Understanding Diffusion: The Relationship Between RMS and Fick's 2nd Law

[Lindsayyyy]

Hello everyone,

I have a question concerning the following:

There is a relationship for diffusion concerning the RMS:

<x^2>= 2\cdot D \cdot T for one dimension and there is also Fick's 2nd Law.

When does the above formula apply?

What I don't understand is that in the RMS formula there is no dependancy on concentration. But if I understood it correctly from Fick's 2nd law the higher the concentration gradient, the higher my change of concentration, which would mean the diffusion process takes place faster.

Can anyone help me?

Thanks in advance

Best regards Lindsayyyy

 

[DEvens]

Need some context. Where does your equation arise?

I'm guessing that your $<x^2>$ means something like $< x^2 \phi(x)> / <\phi(x)>$ so that the concentration divides out. Basically what it is telling you is, a concentrated spot of material will spread out such that the mean square distance it has traveled is proportional to time.