Interfacial-tension-force model for the wavy-stratiﬁed liquid–liquid ﬂow pattern transition
The ﬂow of two immiscible liquids is of common occurrence in a wide range of natural and industrial pro-cesses. The interest in liquid–liquid ﬂow has recently increased mainly due to the petroleum industry, where oil and water are often transported together for long distances. In the current Brazilian offshore scenario, signiﬁcant amount of water is being produced, and it tends to increase. The one-dimensional two-ﬂuid model is used to model the wavy stratiﬁed liquid–liquid ﬂow. A stability analysis is carried out, including the interfacial tension force and a single transition criterion is proposed. A new destabilizing term arises, which is a function of the cross-section curvature of the inter face. The existence of short interfacial waves is considered and the effect of a concave or convex cross-section interface shape is included in the analysis. It is shown that the new interfacial tension term plays an important role in regions of extreme in situ volume fractions. The kinematic wave theory is used to model the observed interfacial wave. New geometrical and kinematic wave data are used to validate the proposed model. Transition boundaries are drawn on ﬂow maps of the superﬁcial velocities and the agreement with present data and data from literature is encouraging. The results help to elucidate the actual nature of the typical wavy structure observed in stratiﬁed ﬂow and can be used for the proposition of more accurate ﬂow-pattern transition models.