# Diffusion of a species through a sphere

1. Jun 20, 2013

### chatoma

Hi guys,

This is my first post here, this place looks like a great resource. Well, jumping straight in, I have a couple of questions on diffusion.

At work, I did a couple of experiments with Ion Exchange Resins. Not getting the results we wanted, my boss asked me to do an analysis of diffusion in two scenarios: through a simple "plate" (in 1 dimension), and through a sphere (in 3 dimensions).

Now, I am a Chem Eng, so this should be easy, but I have found myself struggling way more than I should with this topic; its a bit embarrassing at this point. For the first scenario, I used Ficks First Law, and I think that process was rather straightforward.

However, for the second scenario, I am completely stuck. So basically, I'm looking at diffusion in 3 dimensions; from the center of the sphere and to the outside. I don't think I need to complicate myself too much with technical details, so I'm assuming steady-state and I want to use Fick's First Law again. As I understand it, for 3 dimensions, Fick's Law is: J = -D∇C (where J=Diffusive flux, D=Diffusion Constant, C=Concentrations).

Now if I'm correct, this would work out as: J = -D(∂C/∂x + ∂C/∂y + ∂C/∂z). Would you guys agree, thus far, I am on the right track? If so, now the embarrassing part is that I'm not sure what to do next. That means, I'm not sure how to solve for J. Also, I was going through some reading material, and I saw that using spherical coordinates might make my life easier; is that correct?

Although its been two years, I can't believe I've forgotten so much about mass transfer...I'm actually kind of glad I'm getting these assignments so that I can brush up on this essential stuff. But anyways, any help is appreciated, and any clarifications/questions, I'll try to answer them in a timely fashion. Thanks!

chatoma

2. Jun 20, 2013

### Staff: Mentor

The equation is solved for J.

If you have a spherical symmetry, spherical coordinates are better, indeed.