Abstract
Global linear stability analysis of the creeping flow of an Oldroyd-B liquid, confined between eccentric cylinders co-rotated at equal angular speeds Ω, is performed using a submatrix-based transformation algorithm [K. Arora, R. Sureshkumar, J. Non-Newtonian Fluid Mech. 104 (2002) 75]. The eccentricity parameter ε is defined as the ratio of the distance between the cylinder centers to the average gap width d. In the limit as ε → 0 and for narrow gaps, the base flow corresponds to a solid body rotation. A flow instability is predicted even when ε ≪ 1. For sufficiently large values of the solvent to total viscosity ratio β, the most dangerous disturbance is time-periodic with frequency ≈0.1 Ω/δ, where δ denotes the ratio of d to the inner cylinder radius. The critical Weissenberg number Wec, defined as the product of the fluid relaxation time and the characteristic shear rate at the onset, obeys a scaling law of the form Wecε2δ1/2 = K where K is an O(1) constant that is dependent on β. This scaling is explained based on the effect of the variation in ε on the convection of the stress perturbations by the base flow. Predictions of Wec are in qualitative agreement with the onset Weissenberg number for a time-dependent secondary flow experimentally reported for non-shear thinning viscoelastic polymer solutions [I.M. Dris, E.S.G. Shaqfeh, J. Non-Newtonian Fluid Mech. 80 (1998) 1].
Original language | English (US) |
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Pages (from-to) | 36-44 |
Number of pages | 9 |
Journal | Journal of Non-Newtonian Fluid Mechanics |
Volume | 132 |
Issue number | 1-3 |
DOIs | |
State | Published - Dec 15 2005 |
Externally published | Yes |
Keywords
- Eccentric cylinders
- Elastic instability
- Oldroyd-B
- Solid body rotation
- Viscoelastic
ASJC Scopus subject areas
- General Chemical Engineering
- General Materials Science
- Condensed Matter Physics
- Mechanical Engineering
- Applied Mathematics