Discussion Forum

Hi,

I want to study the Advection-Diffusion-Reactions coupled system of equations in COMSOL using “transport of diluted species” interface or any other suitable interface. I have few equilibrium reactions and few as reversible reactions. Study of reversible reactions within “transport of diluted species” interface is easy job but I do not understand how to tackle/write the equilibrium reactions.

I am referring here two equilibrium reactions (given in COMSOL library model; protein adsorption);

Sa+A<=>S+Aa (1)
r_1=k_1^f c_Sa c_A-k_1^r c_S c_Aa
K_1^eq=c_Aa/c_A .c_S/c_Sa
Sa+B<=>S+Ba (2)
r_2=k_2^f c_Sa c_B-k_2^r c_S c_Ba
K_2^eq=c_Ba/c_B .c_S/c_Sa

The mass balances for the species in a time-dependent diffusion/reaction system are

(∂c_A)/∂t+∇.(-D_A ∇c_A )=- r_1 (3)
(∂c_B)/∂t+∇.(-D_B ∇c_B )=- r_2 (4)
(∂c_S)/∂t+∇.(-D_S ∇c_S )=r_1+ r_2 (5)
(∂c_Aa)/∂t+∇.(-D_Aa ∇c_Aa )= r_1 (6)
(∂c_Ba)/∂t+∇.(-D_Ba ∇c_Ba )= r_2 (7)
(∂c_Sa)/∂t+∇.(-D_Sa ∇c_Sa )=-r_1- r_2 (8)

The combined information in equilibrium expressions and the mass balances (removing r_1 and r_2) results in the following system of equations required to solve for(Equations 9 through 14);

∂/∂t (c_S-c_Aa-c_Ba )+∇.(-D_S ∇c_S+D_Aa ∇c_Aa+D_Ba ∇c_Ba )=0 (9)
∂/∂t (c_A+c_Aa )+∇.(-D_A ∇c_A-D_Aa ∇c_Aa )=0 (10)
∂/∂t (c_B+c_Ba )+∇.(-D_B ∇c_B-D_Ba ∇c_Ba )=0 (11)
∂/∂t (c_Sa+c_Aa+c_Ba )+∇.(-D_Sa ∇c_Sa-D_Aa ∇c_Aa-D_Ba ∇c_Ba )=0 (12)
K_1^eq c_A c_Sa-c_Aa c_S=0 (13)
K_2^eq c_B c_Sa-c_Ba c_S=0 (14)

I need help/guidance about how to write the above equilibrium formulations (Equations 9 through 14) in COMSOL for study of Advection-Diffusion-Reactions.

Best Regards,