The purely elastic stability and bifurcation of the one-dimensional plane Poiseuille flow is determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The problem is reduced to a nonlinear dynamical system using the Galerkin projection method. It is shown that elastic normal stress effects can be solely responsible for the destabilization of the base (Poiseuille) flow. It is found that the stability and bifurcation picture is dramatically influenced by the solvent-to-solute viscosity ratio, ε. As the flow deviates from the Newtonian limit and ε decreases below a critical value, the base flow loses its stability. Two static bifurcations emerge at two critical Weissenberg numbers, forming a closed diagram that widens as the level of elasticity increases. [S0021-8936(00)00703-0]
Finite-Amplitude Elastic Instability of Plane-Poiseuille Flow of Viscoelastic Fluids
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, April 28, 1999; final revision, July 27, 1999. Associate Technical Editor: A. K. Mal.
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Khayat , R. E., and Ashrafi , N. (July 27, 1999). "Finite-Amplitude Elastic Instability of Plane-Poiseuille Flow of Viscoelastic Fluids ." ASME. J. Appl. Mech. December 2000; 67(4): 834–837. https://doi.org/10.1115/1.1308580
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