# Problem about single component multiphase SC model

Dear all,

I just turned to SC model. it can simulate single component multiphase flows with large density ratio.and i want to know how large density ratio this model can reach?can it reach to 1000? and why?
if the density ratio in this model can’t reach which model can?
first i think because it use mxawell construction, the density ratio with the SCMP model can’t reach too large.

Many thanks.

zhrleo

Dear zhrleo,

Usually you can achieve the gas-liquid density with usual Shan-Chen potential around 70-100. It can’t reach further because of spurious currents. But you can use some modifications of Shan-Chen model to achieve higher gas-liquid ratio:

1. Multirange model
PHYSICAL REVIEW E 75, 026702 ?2007?
Generalized lattice Boltzmann method with multirange pseudopotential
M. Sbragaglia,1 R. Benzi,2 L. Biferale,2 S. Succi,3 K. Sugiyama,1 and F. Toschi3

2. Different equation of states
PHYSICS OF FLUIDS 18, 042101 ?2006?
Equations of state in a lattice Boltzmann model
Peng Yuan and Laura Schaefer

Hopefully it will help,
Alex

Hi Alex,

Thank you so much for your help. I got some clues from the articles you give me.
I have another questions.how to define the density in the LB simulation?if i can define the density by LB simulation?

Dear zhrleo,

Could you please clarify - what do you mean by define the density? You initialize the density as you want on your grid, and then calculate it through sum of the populations.

Alex

I mean I want to simulate gas-liquid system. I set the liquid density 100 and gas density 1 in my LB,but I didn’t get the result.I know gas liquid can coexist only under the critical temperature. I want to define the density first to simulate at known temperature

Dear zhrleo,

You can’t initialize any densities you want for usual Shan-Chen model. First you need to calculate them from Maxwell reconstruction for certain temperature, i.e. G, and only then initialize. Please let me know if you need more details.

Hopefully it will help,
Alex

Hi Alex,

I know there are different densities for certain temperature (In S-C model with G to show temperature )from Maxwell reconstruction.if define densities by the equations below?

p=nl/3+Gpai(nl)/6
p=ng/3+G
pai(ng)/6
definite integral from ng to nl (p-n/3-G*pai(n)/6)1/n^2dn=0

I can’t slove the equations easily,do you have a good idea?
and do you help me to plot the Maxwell reconstruction curve?

best wishes

zhrleo

Dear zhrleo,

You are absolutely right. You need to solve those equations. I had some files in Mathematica and Mathcad to calculate the Maxwell reconstruction curve. Yesterday, I tried to find them but didn’t succeed. If you need them I will have another look to find them.

Also, those curves are presented in papers - I think original Shan-Chen papers, Succi and Sbragaglia papers and for different equations of states in

PHYSICS OF FLUIDS 18, 042101 ?2006?
Equations of state in a lattice Boltzmann model
Peng Yuan and Laura Schaefer

Hopefully it will help,
Alex

Hi Alex,