New averaged topological equations (ATEs) were obtained from a geometric description of a dispersed two-phase flow using the derivatives of a multi-step and a multi-delta distribution functions as well as a local volume averaging technique. Similar distribution functions were also defined and combined for the obtention of averaged transport equations for multiphase systems considering relevant interfacial effects. A consistency test performed on the set of averaged transport equations shows that the approach followed renders a self-consistent set of governing equations for a multiphase system with an arbitrary number of phases and relevant interfacial effects. Combination of the ATEs and the averaged mass transport equations was proposed to be the foundations of an averaged kinematics of dispersed two-phase flows. The commonly used drift flux model was in turn analyzed and some of its limitations were established as a consequence of the introduction of the ATEs.;Parameters involved in the ATEs are the propagation speeds and the dimensionless strengths of volume fraction waves and specific interfacial area waves, as well as the averaged mean curvature of the dispersed inclusions. An impedance technique was adopted for the obtention of the propagation speed of volume fraction waves and for the objective characterization of several flow patterns in bubble columns and in three-phase fluidized beds. Two important propagation speeds were found in bubble columns under churn-turbulent operation. The smaller one is closely constant and characteristic of homogeneous bubbling conditions; the other one is characteristic of clusters of big bubbles. In three-phase fluidized beds the existence of only one important propagation speed was detected as well as two flow pattern transitions: one of them between the coalesced and the dispersed bubbling flow patterns and the other between one of these flow patterns and the churn-turbulent flow pattern
