The instability mechanism of single and multilayer Newtonian and viscoelastic flows down an inclined plane |
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Authors: | Chao-Tsai Huang Bamin Khomami |
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Institution: | (1) Department of Chemical Engineering The Material Research Laboratory Washington University, St. Louis, MO 63130-4899, USA e-mail: bam@poly1.che.wustl.edu, US |
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Abstract: | The instability mechanism of single and multilayer flow of Newtonian and viscoelastic fluids down an inclined plane has been
examined based on a rigorous energy analysis as well as careful examination of the eigenfunctions. These analyses demonstrate
that the free surface instability in single and multilayer flows in the limit of longwave disturbances (i.e., the most dangerous
disturbances) arise due to the perturbation shear stresses at the free surface. Specifically, for viscoelastic flows, the
elastic forces are destabilizing and the main driving force for the instability is the coupling between the base flow and
the perturbation velocity and stresses and their gradient at the free surface. For Newtonian flows at finite Re, the driving
force for the interfacial instability in the limit of longwaves depends on the placement of the less viscous fluid. If the
less viscous fluid is adjacent to the solid surface then the main driving force for the instability is interfacial friction,
otherwise the bulk contribution of Reynolds stresses drives the instability. For viscoelastic fluids in the limit of vanishingly
small Re, the driving force for the instability is the coupling of the base flow and perturbation velocity and stresses and
their gradients across the interface. In the limit of shortwaves the interfacial stability mechanism of flow down inclined
plane is the same as plane Poiseuille flows (Ganpule and Khomami 1998, 1999a, b).
Received: 20 October 2000/Accepted: 11 January 2001 |
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Keywords: | Free surface instability Interfacial instability Viscoelastic fluids Linear stability analysis Energy analysis |
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