates; four-constant Oldroyd model; phenomenon of hysteresis; stability; singularities; nonexistence
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\textit{M. A. Brutyan} and \textit{A. G. Kulikowskij}, Fluid Dyn. 31, No. 6, 819--827 (1996; Zbl 0888.76004); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza. 1996, No. 6, 29--39 (1996)

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