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Given

1) A fluid with known properties

2) a gas mixture above the fluid with known properties

3) A number-density of gas dissolved in the fluid

Is there a way I can find out the rate at which the gas is released from the fluid?

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There are a few different ways to do this, depending on your acceptable trade-off between model complexity versus accuracy. I might first try something such as the following:

Use Henry's Law to relate the partial pressure of the gas of interest above the liquid to the equilibrium concentration of that gas in the liquid. Assume the gas maintains that concentration just at the infinitessimally thin surface of the liquid that is in direct contact with the gas, and use that as a concentration boundary condition for the top surface of the liquid. Then use Fick's law of diffusion to model the mass transport of the dissolved gas in the liquid up toward the surface. You would need to know the (temperature-dependent) diffusion coefficient of that gas in that liquid (hopefully something you can look up). Based on your geometry, you can either model the liquid as being semi-infinite in depth (in which case your solution will take the form of an error function vs. time for the gas mass flux), or you can model the liquid as being of finite depth, with the bottom boundary condition being a zero-flux boundary condition (i.e. no additional gas dissolves into the liquid from below). Do this as a 1-dimensional problem.

This model assumes that the partial pressure of the gas above the liquid remains constant (i.e. the amount of gas escaping the liquid is negligible compared to the reservoir of gas, and is instantly dissipated away from the surface. For a more complex & accurate model, you'd need to model the diffusion (and possibly advection if there is any gas flow or temperature differences causing natural convection) of the escaped gas within the gas mixture above the liquid. In this case, you would need a boundary condition for the top of the gas, and you would connect the diffusion in the two regimes by conserving total mass flux of gas across the liquid-gas interface.

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  • $\begingroup$ Doesn't this require knowledge of the cover-gas above the resiviour as an intial condition? What if I start with the reseviour open to atmosphere in there is zero partial-pressure of the dissolved gas For example, if I have krypton dissolved in water, and the water is 'instantaneously' opened and placed in atmosphere. $\endgroup$ Oct 18, 2017 at 18:58
  • $\begingroup$ Yes, one of the implied assumptions with this approach is that all aspects of the gas above the liquid are treated as both known and constant in time. Based on the situation, if this is a severely inaccurate assumption to be making, then you would have to model the gas diffusion dynamics too and couple that to the liquid diffusion dynamics $\endgroup$
    – Sean49
    Oct 19, 2017 at 3:37

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