WEAKLY NONLINEAR BEHAVIOR OF PERIODIC DISTURBANCES IN 2-LAYER PLANE CHANNEL FLOW OF UPPER-CONVECTED MAXWELL LIQUIDS

The stability of a plane Couette-Poiseuille flow consisting of two lay ers of different fluids is analyzed. The fluids have different viscosi ties, densities and relaxation times and there is surface tension at t he interface. The center manifold reduction method is used to derive t he final amplitude evolution equation. The nonlinear calculations are carried out with two alternative approaches. One approach is to keep t he combined volume flux fixed, and the other is to keep the pressure g radient in the horizontal direction fixed. Numerical results are prese nted for the one-fluid Poiseuille flow, and some two-layer Poiseuille flows with reference to co-extrusion through a slit die. Situations wi th subcritical and supercritical bifurcations are described.