Re: abnormal concentration profile near the inner boundary
Are you asking why you get a "diffuse instead of sharp" profile in the interface region?
These types of simulation methods require the solution to be connected (continuous) at cell vertices and edges. If you had a sharp discontinuous jump at a cell edge, it would mean you would have two values at the same time depending on which side you look at, this is not possible. The transition is minimum one cell width, so the solution gets sharper if you mesh is finer in this region.