A Diffuse Interface Model for Two-Phase Flows Based on Averaging

"A diffuse interface model is derived for the direct simulation of two-phase flows with surface tension, density differences between the phases, and phase change. The derivation starts from the balance equations for a sharp interface and uses a formal averaging procedure on an atomic scale to obtain diffuse interface versions of the equations. Two approaches are considered: (i) the two phases have different velocities inside the interface and separate conservation equations are solved for each phase, and (ii) the two phases have the same velocity inside the diffuse interfuce and mixture conservation equations are solved. Based on a superposition of microscopic (atomic-scale) and macroscopic interface morphologies, an expression for the interfacial momentum source term is introduced that models surface tension effects and accounts for immiscibility between the phases.IntroductionDiffuse interface methods have been a popular tool in the direct simulation of two-phase flows [I]. In diffuse interface approaches, the interface between the two phases is characterized by a rapid but smooth transition in the properties, such as density and viscosity. Usually, a phase function ? is introduced to represent this transition, and the evolution of ? in the domain is computed from a separate equation or recipe. A unique set of conservation equations (e.g., mass and momentum) is solved on the entire domain, irrespective of the phase present, by accounting for the transition in the properties and introducing terms that account for interfacial sources. The continuum surface force (CSF) model of Brackbill et al. [2], which accounts for surface tension, is an example of the latter. The volume-of-fluid (VOF), level set, and phase-field methods are all examples of diffuse interface approaches. The major advantage of diffuse interface methods is that explicit tracking of the interface and the application of traditional sharp interface conditions are avoided. A disadvantage can arise from the artificial smearing of what is in reality an interface of atomic-scale width; however, techniques have been developed to overcome this problem."