To provide a physical interpretation of Eq. (B.1), which is Eq. (2.4.9) with γv = 1, we consider a dispersed system and an averaging volume in the shape of a rectangular parallelepiped ΔxΔyΔz with its centroid located at (x, y, z), as illustrated in a. Its top view is shown b.

Clearly, for those elements of the dispersed phase k that are completely inside the averaging volume, where δAk is the closed surface of the element. Such an element, labeled ⓐ in b, may be a bubble or a droplet, spherical or nonspherical. Next, we consider those elements of the dispersed phase that are intersected by the boundary surface ΔAx + (Δx/2). One such element is labeled ⓑ in b. The unit outdrawn normal vector nk can be represented by where i, j, and k are unit vectors pointing in the positive directions of x, y, and z-axis, respectively, and e1, e2, and e3 are the direction cosines of nk. If we denote the portion of the interfacial area of element ⓑ that is inside the averaging volume v by δAk, [x + (Δx/2)], and its area of intersection with the surface ΔAx + (Δx/2) by δAk, x + (Δx/2), then