Viscous stress modeling for one-fluid approach in Newtonian two-phase flows

A crucial issue in two-phase flows is related to the modeling of viscous stresses. A new general viscous stress model for Newtonian two-phase flows is derived theoretically from the Navier–Stokes equations and jump conditions at the interface. The model is developed within the framework of the one-fluid approach. The only assumptions are incompressibility, no phase change, and constant surface tension. It is argued that this new modeling allows a theoretical definition of the equivalent viscous stress in the vicinity of interfaces. Moreover, for computational fluid dynamics, it can be seen as the physical justification for using both harmonic and arithmetic averages to define the one-fluid viscosity.