Create balance with an equation between the weight of the particles, the air pressure and the centrifugal forces according as altitude from ground level, then prove how the particles not thrown to the space under the effect of the most one of largest physical power that "diffusion" only there on the edge of the atmospher.
That's easy! We don't need any new equations.
At the altitude of geostationary satellites, 35,786 km, the centripetal acceleration exactly matches the gravitational acceleration.
So,
if the atmosphere at that altitude rotated at the same angular velocity as the earth (I don't believe it would, but just assume it does) there would no longer be any nett attraction to keep it on the earth.
But, at that altitude, the mean density of the atmosphere is only 4.04 x 10
-19 kg/m
3 compared to 1.225 kg/m
3 at sea level.
That density would be far better than an extreme high vacuum.
In other words even if the atmosphere at that altitude were rotating with the earth there is simply not enough there for diffusion to matter.
Actually at that altitude an insignificant amount of atmosphere is lost but some gases are also collected from the Solar Wind.