Closure relations for the shear stresses in two-fluid models for laminar stratified flow

New closure relations for the wall and interfacial shear stresses are suggested for the two-fluid model for stratified laminar pipe flows. The new closure relations are formulated in terms of the single-phase-based expressions, which are augmented by the two-phase interaction factors. The two-fluid model is tested against the exact solution of fully developed laminar pipe flow with a flat and smooth interface. The predictions of the two-fluid model for the pressure gradient and holdup favorably compare with those obtained by the exact solution for a wide range of dimensionless parameters in co-current and counter-current laminar flows. The two-fluid model is also capable of handling the change in the direction of the wall shear-stress when gravity driven backflow in either of the phases is encountered. Additionally, it also correctly predicts the multiple holdups and the operational conditions for their possible occurrence. (C) 2004 Elsevier Ltd. All rights reserved.