Interfacial Instability in Couette-Poiseuille Flow of Two-Layer Viscoelastic Fluids

Linear stability analysis of shear flow in two-layer viscoelastic fluids, modeled using the upper convected Maxwell (UCM) framework, is performed. The present study investigates plane Couette flow under low Reynolds number conditions, with and without an applied pressure gradient, to understand how differences in elastic properties affect interfacial stability. The numerical analysis spans a broad range of disturbance wavenumbers to construct a stability map based on fluid Weissenberg numbers, highlighting regions of interface stability. The study also considers the influence of pressure gradients on the stability of coating processes for optical fibers. Results show that adverse pressure gradients increase interface stability when the more elastic fluid is in the region of lower shear rates, while favorable pressure gradients enhance stability when the less viscous fluid has higher elasticity. Further analysis reveals that viscosity stratification, combined with elasticity differences, impacts stability, with adverse pressure gradients stabilizing interfaces when the more viscous fluid is more elastic, and favorable pressure gradients stabilizing interfaces when the less viscous fluid is more elastic.