The importance of the inertial coupling in the two-fluid model of two-phase flow

The new flux representation of the two-fluid model of two-phase flow, where the mixture is described in terms of the volumetric and drift fluxes, is currently the most consistent formulation to treat the inertial coupling between phases. In this representation, the dynamics of the relative motion between phases is revealed as a non-linear wave propagation equation. It is shown that the character and stability of this equation is determined by the balance between the inertial coupling and the interfacial drag. A novel stability criterion is derived that can be used to assess the interfacial closure laws and as a tool to determine the conditions under which a drift-flux correlation is stable. A family of inertial coupling functions for vertical two-phase flow, based on topologies of bubble's vortical wakes, is derived and the corresponding coupling parameters are assessed using available experimental data. The resulting stability maps reveal the occurrence of an unstable region at intermediate void fractions bound by a bistable condition at low and high void fractions, which can be associated with the slug flow-pattern regime.