Can Fick's Law Help Calculate Diffusion Time for a Spherical Balloon?

[Hilarycheung]

How to calculate the time needed for a perfectly spherical balloon with radius R to become R/2 due to diffusion of the gas inside, which is assumed to be nitrogen, by using Fick's Law of diffusion. Let the Young's Modulus be E.



Fick's First law: J=-D∂C/∂x




the change in pressure result to the change of the thickness of the balloon surface, which implies the diffuse distance will change, but i have difficulty on linking this together.

 

[aralbrec]

Can you assume the diffusion is really slow so that it's almost steady state? Then the concentration gradient inside the balloon wall will be a straight line joining the outside concentration of gas (constant) with the inside concentration of gas (is it constant?). As time passes, the wall thickens and the slope, controlled by those two fixed points, reduces so the diffusion rate reduces. If the density of the balloon wall is changing then maybe D is also a function of time?

Fick's first law is also formulated in terms of difference in pressure through a polymer of given permeability, just fyi.

This is not really my area but since no one answered, I thought I'd add a little and then ask you the questions :) I also think if the steady-state assumption can't be made, you'll have to look at Fick's second law but I think that is probably much more complicated than is intended for this question.

 

[Hilarycheung]

Thank you for your replying=)
i think there are too little information given, i should have done more research.