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

The interfacial stability of pressure driven channel flow consisting of a highly elastic Boger fluid superposed on as silicone oil is investigated experimentally 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 study (Khomami and Su, 1999) it was demonstrated experimentally and theoretically 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 regime is examined. Specifically, the Stuart-Landau equation is used to examine the shape of saturated waves. It is shown that the bifurcations are primarily supercritical and the theoretical wave forms compare favorably with experimental 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. ©2000 Elsevier Science B.V. All rights reserved.