Mechanics and stability of multilayer extrusion.

Abstract

The primary objective of this work is to investigate an interfacial instability in multilayer extrusion. The problem is first approached by means of a lubrication theory for multilayer flows of Newtonian liquids. Although the theory correlates flow rates with thicknesses of individual layers, it is unable to predict the known interfacial instability. In the next step of building an improved model, two-dimensional linear stability analysis is performed for multilayer channel flow of an arbitrary number of layers of Newtonian and viscoelastic liquids. The constitutive equation is a modified Oldroyd-B model with viscosity represented by the Carreau viscosity function. Asymptotic solutions at long wavelengths and numerical solutions at wavelengths of O(1) are obtained. The investigated parameters include the viscosity, flow rate and density ratios, the shear-thinning parameters, the relaxation and retardation times, the interfacial tensions, gravity and the Reynolds number. Viscosity stratification and inertial effects are primarily responsible for the onset of instability. At very small Reynolds numbers, or for highly viscoelastic liquids, the critical parameters can be estimated using cost-efficient asymptotic analysis. Under certain circumstances, multilayer flows of viscoelastic liquids can be stable at all wavelengths--thereby, operating diagrams of stable flows can be constructed. Although the neutral stability diagrams of Newtonian flows are not affected by the Reynolds number, instability in viscoelastic flows is enhanced by increasing Reynolds number. Symmetric and nearly symmetric configurations in three-layer flows are unstable when the core layer is more viscous than the outer layers. Shear-thinning always destabilizes the flow, whereas interfacial tension always stabilizes the flow. These theoretical results agree with many critical industrial observations. Two-dimensional multilayer flows through long converging channels are also investigated using the modified Arnoldi's algorithm for computing leading eigenvalues in a large, sparse generalized eigenvalue problem. The critical flow-rate ratios in long converging channels are found to be independent of the shapes and of the ratios of the thicknesses at the two ends of the channels. These results agree well with the approximate one-dimensional analysis at various cross-sections in the die, indicating that the most dominant instability is at the inlet of the die. Thus, the ultimate objective of providing guidelines to avoid interfacial instabilities in multilayer extrusion is achieved in this work.