about phasefield or second gradient theory
Recently, I study the papers about using the phasefield or second gradient theory to simulate twophase flow. I am a little confused.
In short, does this method just add some special terms into NS equation, and using the van der vaals equation of state to closing the equations? any one can give me a hint? thanks a lot 
Re: about phasefield or second gradient theory
I know twophase flows well but I have never heard about phasefield or second gradient theory. If you can give me a reference to a recent publication in this area, may be I can help. If you want to model compressible or variable density flows you need an equation of state that gives a relationship between density, temperature, and pressure. It can be van der Vaals equation or any other equation that is appropriate for your system.
Angen 
Re: about phasefield or second gradient theory
You can ask Junseok Kim, he knows everything about it.
http://www.ima.umn.edu/~junkim/papers.htm Also Jacquemin (?) in NASA microgravity program is the person to contact. 
Re: about phasefield or second gradient theory
The paper is: Jamet et la. The second gradient method for the dirext numerical simulation of liquidvapor flows with phase change. Journal of computational physics 169, 624651, 2001 I do not know the specific van der waals equation to close the equations in (6)(8) stated in the paper.
thanks a lot 
Re: about phasefield or second gradient theory
Thanks for a link. I am going to explore some of these ideas.
Angen 
Re: about phasefield or second gradient theory
Thanks for a reference. I am going to get a copy of the paper and later I may be able to say more. Meantime you can find information on van der Vaals equation in any textbook in thermodynamics.
Angen 
Re: about phasefield or second gradient theory
I have got the paper. It is interesting how some ideas that were quite popular in 40ies and 50ies see a renewed interest. At that time the concept of finite size of vaporliquid interface was mainly used to caluculate surface tension based on the molecular properites. Here it is used as a way to determine the location of liquid vapor interface fully in a macroscopic contest. It is my feeling that although this idea may be useful for systems that are close to critical point it's usage is more problematic to the systems close to a triple point.
van der Vaals equation apears in the paper in reference to two different equtions. The first one is eq (1) in the paper expressing free energy in terms of bulk free energy plus a term dependent on pressure gradient. If you use eq. (4) you can recover a classical equation for free energy with surface tension. The second type is the famous van der Vaals equation of state (not written down in the paper) as depicted by isotherms in Fig. 3. However, authors are using mainly a modified equation of state due to the finite size of liquidvapor interface. If you would like to implement this method and have trouble to close equations the best would be to contact authors. There are email addresses of the first two authors. If you decide to implement this method please let us know your opinion about it. Angen 
Re: about phasefield or second gradient theory
Your commend has been highly appreciated. I am quite new to this field. I do not want to implement this method totally, I just want to figure out how it could simulate the contact angle. maybe I can simulate the contact angle using the conventional cotinuum surface tension method.
In addition, do you have any commend on the simulation of the contact angle or contact line. Thanks a lot. 
Re: about phasefield or second gradient theory
The only way I determined contact angle in the past was by using a static balance of three surface tensions between solid surface, liquid and air. That is not necessarily valid for moving boundaries. I read a paper by Smolarkiewicz where he solve a problem of half drop on the surface spreading under the influence of gravity. I do not remember exact reference. It seems to me it was Journal of Computational Physics in late 90ies. For more information on contact angle you may try to search through Google with "Dynamic surface tension" or "Dynamic contact angle".
Angen 
Re: about phasefield or second gradient theory
Mr. Angen. Thanks for your comment. I am interested that paper just because it can simulate the contact angle. I will find more about it. thanks

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