What is the barometric height formula for a mixture of gases?
The main problem I can see, the curves describing the minimal energy (kinetic + gravitational/centrifugal) won't be any more a simple derivative, but a functional equation.
I think, this or similar equations could be useful in very separate areas (isotope separation, estimating high atmosphere components of planets, etc.) Despite I couldn't find anything with google about this.
So, the question is: we have a high gas mixture in constant g gravity and T temperature. We know the $p_1$, $p_2$, ... partial pressures of the gases on the $h=0$. Of course we know every relevant constants of the gases, too. What is their minimal-energy, isothermic, height-dependent partial pressure function $p_n(h)$?