The Stability in Couette–Taylor Flow of a Viscoelastic Kelvin–Voigt Fluid

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Abstract

This paper considers the stability of a flow of a weak polymer solution between concentric cylinders, the inner of which rotates. A case of Kelvin–Voight model, frequently called Oskolkov model, was used to describe the movement of the fluid. This model is applicable for highly diluted solutions, where the relaxation time is much less than the typical flow time scale and the elastic forces are much less the viscous. The stability was investigated by the linear approach using the differential sweep numerical method. It is found that for axisymmetric perturbations, as well as in the case of small gap between the cylinders, the critical Reynolds numbers are close to the case of Newtonian fluid. In the case of medium and small values of the inner cylinder radius, the viscoelastic fluid is less stable with respect to the non-axisymmetric disturbances than the viscous one. The critical Reynolds numbers for the non-axisymmetric spiral perturbations may be lower than for the axisymmetric Taylor vortices.

About the authors

A. V. Proskurin

Lavrentiev Institute of Hydrodynamics of Siberian branch of Rassian Academy of Sciences; Novosibirsk State University

Email: k210@list.ru
Novosibirsk, Russia; Novosibirsk, Russia

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