Modeling the Diffusion of Fluorophores - Boundary Conditions Question

[phil ess]

I am trying to model the diffusion of fluorophores in a cell with a source in the middle by solving the appropriate differential equation. I can solve the PDE easily enough, however as I haven't done DE's in a while, I need a refresher on how to apply the appropriate boundary conditions for my problem!

I am basically solving the diffusion equation with a source term in cylindrical coordinates with no theta dependence. Initially the concentration of fluorophores is C(r,z,t=0)=C₀, and I am assuming a sufficiently large volume that the net concentration of fluorophores is basically constant, and that at large r and z, C(r,z,t)=C₀.

How do I impose these boundary conditions mathematically when solving the diffusion equation? I have looked for online resources but it's difficult to find anything that addresses this specifically.

Any help is greatly appreciated! Also, if more information is needed please let me know!EDIT

Ok it seems easy enough, duh, the boundary conditions are just C(r,infinity,t)=C(infinity,z,t)=C₀ ?

And of course I assume a solution of the form C(r,z,t)=R(r)Z(z)T(t)

So does the initial condition then imply that R(r)Z(z)=C₀?

And what about the others?

Solving by separation I find a first order DE for T(t), a second order Bessel type for R(r) and another second order for Z(z), but again, I don't remember how to apply these boundary conditions!

Thanks again!

EDIT

I guess it would probably be useful to see the equation I am solving!

$$\frac{dC(r,z,t)}{dt} = -I \stackrel{2}{} (r,z) + D \nabla\stackrel{2}{} C(r,z,t)$$

Where the Del operator is in cylindrical coordinates with no theta dependence, as noted above

 

[Valerie Park]

.For the boundary conditions, I think what you said is correct, C(r,z,t)=C0 for r-> infinity, z-> infinity.And for the initial condition, it is C(r,z,t=0)=C0.The last thing I need to figure out is how to apply these conditions to the two second order DEs that I get after separating variables.Thanks again!