STABILITY OF 2-LAYER POISEUILLE FLOW OF CARREAU-YASUDA AND BINGHAM-LIKE FLUIDS

In this paper we present the linear stability analysis of the interfac e between two non-Newtonian inelastic fluids in a straight channel dri ven by a pressure gradient. Two theological models of non-Newtonian be havior are studied: (a) Bingham-like fluids and (b) Carreau-Yasuda flu ids. For each theological model, the linearized equations describing t he evolution of small two-dimensional disturbances are derived and the stability problem is formulated as an eigenvalue problem for a set of ordinary differential equations of the Orr-Sommerfeld type. Discretiz ation is performed using a pseudospectral technique based on Chebyshev polynomial expansions. The resulting generalized matrix eigenvalue pr oblem is solved using the QZ algorithm. The results on the onset of in stability are presented in the form of stability maps for a range of z ero-shear-rate viscosity ratios, thickness ratios, power-law constants , material time constants, Yasuda constants, apparent yield stresses a nd stress growth exponents. Increasing the stress growth exponents or apparent yield stresses of the viscoplastic fluids has a stabilizing e ffect on the interface. For shear thinning fluids, increasing the zero -shear-rate viscosity ratio or shear thinning of the fluids destabiliz es the interface. The effect of other parameters can be stabilizing or destabilizing depending on the flow configuration and wavelength.