Stability analysis of spherical viscous fluid-Oldroyd B viscoelastic fluid interface: A viscous potential flow approach

Abstract

The present study investigates the stability of a spherical interface formed by a combination of a viscous fluid and an Oldroyd B viscoelastic fluid using the linear stability analysis. The spherical geometry consists of a viscous fluid occupying the inner sphere, while the outer sphere is filled with the viscoelastic fluid. The governing equations are derived based on the viscous-viscoelastic irrotational theory, and their solutions are obtained using mathematical methods. The analysis results in a third-degree polynomial equation that describes the growth of perturbations, which is then evaluated numerically. It is found that the perturbations grow more rapidly at the interface between the viscoelastic and viscous fluids than at the interface between the viscous fluid and the surrounding medium. The instability of the interface increases with an increase in the Weissenberg number, which is a dimensionless parameter that characterizes the viscoelasticity of the fluid.