Boundary conditions at an interface

The boundary conditions at an interface are based on the requirements that (1) two bodies in contact must have the same temperature at the area of contact a id (2) an interface (which is a surface) cannot store any energy, and thus the heat fltbc on the two sides of an interface mu. H he the same. The boundary conditions at the interface of two bodies A and B in perfect contact at x = xq can be expressed as (Fig. 2-37)... 

In this expression, Ca = pU/ys is the capillary number based on the clean interface value of the interfacial tension. To proceed beyond this, we need to specify the gradient of the interfacial tension at the surface of the drop. For this purpose, we return to Section N of Chap. 2, where we discuss the boundary conditions at an interface with adsorbed surfactant. 

In this section, we begin by reviewing the implicit representation of an interface as the level surface of a function defined over all space, together with appropriate definitions of the unit normal vector and the curvature at that interface. We then present a key result from vector calculus that is needed in deriving the proper boundary conditions at an interface. This sets the stage for the formulation of two-phase flow problems including the governing equations and boundary conditions, as well as a whole-domain formulation that combines the two. 

---