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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.

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  • $\begingroup$ Carrier flux at a semiconductor interface contains both drift and diffusion terms. $\endgroup$ – Jon Custer Nov 17 '17 at 13:52
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Interface is by definition a separating surface across which there cannot be bulk flow. So if follow an interface (Lagrangian approach, and not Eulerian) the only way mass can be transferred across the interface is by diffusion.

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