Comprehensive approach for constructing liquid-liquid flow patterns map and convergence to gas-liquid systems

The construction of general two-fluid flow pattern map is presented. The departure from a steady stratified configuration to other bounding flow patterns is analyzed by exploring the stability and well-posedness of the governing equations. In view of the relationships between stability and well-posedness it is shown that the condition for ill-posedness is sufficient to indicate instability while the condition of well-posedness is necessary but insufficient to ensure stability. Of particular interest to flow pattern transition is the stability and well-posedness map (SWP), which defines the boundaries of stability and well-posedness of the long waves modes as a function of operational conditions. It is shown that the integrated frame of stability and well-posedness considerations comprehensively predict the complete stratified/nonstratified transitional boundary in a unified model for horizontal, inclined, various tube sizes, liquid-liquid and gas liquid flows. The transitional boundaries between the other flow patterns encountered in liquid-liquid systems are obtained based on mechanistic models.