For space-dependent boundary conditions, I want to test a scenario as shown in the image. I want to set up the boundary condition for the interior boundary (7) along with other boundaries. Note that concentration in R2 is always greater than R1 and there is a known measured diffusion flux profile through the interior boundary (7).

From diffusion-advection module, it seems the option I can choose is the "flux discontinuity". For the test example, I just used the fixed diffusion flux as the boundary condition for (7). I will also use the space-dependent diffusion flux along X as the interior boundary condition later.

However, I always found such boundary setup was not right for simulations, with materials unbalanced. My questions are:

(1) Is it the right setup for the interior boundary? What is the rule of setting positive or negative values?

(2) if boundary (2) and (4) are for flow-in and boundary (3) and (6) are for flow-out, will the diffusion flux from the top directly go out through these boundaries? I found the materials cannot be balanced, so I am wondering if there is some leaking from the test domain of R1 and R2.