I’m working on single component multiphase flow - phase transition. In the published models, we only difine a single relaxation time for the system, both liquid and vapour have the same viscosities. In practical, how can we get different viscosities for two phases, multispeed or define relaxation time as a function of density?

this is a very interesting question. In my group a similar question appeared: Is it possible to model a fluid with shear dependent viscosity. My first idea would be to use tau as a function of density or shear rate or anything else, meaning that the viscosity is not constant anymore, but a function of some observable(s).
However, in order to show that this idea is practical, a Chapman-Enskog analysis should be performed. Maybe a non-constant viscosity would mess up with other observables.
I accompany Phoenixchen and would also be glad for some more established concepts.

instead of playing with the single-component ShanChen model, you could try to play with Multi-Component ShanChen model.
Let’s think in terms of your problem. You have two phases, the gas phase and the liquid phase. Using the Multicomponent algorithm you would have two particle distribution functions which will evolve in space and time following a BGK dynamic for example.
For each BGK dynamic (we could say for each phase) you will have the possibility to choose a relaxation time which that will give you the viscosity of each of your phases.
You could then set the two relaxation times in such a manner that your viscosities ratio could be different than 1. Anyway … to play too much with values of relaxation times far from the unity could give you some problem of… umm … stability. From my experience it’s not too difficult to handle viscosity ratios around 4.
If you want to take a look at the diagram of phase that you should expect using the multicomponent ShanChen model , I would suggest to take a look at this paper:

“Proposed approximation for contact angles in Shan-and-Chen-type multicomponent multiphase lattice Boltzmann models”

Authors: Haibo Huang, Thorne, Schaap, Sukop

Physical Review E 76. 066701 (2007)

there you can find some explanation on the Multicomponent model, the “diagram of phases” or something close to it (at least this is what I think it represent fig.2 in the mentioned paper. I would also say that instead of having phase transition you would have phase separation) and references to many other helpful papers.

In the book of Sukop about Lattice Boltzmann, both the Single Component and the MultiComponents methods are explained.

Umm… Indeed, in case you are interested, the Multicomponent ShanChen model is implemented in OpenLB.

Thanks, Timm and Ciao.
Since I’m new to LBM. These days, i’m working on the SCMP model without considering the viscosity issues, which is my next step. I’ll update my state on it.

I validated SC multiphase model on caviation flow. For 2D, the bubble growth agrees with Rayleigh-Plesset equation very well (withou considering viscosity variation). Now, I can dig a little deeper on this model - the viscosity-density relation.

Timm’s idear rings the bell with me! Do you study Rheology? I worked on it for 2 years as a postdoc.

my research topic is hemorheology (blood rheology). Right now I am studying literature and collecting ideas for the simulation of a collective of red blood cells. Multiphase models are insufficient to simulate blood on the smallest scale, since the membrane dynamics of the cells has to be captured accordingly.
An important point is that red blood cells have an interior viscosity five timer larger than the outside plasma fluid. Most people ignore this in their simulations, but for a detailed approach this has to be taken into account. So I would also be very glad for ideas.