# Modeling the Diffusion of Fluorophores - Boundary Conditions Question

## Main Question or Discussion Point

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.

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?

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 Im 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

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