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Capillary instability due to a shear stress on the free surface of a viscoelastic fluid layer. (English) Zbl 0761.76021

Summary: We investigate the hydrodynamic instability of a viscoelastic fluid layer subject to a shear stress on its free surface. Use is made of the Oldroyd viscoelastic fluid model. The stability of two kinds of main flows which satisfy the balance of momentum and constitutive equations is investigated. They are the Couette flow (linear velocity profile) and the return flow (parabolic velocity profile, representing one cell inside a slot). The small-wavenumber approximation is used to solve the Orr- Sommerfeld equation for the two main flows.

MSC:

76E05 Parallel shear flows in hydrodynamic stability
76A10 Viscoelastic fluids
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