Henry's law solubility
 

Hi,

I am using the reactingMultiphaseEulerFoam to model migration of oxygen between a liquid and gas. The solution/dissolution of gases is modelled using Henry's law. Looking at the header file (Henry.h) i see that the model asks for the dimensionless Henry constant which is usually the ratio of the mass of the species in the liquid and gas. The source file however (Henry.C) multiplies the constant by the liquid density and divides by the gas density. This suggests that the input should actually be the volumetric ratio of the species. Is that correct? Should we give the values of k as the volume of the species in the liquid over the volume of the species in the gas?

Thanks in advance for your help

Cheers
Mike

Hi Michael,
if you have a look into bubbleColumnEvaporatingDissolving the Henry constant for air dissolved in water is 1.492e-2 that corresponds to moles of gas dissolved per liter of solution/moles of gas, as you can see from here:

ftp://mana.soest.hawaii.edu/pub/rluk...0and%20Air.pdf

Simone

Hi Simone and thanks for your response.

I am slightly confused with the denominator. Could you please clarify? Is it the number of moles of the gas per unit volume outside the liquid?


Thanks again for your help

I think so, is the number of moles of the component per unite volume in the gas phase, i.e. the gas-phase concentration of the component.

Yeah. I think that is the only thing that makes sense.

Thanks. This has been very helpful

Did you understand why there is liquid density divided by gas density?

Yes. Henry's constant is K=Cs/Cg (Cs is the concentration in solution and Cg in the gas). However, we don't directly have Cg. We have the percentage of that species in the total gas Yg. Also, the function in Henry.C actually returns the percentage of the species in the solution, Ys. So
Cs = Ys*Rs (mass of the specific species per unit volume of solution)
Cg = Yg*Rg (mass of the specific species per unit volume of gas)
where Rg and Rs are the densities of the gas and solution.

Inserting these into the first equation and re-arranging a bit we get:
Ys = K*Yg*Rg/Rs


Does that make any sense?

The formula that you reported is the implemented one in Henry.C, but if C indicates the number of moles of the component per unite volume, the right formula should be:

Ys = K*Yg*Rg/Rs*Ms/Mg

where M is the molecular weight.
Is something missing in the code? :confused:

Yes. But you are forgetting that Ms and Mg refer to the same species, i.e. whether oxygen is dissolved in a liquid or free in a gas, it always has the same molecular mass.

You are right!
Thanks!:)

Hello,
Can i ask you the copy of said pdf file (bubbleColumnEvaporatingDissolving) as link is not working anymore? many thanks in advance.

Regards,
Umer

Hi Umer,

I don't really know if there is a pdf. However, you can find the test case in the tutorials of your OpenFOAM installation under
OpenFOAM-dev/tutorials/multiphase/reactingTwoPhaseEulerFoam/laminar/bubbleColumnEvaporatingDissolving

Henry's law is defined in constant/phaseProperties.

Hope this helps

Mike

Hello Mike,
thanks but i am looking for something that explains this tutorial. I am running this tutorial “bubbleColumnEvaporatingDissolving” but I am not sure about few things in it like (air.gas, air.water) I set in the “0” directory. When I see results on paraView>air.gas . Can you say few quick words about it. May be it will work for me.

1. air.gas, air.liquid shows mass fraction or volume fraction? or Is it showing mass fraction in each phase gas/liquid? It means mass fraction "Yair" is multiplied with "alpha.gas"?
2. How diffusivity Df is calculated in the solver? Or its just a constant?
3. How this solver calculate concentration gradient dY? Is it coming from Henry’s Law Ys=k.Yg.rhog/rhos then it is multiplied with rho.phase to get the concentration gradient dY for mass transfer term? mass transfer= K. Df. dY

Best Regards,
Umer

Hi Umer,

I found this which might help
http://www.tfd.chalmers.se/~hani/kur...eEulerFoam.pdf

To try and answer your questions:
1. alpha.air and alpha.gas are volume fractions. The Y.air Y.gas are the mass fractions.
2. In phaseProperties you give the Schmidt number. This, along with the density, can give you the diffusivity (so I suppose it is constant)
3. You basically define how your mass transfer is modelled in the phaseProperties file under interfaceComposition. Henry's law is one of the options. While I haven't found any documentation specifically for OpenFOAM, it is relatively similar to the way Fluent does it. Have a look at
https://www.sharcnet.ca/Software/Ans...-3A72B96D.html

Hope this helps
Mike

Hello Mike,
many thanks for the information you provided. The provided link is good to understand the solver. Can you tell me how can i calculate total mass of air present in the domain?
lets say if i inject mass 1kg/sec then after 5 seconds it should be 5kg but due to mass transfer it will be less. is there any way to check that?

Regards,
Umer

Hi, I am dealing with a similar case. But is it possible to move the boundary and compress a chamber while dealing with two phases by this reactingMultiphaseEulerFoam?

Fluent's link
 

Hi foamers,

Fluent's link is not working right now. Could you please help me find the correct one at this time?

This thread really help me.

Thanks a lot!
:)