On the Stability of Parallel Flows of Viscoelastic Liquids

摘要

A general linear hereditary stress-strain law is used in studying the stability of plane parallel flows of viscoelastic liquids. A stability equation valid for liquids of arbitrary memory is derived by superposing an infinitesimal, two-dimensional, periodic disturbance on the primary flow. It is shown that in the case of liquids with short memory this stability equation reduces to the one given by Walters in 1962. An asymptotic solution to the stability equation is obtained using the method of inner and outer expansions, as presented by Graebel in 1966. Corrections to his expansions are noted, and the results are compared to those obtained by Chan Man Fong and Walters in 1965. The results indicate that the elastic property of the liquid has a destabilizing effect on the flow. In addition the sum of tensor quantities associated with a given particle at various times is discussed. A comparison of the sum obtained by adding corresponding components when they are referred to the same set of material axes and the sum obtained by adding corresponding components when they are referred to the same set of spatial axes is given. (Author)