Simulating mass transfer with interface capturing schemes

Interface-capturing schemes with a non-conservative volume fraction advection equation have been used in various multi-component problems, such as bubble collapse and aerodroplet breakup. For some flows, such as fuel droplet combustion in detonation waves, mass transfer (diffusion) in the gaseous phase requires source terms in the species continuity equations. Such source terms are described using mass fractions rather than volume fractions. Thus, a consistent framework relating the mass and volume fraction equations must be derived that applies to both single-fluid and mixture regions. In this preliminary work, we derive a consistent source term for the volume fraction equation in our interface-capturing model. While this procedure is expected to work with any source term, it is tested with mass transfer problems via binary diffusion using the stiffened gas equation of state.