[wysky]

Dear,


I would like to study the transport by diffusion and convection in the solid and fluid regions of a species. Assuming to have two boxes representative of the solid (1) and gas (2) domains that are connected by means of an interface as reported in Figure 1.


The system can be described by the mass transport equations reported in Figure 2.

I have created two additional variables C_solid and C_gas which are volumetric [m^-3] and scalar.
At the interface (dotted red line) there is a mass flow of the species from the solid to the gas domain. The boundary condition in this region should ensure the flux continuity as stated in equation reported in Figure 3, but also the discontinuity in the concentration profile at the boundaries between solid and gas phases as shown in Figure 4.

Thanks to the Fick law, I can introduce a simplified correlation between Cs0 and Cg0 that are functions of the distance (dsol and dgas) from the cell center to the surface in the gas/solid phase and using some assumptions it is possible to obtain an expression of Cs0 and Cg0 in function of Cs and Cg as reported in Figure 5.

My requests are:
Is there a method for implementing a boundary condition at the interface able to maintain the flux continuity ensuring the discontinuities of the concentrations?
Is it possible to implement a boundary condition using the stiff-spring?

Thanks in advance for your help!

Kind regards,
Alex