Natural modes of the two-fluid model of two-phase flow

A physically-based method to derive well-posed instances of the two-fluid transport equations for two-phase flow, from Hamilton principle, is presented. The state flow represented by superficial velocity and drift-flux, instead average velocities each fluid. This generates conservation two principal motion modes naturally: global center-of-mass relative between fluids. Well-posed can be obtained modelling storage kinetic energy in fluctuations structures induced interaction fluids, like wakes vortexes. In this way, regularized without losing process instabilities responsible flow-patterns formation transition. specific case vertical air-water analyzed showing capability present model predict slug regime as trains non-linear waves.