LINEAR-STABILITY OF FREE SHEAR-FLOW OF VISCOELASTIC LIQUIDS

The effects of viscoelasticity on the hydrodynamic stability of plane free shear flow are investigated through a linear stability analysis. Three different rheological models have been examined: the Oldroyd-B, corotational Jeffreys, and Giesekus models. We are especially interest ed in possible effects of viscoelasticity on the inviscid modes associ ated with inflexional velocity profiles. In the inviscid limit, it is found that for viscoelasticity to affect the instability of a flow des cribed by the Oldroyd-B model, the Weissenberg number, We, has to go t o infinity in such a way that its ratio to the Reynolds number, G is-p roportional-to We/Re, is finite. In this special limit we derive a mod ified Rayleigh equation, the solution of which shows that viscoelastic ity reduces the instability of the flow but does not suppress it. The classical Orr-Sommerfeld analysis has been extended to both the Giesek us and corotational Jeffreys models. The latter model showed little va riation from the Newtonian case over a wide range of Re, while the for mer one may have a stabilizing effect depending on the product sWe whe re s is the mobility factor appearing in the Giesekus model. We discus s the mechanisms responsible for reducing the instability of the flow and present some qualitative comparisons with experimental results rep orted by Hibberd et al. (1982), Scharf (1985a, b) and Riediger (1989).