Reaction-Transpot problem (reaction rate can see as infinitely large)

zy-nwu

Hello there,
I encountered a problem. It is a mass transport (convection and diffusion) and momentum transport coupled problem in porous media under the ALE frame. Here the ALE frame only considers the moving of upper boundary. The mass (solute) transport considers only one phase (A, water) and one component (solute A).  Each computing step, if the depth y> D (D, a known depth to the upper boundary), and if the concentration of solute A--(C_a) is larger than the reference solubility-- (C_s), then the C_a-C_s part will turn to phase B (Solid, doesn't participate the convection and diffusion process, but only migrates with the moving upper boundary through ALE); but if the depth y< D, and if there has phase B, it will turn in to phase A immediately (so the reaction rate can see as infinitely large).
So I choose Darcy's law to describe the momentum transport, and 'convection and diffusion' to describe the solute A transport in phase A. But I'm confused on how to form a formula to express the conversion between the phases, and trace the amount of phase B(S_b).
What I have tested is that I use an ODE like PDE (like dS_b/dt=R) for accounting the amount of phase B (S_b), and add a source for the mass loss or gain on both equations; however, I don't know how big should I set the R (reaction rate), since there have negative values in results which are not right, when I set the
R= -S_b*(y<D)+(C_a-C_s)*k*(y>D).
Overall, I want to know how can I write the formula when the reaction rate can see as infinitely large for handling the negative value problem; or there is any other way to describe the conversion between the two phases and its switch beneath the known depth 'D'.
Hope for your help. Thanks in advance!   
Regards,

ZY

wangyafei

I think if you write your problem in CHINESE, u willl get more attention