Abstract
Flow between two plates is considered for a fluid obeying the DeWitt rheological equation of state with the Jaumann derivative. It is found analytically that the steady-state Couette flow is stable or unstable with respect to plane shear perturbations when the Weissenberg numbers are less or greater than unity, respectively. The flow acceleration stage is studied analytically and numerically, a comparison with the case of an Oldroyd fluid is carried out, and the neutral stability curves are constructed. The fundamental role of perturbations of the type considered among the set of instability types which can act on the fluid in such a flow is noted.
Similar content being viewed by others
REFERENCES
Chang Dey Khan, Rheology in Processing Polymers, Khimiya, Moscow (1979).
V. A. Gorodtsov and A. I. Leonov, “Linear instability of the plane Couette flow of a viscoelastic fluid,” Prikl. Mat. Mekh., 31, 289 (1967).
Y. L. Joo and E. S. G. Shaqfeh, “Observation of purely elastic instabilities in the Taylor-Dean flow of a Boger fluid,” J. Fluid Mech., 262, 27 (1994).
I. A. Makarov, “Simulation of the stabilization stage of rheometric flow of a viscoelastic fluid,” Inzh.-Fiz. J., 74, No. 3, 173 (2001).
L. S. Pontryagin, Ordinary Differential Equations [in Russian], Nauka, Moscow (1982).
I.A. Makarov, “Simulation of rheometric flow of a Newtonian fluid using the finite element method,” Inzh.-Fiz. J., 73, No. 5, 927 (2000).
M.A. Fontelos and A. Friedman, “The flow of a class of Oldroyd fluids around a re-entrant corner,” J. Non-Newtonian Fluid Mech., 95, No. 2/3, 185 (2000).
A. S. Monin and A. M. Yaglom, Statistical Hydromechanics, Vol. 1 [in Russian], Gidrometeoizdat, Saint-Petersburg (1992).
Rights and permissions
About this article
Cite this article
Makarov, I.A. Stability of Rheometric Viscoelastic Fluid Flow with Respect to Shear Perturbations. Fluid Dynamics 38, 168–174 (2003). https://doi.org/10.1023/A:1024256615699
Issue Date:
DOI: https://doi.org/10.1023/A:1024256615699