Interfacial instability in pressure-driven core-annular pipe flow of a Newtonian and a Herschel–Bulkley fluid

Abstract

The linear stability characteristics of pressure-driven core-annular flow of a Newtonian core fluid and a Herschel–Bulkley annular fluid is investigated. The fluids are assumed to have the same density and separated by a sharp interface. The modified Orr–Sommerfeld equations for each layer are derived and solved using an efficient spectral collocation method considering a configuration without any unyielded region. The effect of various dimensionless parameters, such as the Bingham number (Bn), the flow index (n), the interface radius (R0) and the inverse capillary number (Γ) on the instability characteristics of the flow is investigated, and an energy budget analysis is conducted to explain the physical mechanism of the instability observed. We found that axisymmetric mode is the most dominant unstable mode for the interfacial flow configuration considered in the present work, which is in contrast to miscible core-annular flows. It is observed that increasing Bn has a non-monotonic effect on the growth rate of the axisymmetric mode, and two dominant modes appear at high Bn. We found that increasing the thickness of the core fluid increases the bandwidth of the unstable wavenumbers and destabilises the short waves; however, displays a non-monotonic trend in the growth rate curves. The instability behaviour observed for different sets of parameters are investigated by conducting an energy budget analysis and analysing the disturbance eigenfunctions and the basic velocity profiles.