Foundation of the interfacial area transport equation and its closure relations

The interfacial area transport equation is derived from the statistical model of fluid particle number transport equation. The resulting equation includes the source and sink terms due to the particle interactions and interfacial phase change. The consistency of this new approach is demonstrated in terms of the macroscopic continuity equation of a bubbly flow field. The basic mechanisms affecting these source and sink terms are discussed. The general framework to develop the closure relations for the fluid particle interaction and phase change terms is presented. Finally, the one-dimensional interfacial area transport equation is used to identify possible methods to relate the source and sink terms to experimentally measurable interfacial parameters, such that experiments can be used to establish models for these terms.