An experimental/theoretical investigation of interfacial instabilities in superposed pressure-driven channel flow of Newtonian and well characterizedviscoelastic fluids Part II: Nonlinear stability

The interfacial stability of pressure driven channel flow consisting of a h ighly elastic Boger fluid superposed on as silicone oil is investigated exp erimentally and theoretically. The viscosity of the two fluids used in the experiments are closely matched, hence any interfacial instability observed in this flow is primarily caused by elastic effects. In Part I of this stu dy (Khomami and Su, 1999) it was demonstrated experimentally and theoretica lly that this flow system is linearly unstable for a range of depth ratios. In Part II, the dynamics of interfacial waves in the weakly nonlinear regi me is examined. Specifically, the Stuart-Landau equation is used to examine the shape of saturated waves. It is shown that the bifurcations are primar ily supercritical and the theoretical wave forms compare favorably with exp erimental measurements. Moreover, it is found that in the weakly nonlinear regime most of the energy transfer occurs between the primary mode and the second harmonic for the fluid system considered. (C) 2000 Elsevier Science B.V. All rights reserved.