Momentum jump condition for deformable Newtonian interfaces: Rigorous derivation

Abstract This paper discusses the momentum jump condition across a viscous interface, which shows Newtonian behavior, i.e., is a Boussinesq surface fluid, by reviewing and expanding the works of Edwards et al. (1991) and Slattery et al. (2007). The necessary geometrical/mathematical tools for the derivation of the jump condition, and the jump condition itself are systematically derived for different cases defined based on the functional form of the surfaces. The momentum jump condition for interfaces with various degrees of deformability are presented both for arbitrary coordinate systems and explicitly in the Cartesian, the cylindrical and the spherical coordinates. Finally, the jump condition is simplified for thin rectangular and cylindrical films, and the contribution of the surface viscosities in the thin film limit is discussed.