density gradient driven mass flows in gases
I am struggling to understand how the following problem can be stated within the two-species species Navier-Stokes equations with diffusion.
The following is an incompressible, low-pressure gas flow in the hydrodynamic regime.
Consider a long thin tube, left half filled with a light gas (hydrogen, helium), the right half with a heavy gas (Argon, Xenon). The two halves are separated by a barrier. Gases are at same temperature and pressure.
At time t=0, we remove the barrier, and the gases start diffusing. Since the light gas is diffusing in to the heavy gas, and the other way around, there is a mass flow from the right to the left.
I can derive diffusion driven mass flow the diffusion equations. How do I couple that with the Navier Stokes equation?
Momentum transfer is handled by the Navier-Stokes equations. But the NS equations only have external forces and the pressure gradient as the driving term. Is the diffusion the external forcing term?
What am I missing?
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