Purely irrotational theories of stability of viscoelastic fluids

Abstract

As in the case of viscous fluids, very good approximations to exact results for viscoelastic fluids can be obtained from purely irrotational studies of stability. Here we consider RT instability (§21.1) and capillary instability (§21.2) of an Oldroyd B fluid. Viscoelastic effects enter into the irrotational analysis of RT instability through the normal stress at the free surface. For capillary instability, the short waves are stabilized by surface tension, and an irrotational viscoelastic pressure must be added to achieve excellent agreements with the exact solution. The extra pressure gives the same result as the dissipation method as is true in viscous fluids where VPF works for short waves and VCVPF and DM give the same results for capillary instability. Rayleigh–Taylor instability of viscoelastic drops at high Weber numbers Movies of the breakup of viscous and viscoelastic drops in the high-speed airstream behind a shock wave in a shock tube have been reported by Joseph, Belanger, and Beavers (1999; hereafter JBB). They performed a RT stability analysis for the initial breakup of a drop of Newtonian liquid and found that the most unstable RT wave fits nearly perfectly with waves measured on enhanced images of drops from the movies, but the effects of viscosity cannot be neglected. Snapshots from these movies are displayed in figures 21.1 to 21.4 and 21.9; data for the experiments are shown in table 21.1.