The stability of two concentric non-Newtonian fluids in circular pipe flow (Q1821631)

The flow of two concentric non-Newtonian fluids, under constant pressure gradient in a circular tube, is studied by linear stability analysis. The viscosities of the two fluids are different and their dependence on shear stress is described by the Ellis model. It is found that the steady state flow can be unstable, depending on certain combinations of the values of physical parameters, to infinitesimal axisymmetric disturbances of large wavelengths, for any Reynolds number however small. The flow is predominantly stable if the inner fluid is more viscous and predominantly unstable if the outer fluid is more viscous. Stronger dependence of viscosity on shear stress can both stabilize and destabilize the flow. Interfacial tension is also destabilizing when the Weber number is smaller than about \(10^ 4\).