2008 Volume 16 Issue 1 Pages 11-29
A gas-liquid interface contains various complex physics and unknown phenomena related to thermodynamics, electromagnetics, hydrodynamics, and heat and mass transfer. Therefore, a modeling of gas-liquid interface is one of key issues of the numerical research on multiphase flows. Currently, the Continuum Surface Force model (CSF) is popular to model a gas-liquid interface in computational fluid dynamics. However, the CSF model cannot explain the physics of the gas-liquid interface because it is derived through a mechanical energy balance at the interface. In this study, by assuming a gas-liquid interface as a fluid-membrane with a thin but finite thickness, we develop a new gas-liquid interface model based on thermodynamics via mathematical approach. In particular, we derive an equation of free energy based on a lattice gas model including the effect of the electric double layer caused by a contamination on the interaction between the bubble interfaces. Finally, we derive a set of new governing equations for fluid motion based on a mesoscopic concept. The free energy is incorporated into the Navier-Stokes equation as new terms by using Chapman-Enskog expansion. Moreover, by using the new governing equation, we derive the jump condition at the gas-liquid interface based on thermodynamics. Then, we compare the obtained thermodynamic jump condition with the conventional one. As a result, we reveal that the conventional jump condition is true under a specific condition and that thermodynamic jump condition provides more general formalism than the conventional one.