A very common boundary condition for mass transfer is to know the concentration at the boundaries. This could happen for several physically realistic reasons: you measure the concentration, the boundary is between phases and you have equilibrium data that tells you the concentration (i.e., the boundary (interface) is at the saturation concentration), you have a rapid (infinitely fast) reaction occurring at the boundary so that the concentration at there is zero.
As with heat transfer, it is critical that we realize that we can only use this condition if we actually know a value for the concentration
We can specify a constant flux at the boundary. This is useful as the symmetry condition (at the center of a shere or cylinder) where the flux would be zero, if we know that one boundary is impenetrable so that the flux is zero, if we know what the value of the rate of reaction is (since we could set the flux at the boundary equal to this value), or if we simply measure the flux/flow of mass.
Again, we can combine the two, and specify that the flux is somehow related to the concentration. This would happen at an interphase boundary where we might know that diffusion is equal to convection.
Identify reasonable boundary conditions in a mass transfer problem (explain when each is most useful)