AVERAGED TRANSPORT-EQUATIONS FOR MULTIPHASE SYSTEMS WITH INTERFACIAL EFFECTS

The transport equations for a multiphase system are averaged by developing and using spatial and time-averaging theorems for surface-defined fields with an arbitrary parameterization of the surface. Intrinsic and composite distribution functions, used in the averaging process, are defined and their basic properties are investigated. The averaging process shows the interaction between the homogeneous regions (phases, interfaces and contact lines) in a multiphase system. Net flux terms going from one region to others are visualized to be structured in a cascade-like process from the phases to the interfaces and from the interfaces to the contact lines. To confirm the validity of the resulting averaged transport equations, a consistency test is established. It is shown that the test is satisfied by the set of averaged flux terms between the homogeneous regions in the multiphase system. It is also shown that the summation of the averaged transport equations over all the phases, interfaces, and contact lines, satisfies the consistency test. Distributional mixture properties and a general balance for the whole mixture in the averaging volume are used for the establishment of this test.