Multiple holdup solutions in laminar stratified flow in inclined channels

• Two-fluid laminar–laminar stratified flow in an inclined channel is studied.
• Multiple hold-up solution regions are shown to be enclosed in back flow domain.
• Catastrophe theory is investigated to address multiple solution problem.
• Minimization of energy dissipation is considered to analyze multiple solutions.
• Long-wave stability analysis is revisited.

This study exposed results of investigations on the two-fluid laminar–laminar stratified flow in an inclined channel. Multi-holdup regions have been mapped and visualized in a new way by plotting solution surface of the holdup equation. This representation clearly exhibits the link between backflow situation and multiple holdup solution occurence. The multiple solution problem can be addressed following different approaches. First, the solutions of the two-fluid system are interpreted in term of the minimization of a potential function. Secondly, the minimization of the dissipation rate at the feasible holdup is investigated and thirdly, a long-wave stability analysis is considered.

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