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.

本文通过回顾和扩展Edwards等人的工作，讨论了穿过粘性界面的动量跳跃条件，该条件表明牛顿行为，即Boussinesq表面流体。（1991）和Slattery等。（2007）。对于基于曲面的功能形式定义的不同情况，系统地导出了用于得出跳跃条件的必要几何/数学工具以及跳跃条件本身。对于任意坐标系，以及在直角坐标，圆柱坐标和球坐标中，都给出了具有各种可变形程度的界面的动量跳跃条件。最后，简化了矩形和圆柱形薄膜的跳跃条件，并讨论了表面粘度对薄膜极限的贡献。