Combining Advective Transport Equations for Two Solutes: Help Needed!

[nikokampman]

I want to combine the advective transport equation for two solutes such that

dC₁(z)/dt=D(d²C₁(z)/dz²)-v dC₁(z)/dz + J1

and

dC₂(z)/dt=D(d²C₁(z)/dz²)-v dC₂(z)/dz + J2

where C is the concentration in the fluid, t = time, z = distance, v = velcity, D = dispersion coefficient, and J is a flux term for C to the fluid

I want to combine to yield

d(C₁/C₂)/dt = ?

I can't work out the specific form of the chain rule or quotient rule I need to use... can anyone please help me? Be most appreciated!

 

[Chestermiller]

I don't think that that can be done. One must solve for the concentrations separately.