Plateau–Rayleigh instability in low-viscosity ratio stratified liquid–liquid flow

Abstract

Stratified liquid–liquid flow is still an open research subject due to the complex interfacial interactions and its hydrodynamic stability in specific operational conditions. The literature contains different theories explaining the stratified flow transition. A recent theory suggests that the interface’s cross-section curvature is related to capillary instability, which effect is stronger at high water volumetric fractions. At such conditions, interfacial tension contributes to forming a concave interface at the flow’s cross-section. Nevertheless, as far as the authors are concerned, no experimental study has quantified the magnitude of the destabilizing interfacial-tension term related to the interface’s cross-section curvature, which can lead stratified flow to transition to plug flow. We measure such an effect in a horizontal stratified oil–water pipe flow with low Eötvös number using Planar Laser-Induced Fluorescence (PLIF) and shadow sizing techniques in a novel experimental facility. Mineral oil and tap water with a low-viscosity ratio of 1.44 were used. Geometrical and kinematic properties of the interfacial wave at the flow’s longitudinal diametrical vertical and cross-section planes for stable and unstable flow conditions were determined by a homemade scanning algorithm that identifies the oil–water interface. The interface’s cross-section curvature of stratified pipe flow was measured for the first time. A novel expression was proposed to correlate the interface’s cross-section curvature with the mean water height, which is associated with the interfacial tension force that has a dominant effect on transition. A linear stability analysis based on the 1-D two-fluid model was carried out and suggested that capillary instability can be strong enough to promote the transition from stratified to plug flow at some specific flow conditions. The interfacial tension force is the main source of instability, but viscosity and inertial forces also significantly affect the transition of stratified flow. Furthermore, the results indicated that the stabilizing effect of interfacial tension is the force responsible for the stability of the stratified flow studied in this work. The neutral stability transition boundary from stratified smooth to wavy stratified was predicted by applying a general stability criterion.