I am meeting with a problem, that is how to establish the diffusion equation for the transport of tracer in a vertical porous plane, in which we inject tracer at the bottom (I) and produce at the top (P) of plane. (see the figure)
The plane is initially saturated by water. Then we inject dye tracer at I, tracer step by step moves from bottom to the top under gravity effect and produce at P. But, I don't know how can we treat the gravity in the diffusion equation??
dC/dt + u.dC/dx = D.d2C/dx2
Looking forward to helping from all of you.
Thank you in advance!!