THIN-FILM CORE-ANNULAR FLOW OF UPPER-CONVECTED MAXWELL-LIQUIDS

Pressure-driven pipe flow of two upper-convected Maxwell liquids in a vertical core-annular arrangement is studied. The annulus and core liq uids have different relaxation times and viscosities. Weakly nonlinear evolution equations which describe the interface shape are derived. L ubrication theory is used in the annulus but not in the core. Motions periodic in the streamwise direction are addressed, with the aim of de scribing short-time behavior driven by capillary forces. Numerical and analytical results for the spatio-temporal dynamics are given for two subcases. In the first case, the liquids have the same viscosity. Whi te noise non-axisymmetric initial data are found to evolve into axisym metric motion. When axisymmetry is assumed, the evolution equation is a Kuramoto-Sivashinsky equation; the bifurcation parameter depends on the fluid elasticities, interfacial tension, Reynolds number and Weiss enberg number. The second case concerns axisymmetric motions with wave lengths in the axial direction that are long compared with the annulus thickness. This asymptotic analysis places a restriction on the size of the Weissenberg number. A jump in the viscosities introduces disper sion, which may be enhanced by fluid elasticity; this can lead to a tr ansition from an unstable regime or a chaotic regime to one in which o rganized traveling wave pulses move in the axial direction. (C) 1997 E lsevier Science B.V.