Wall and interfacial shear stresses in laminar two-phase stratified flow in pipes

Exact solutions for separated two-phase flows are useful as a benchmark for numerical codes and for testing closure relations for simplified 1D Two-Fluid models. In particular, the correct representation of the wall and interfacial shear stresses is essential for the modeling of these flows. In this study, a complete set of exact solutions for laminar stratified two-phase flows in inclined pipes is used to explore the wall and interfacial shear stresses. We examine all possible configurations with concave and convex interfaces, which are related to the contact angle of the phases with the pipe surface. A closed-form analytical expression for the average interfacial shear stress was obtained for all cases of stratified two-phase flow. The limiting behavior of the local shear stresses at the triple-point (TP) region, where the interface meets the pipe wall, is determined by residue calculus. It is shown that the shear stresses behavior upon approaching the TP is determined by the fluid's viscosity ratio and the contact angle. The combinations of those parameters that result in convergence or divergence of the shear stresses at the TP are identified. The usefulness of the analytical expressions obtained for correctly predicting the shear stresses variation upon approaching the TP is demonstrated and discussed.