Some Problems in the Stability of Flows of Viscoelastic Fluids.

摘要

Three problems in the stability of viscoelastic flows have been theoretically investigated. The case of plane Couette flow has been solved by the classical energy method of Orr. For two-dimensional disturbances of any magnitude the presence of elasticity has been found to stabilize the flow. This result suggests that the viscous sublayer thickness must increase during the so-called Toms phenomenon. It has been found that the results are identical for three fluids, namely the second-order fluid and the Walters fluids A' and B', although the normal stress behavior of these fluids are quite different. This insensitivity to the constitutive equation has been shown to be a result of the two-dimensionality of the problem. Linear stability theory has been used to investigate the stability of two flows of the Oldroyd fluid, namely the plane Poiseuille flow and the circular Couette flow. For both flows the presence of elasticity has been found to destabilize the flow and to increase the critical wavenumber.