paperclip - you already posted this same question on the Physics forum, so you know there are other forums out there.
Personally, I know Ficks law & Stokes-Einsteins law of diffusion in a very general sense and I cannot derive what you are looking for. I believe that would be a question more appropriate to someone who is in a PhD course in chemistry. Obviously, the folks on the Physics forum didn't answer your question.
I do know that Ficks law can be applied to glass, which is technically a liquid. But, Ficks law 1 is applied to steady state when the concentration in the volume doesn't change. Ficks law 2 is applied to a non-steady state with continually changing diffusions. Einstein's law describes molecular movement in a liquid or a gas when particles move independently of each other. Stokes law describes spherical particle movement only, I think.
Your extrapolation of these equations to describe an AVERAGE diffusion rate is beyond what I know or have the ability to do. However, when I think of colloidal dispersions, I'm not sure there is an average law which describes them as a group, but there might be one which would describe them individually.
Good luck with your work. I think you have plenty of time between now & Easter (6 months?) to pursue the topic with the new professor. But - I'm curious, if you've not covered this yet, why pose the question? Perhaps after being presented with the material in a cohesive fashion, it will become clear.....
