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