# Multicomponent SC model

Dear all,
I have provided a FORTRAN code for simulating segregation of species in a two-component flow based on multicomponent SC model. In Sukop’s book, the interaction force is given by:

F[sub]1[/sub] (x)= -G*psi[sub]1[/sub] (x,t)*Sigma [sub]a=1 to 8[/sub] [w[sub]a[/sub]*psi[sub]2[/sub] (x+e[sub]a[/sub]delta t, t) e[sub]a[/sub] ]

Where the weights w[sub]a[/sub] are 1/9 for a = 1, 2, 3, 4, and 1/36 for a = 5, 6, 7, 8. In other references, I could not find such weights in the formulation of the interaction force. For example see Matlab example written by Malaspinas et al. (2008).Can any one help me to know the reasons of this disagreement?

Hi,

your force term seems to be fine to me (for reference … look at the early works of Shan about the Multi Component Model and pay attention to the fact that in one of the first paper the use an exagonal lattice instead of a D2Q9) . Moreover you are right… in the script written by Orestis something is missing.
I’ll ask to Orestis to correct the matlab script.

Ciao
Andrea

Thanks ghassemi for reporting the error, and thanks Andrea for correcting it. It’s amusing to see how good a multi-phase simulation can look, even though it contains a bug…
The code on lbmethod.org has been updated. You may need to empty your browser cache before re-downloading it, to be sure to get the new version.

Thanks Andrea and Jonas;
I downloaded the updated matlab script. I compared the script with my Fortran code and got similar results with the same input parameters. In the updated script, the value of G has been changed from -0.05 to -1.2 . Altough I have no experience on choosing the value of G for modeling multicomponent problems; searching some papers I found that G is usually in the order of 0.01 to 0.1. But in this problem, using so small values does not lead to segregation of fluids! May be the codes have still some bugs!? Or if everything is correct, please let me know how one can select G for a specified problem? and which parameters it depends on?

Hi;
In the above equation, is G a dimensionless parameter? If so, what is the true dimension of F?

A G in the area of 0.01 to 0.1 looks awfully small to me, but maybe they have been operating on hexagonal grids. Even so, Shan and Chen’s original 1993 paper used a G>1/6.

Remember, since the D2Q9 model introduced the w[sub]a[/sub] weights, you need to multiply G up by a factor 9 in order to compensate for it.

I don’t think there is any really easy way to figure out which G you want to use, or even which G is needed to segregate fluids at all. Shan and Doolen 1996 (“Diffusion in a multicomponent lattice Boltzmann equation model”) gave an equation where G[sub]C[/sub] (the lowest G you can have in order to get segregation of phases at all), is smallest if the amount of red and blue fluid is equal, and my experience with S-C seems to agree with them.

Dear Sigvat,
Thanks for your comments.I think you have considerable experience with SC model. Results of my analyses with this model show that the maximum obtainable viscosity ratio between components is about 5. In fact, when I input high viscosity ratio, some miscibility occurs and the ratio of real viscosities (viscosities of the mixture) is alwasys less than 5. Is this correct? Is it possible to simulate two components with viscosity ratio of 10 (e.g. Crude oil and water) with SC model?
Best Regards

I haven’t really tested the different viscosity scenario much, but you may want to read an article by Chin, Boek, and Coveney: “Lattice Boltzmann simulation of the flow of binary immiscible fluids with different viscosities using the Shan-Chen microscopic interaction model”, published in Phil. Trans. R. Soc. Lond. A. (2002) vol 360.

Thank you Sigvat.