### 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 We_{c}, defined as the product of the fluid relaxation time and the characteristic shear rate at the onset, obeys a scaling law of the form We_{c}ε^{2}δ^{1/2} = 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 We_{c} 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

- Chemical Engineering(all)
- Materials Science(all)
- Condensed Matter Physics
- Mechanical Engineering
- Applied Mathematics