there's two separate things at play here Dalton's gas law if i remember correctly states that a static mixture of equal gases will uniformly distribute. We know this to be true, because if it wasn't Argon/helium gas mixtures or virtually any gas mixture would separate out into it's components in our gas cylinders. And the low spots of earth's atmosphere would be full of the heavy gases like argon and xenon.
That is the assumption that they are a STATIC mixture in a container given enough time to fully diffuse (Which doesn't take that long). This diffusion issue is key in high performance engines where the oxygen and fuel vapor only have a fraction of a second to completely mix. Ideally the fuel mixture would be completely mixed before entering the cylinder.
Now lets investigate purging.
In purging we are now talking about displacement in which a very heavy gas such as argon displaces the lighter air mixture over a short period of time. Therefore you would bleed the air out of the top. Some diffusion will take place but the purge volume is generally cycled several times and doesn't have to be 100% perfect for most welding operations.
IF you were to say displace all the air in a fish tank with argon, and wait several hours with an open top, they would slowly diffuse and the oxygen level would slowly increase. IN critical materials that can't handle even very low PPM's of oxygen the atmosphere chamber is either placed under a high vacuum, or purged many times as there will always be some diffusion.