Stability of multilayer extrusion of viscoelastic liquids

Abstract

A linear stability analysis of multilayer plane Poiseuille flow of Oldroyd-B liquids with shear rate dependent viscosities is performed for an arbitary number of layers. Asymptotic solutions at long wavelengths and numerical solutions at wavelengths of O (1) are obtained for two-dimensional infinitesimal disturbances. The asymptotic solutions are identical for viscoelastic and Newtonian liquids in two- and three-layer flows, except for nearly geometrically symmetric configurations in three-layer flows. Multilayer flows of viscoelastic liquids can be stable at all wavelengths; thus, operating diagrams of stable flows can be constructed. Symmetric and nearly symmetric configurations in three-layer flows are unstable when the core layer is more viscous than the cuter layers. For highly elastic liquids, stability is not influenced by elasticity, whereas shear thinning always destabilizes the flow. The analysis provides guidelines to avoid interfacial instabilities, which originate inside dies of multilayer extrusion.