# Why is flux at an interface purely diffusion?

In many textbooks, the flux at the point of interface of two phases/regions is given through Fick's first law, with purely diffusive flux, even when there can be bulk convection in both phases/regions.

Essentially, $$N_{A,y}\vert_{\xi=0}=N_{A,y}\vert_{y=\delta}=-D_{AB}\left.\frac{\partial c_A}{\partial y}\right|_{y=\delta}$$

where $\delta$ is the point of interface. I am wondering why this is. Can you show this mathematically? Intuitively I would say that there is a no-slip condition at the point of interface that allows for no bulk motion, and so flux is purely diffusive. But if we have a moving interface, such as a falling film, I don't understand why this is still valid.

• Carrier flux at a semiconductor interface contains both drift and diffusion terms. – Jon Custer Nov 17 '17 at 13:52