Finite-Amplitude Elastic Instability of Plane-Poiseuille Flow of Viscoelastic Fluids

[+] Author and Article Information
R. E. Khayat, N. Ashrafi

Department of Mechanical and Materials Engineering, University of Western Ontario, London, Ontario N6A 5B9, Canada

J. Appl. Mech 67(4), 834-837 (Jul 27, 1999) (4 pages) doi:10.1115/1.1308580 History: Received April 28, 1999; Revised July 27, 1999
Copyright © 2000 by ASME
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Grahic Jump Location
Steady-state shear stress versus shear-rate curves for ζ=0.2 and ε∊[0,1]. The loci of the two extrema are also shown, which join into one curve denoted here by γ̇c. The curves in the figure resemble the pressure/stretch-ratio related to the inflation of a Mooney-Rivlin material (see Fig. 2 in 20).
Grahic Jump Location
Bifurcation diagrams for the normal stress difference, N(0,∞), at the center of the channel as function of We for ζ=0.2 and ε∊[0.06,0.08]. The smallest diagram corresponds to the highest viscosity ratio, ε. As ε exceeds a critical level (in this case 1/8), the (closed) diagram reduces to zero, as the base flow is always stable. The branches AB, CD, EF, and GH of diagram ε=0.06 are unstable, whereas the branches BC, DE, EF, FG, and HA are stable.




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