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  • 1
    Electronic Resource
    Electronic Resource
    The effects of inertia on the viscoelastic Dean and Taylor–Couette flow instabilities with application to coating flows (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2415-2431 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effects of inertia on the elastic instabilities in Dean and Taylor–Couette flows are investigated through a linear stability analysis. The critical conditions and the structure of the vortex flow at the onset of these instabilities are presented. The results reveal that the purely elastic Dean flow is destabilized by inertial effects. It is also found that inertia destabilizes elastic Taylor–Couette flow if the rotation of the inner cylinder is the flow driving force, while it stabilizes the flow driven by rotation of the outer cylinder. The mechanism of destabilization or stabilization of these viscoelastic instabilities is investigated through an examination of the disturbance-energy equation. It is shown that Dean flow is destabilized by two separate mechanisms: a purely elastic mechanism discussed previously (i.e., energy production due to the coupling of a perturbation velocity to the polymeric stress gradient in the base state) [see Phys. Fluids A 3, 1691 (1991)] and a purely inertial mechanism discussed by Dean [Proc. R. Soc. London Ser. A 121, 402 (1928)] (i.e., energy production from Reynolds stresses). It is also shown that, when rotation of the inner cylinder drives Taylor–Couette flow, the Reynolds stresses produce energy, and thus are destablizing, while for the flow driven by the rotation of the outer cylinder alone, the Reynolds stresses dissipate energy, thus stabilizing the flow. The elastic forces remain destabilizing in both modes of operation. In a second study, a pressure-driven viscoelastic coating flow over a curved surface is examined. The results demonstrate the existence of a purely elastic stationary instability in the coating flow on a concave wall which is very similar to that which occurs in viscoelastic Dean flow. It is demonstrated that the mechanisms of instability in Dean flow and the coating flow are the same, again through an examination of the disturbance-energy equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858483
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  • 2
    Electronic Resource
    Electronic Resource
    Viscoelastic Poiseuille flow through a curved channel: A new elastic instability (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2043-2046 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of the inertialess, pressure-driven Poiseuille flow of an Oldroyd-B fluid through a slightly curved channel is considered. The flow is shown to be unstable in certain flow parameter regimes. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These results reveal that there is a purely elastic, instability in the flow, and the instability is a stationary mode in contrast to the elastic, oscillatory instability that occurs in Taylor–Couette flow [see Larson, Shaqfeh, and Muller, J. Fluid Mech. 218, 573 (1990)]. In addition, the mechanism of the instability is investigated through an examination of the disturbance-energy equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857886
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Viscoelastic Poiseuille flow through a curved channel: A new elastic instability (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1691-1694 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of the inertialess, pressure-driven Poiseuille flow of an Oldroyd-B fluid through a slightly curved channel is considered. The flow is shown to be unstable in certain flow parameter regimes. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These results reveal that there is a purely elastic, instability in the flow, and the instability is a stationary mode in contrast to the elastic, oscillatory instability that occurs in Taylor-Couette flow [see Larson, Shaqfeh, and Muller, J. Fluid Mech. 218, 573 (1990)]. In addition, the mechanism of the instability is investigated through an examination of the disturbande-energy equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858223
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  • 4
    Electronic Resource
    Electronic Resource
    A purely elastic instability in Dean and Taylor–Dean flow (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 524-543 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of the viscoelastic flow of an Oldroyd-B fluid between rotating cylinders with an applied, azimuthal pressure gradient is considered. It is found that this Taylor–Dean flow is unstable in certain flow parameter regimes even in the limit of vanishingly small Reynolds number. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These are determined in the limit as the channel width to radius of curvature becomes small. The present results reveal that the instability is a stationary mode when the pressure gradient becomes the dominant flow driving force, while it is an oscillatory instability when the shearing by the cylinder rotation is dominant. In addition, it is found that the direction of the pressure gradient controls the characteristics of the instability: A pressure gradient applied along the cylinder rotation destabilizes the flow, while if applied against the rotation, the flow is substantially stabilized. The mechanism of these instabilities is also investigated through an examination of the disturbance-energy equation. It is found that the mechanism of the elastic, stationary instability is associated with the coupling of the perturbation velocity field to the polymeric stress gradients in the base flow. To the authors' knowledge this mechanism has not been reported elsewhere. In contrast, the mechanism for the elastic, oscillatory instability in Taylor–Dean flow involves the coupling between the disturbance polymeric stresses and the base state velocity gradients, as reported by Larson et al. [J. Fluid Mech. 218, 573 (1990)] for the elastic, oscillatory instability in Taylor–Couette flow.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858325
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  • 5
    Electronic Resource
    Electronic Resource
    MOLECULAR ORIENTATION EFFECTS IN VISCOELASTICITY (2002)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 34 (2002), S. 417-444 
    Details
    ISSN: 0066-4189
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Recent advances in the computational modeling of molecular conformational and orientational effects in the flow of viscoelastic fluids are described. These advances involve the coupling of molecular models for the underlying microstructure of macromolecules with the macroscopic equations of change. The kinetic theory for polymeric liquids is described along with the most useful micromechanical models for computing the fluid flow of polymeric liquids. Three levels of description are covered for the computation of molecular orientation effects: methods for molecular models for which closed-form, continuum-like evolution equations for average quantities describing molecular conformations can be obtained, hybrid methods that involve coupling direct solution of the Fokker-Planck equation describing the distribution function for molecular orientations with the equations of change, and hybrid methods that couple stochastic simulations of individual molecule trajectories with the macroscopic equations of change. Illustrative results for rheometric flows (flows with homogeneous, fixed kinematics) and complex flows are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.fluid.34.083101.134818
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