Convergence in two-way coupled mass transfer

Dear all,

I am trying to solve the concentration profile in a multiscale non-steady state two-way couple mass transfer problem (specifically, an extractor).

This is as follows:

Concentration at the bed scale (Cbulk): Convection- diffusion equation + source (1)
Concentration at the particle scale (Cparticle): Diffusion with flux boundary condition. (2)

The link between both equations is the flux boundary condition in (2), which is the source term for (1).This boundary condition is given by k*a*(Cparticle-Cbulk).

So far, following the packed bed reactor example, I have been able to couple both scales with a general extrusion coupling.It sort of works for concentration boundary condition but the flow boundary condition is giving me headaches as there is no way that it converges.

This is not a new problem and I am sure that there is an easy approach to deal with such a highly non-linear problems.

Any hint is much appreciated.

Thanks