Need help with Henry's Law

[CapriRacer]

TL;DR

A tire engineer needs help with Henry's Law relative to the infiltration of oxygen into a nitrogen inflated tire.

Tire engineer here!

I'm writing up an article concerning the Law of Partial Pressure of Gases - Dalton's Law.

Tires are ever so slightly permeable, so air leaks out at a rate dependent on the individual partial pressures AND their individual diffusion rates. Please note that it is difficult to estimate the diffusion rates because different tires use differing types of rubber, plus the rubber is not a constant thickness. Please also note that the seal between the tire and the rim is imperfect and also varies a lot.

But if I take the case where the tire is inflated with nitrogen, I know that oxygen leaks back into the tire's pressure chamber. This has been verified by a paper delivered to Tire Society in 2007. Unfortunately, this paper was never published.

This is similar to Henry's Law, but that involves an exchange of gases dissolved in a liquid diffusing into air - and vice versa. Henry's Law is frequently cited when discussing breathing - in particular, oxygen entering the blood vs carbon dioxide exiting the body, through the lungs.

I intend to cite Henry's law to explain this oxygen migration into a tire, but this is gas-to-gas exchange. In my research, I didn't find any mention of gas-to-gas relative to Henry's Law.

Can anyone help me tie up this loose end?

[Unnecessary commercial link redacted by the Mentors]

 

[Chestermiller]

Henry's Law tells us that the concentration of oxygen in the rubber at its outer surface is equal to the partial pressure of oxygen in the air times the Henry's law coefficient: $C_o=p_oH$, where $p_o$ is 0.21 bar. Similarly, the concentration of oxygen in the rubber at its inner surface is equal to the partial pressure of oxygen within the tire gas $p_i$ times the Henry's law coefficient: $C_i=p_iH$. Interior to the rubber, the diffusion flux of oxygen is equal to the diffusion coefficient D times the concentration gradient: $$\phi=-D\frac{\partial C}{\partial x}$$ where x is the distance measured from the inner wall. At quasi steady state, this becomes:$$\phi=D\frac{C_i-C_o}{\delta}$$where $\delta$ is the total wall thickness. Combining the previous equations gives: $$\phi=\frac{D}{H}\frac{p_i-p_o}{\delta}$$