Critical Inclination
Dear FOAMers,
im struggling for about three week with a tiny problem. I want to simulate a simple spherical droplet on an inclined plane and find out at which inclination the droplet (to be more specific the contact line) will start to move. I started with a very simple case (2D). First i used the standard dynamic contact angle modell which is implemented in interFoam. I set theta_A, theta_R, theta_0 (uTheta i still dont know what value it should take). Experimentally, for these contact angles, the droplet should start to slide at about 15 degrees inclination. In the simulation, the contact line moves even at very low inclinations (4 or 5 degrees). I tried to remove the parastic currents, refine the mesh, use alternative dynamic contact angle models, but all this without any success. I am sure that there are no forces that has to be added to the momentum equation. And I am pretty sure this has something to do with the contact angle model but i dont know how or what. Did anyone face such problem and came to a solution ? I would appreciate some help. 
Hello Callahance,
I am having the same problem with the dynamic contact angle model and was wondering whether you ever found a solution? Thanks 
Not really ... I found out that this whole thing has to do with the contact angle model. The models that are implemented in OF (i.e. constantContactAngle and dynamicContactAngle) won't give u good results. The droplet will slide even under 1 degree inclination angle. Other contact angle models are pretty complicated and till now i didnt find a physical correct solution for this (There are alot of tricks u can do in order to get what u want but physically they aren't totally correct)

From what I can tell there are two thing missing. As you already said the model for the contact angle hysteresis seems too basic, and it seems that the resulting force on the contact line is missing from UEqn.H:
f_cl = gamma (cos(theta)  cos(theta_e)) With gamma the surface tension, theta the actual contact angle, and theta_e the equilibrium contact angle. I'm not very familiar with C++, but I guess I'll have to try to implement it. 
Its not that easy. I tried the Kistler Model (you should find it somewhere here in the forum too) and the results weren't so good. Physically, there are no forces acting on the contact line, but rather the adhesion forces between the fluid and the solid surface. These adhesion forces (intermolecular forces) are not implemented (?) in OF. The solution u suggested by adding the force on the contact line is exactly what i meant in my previous reply by "trick". It is physically not really there but it should give you the results you want.
By the way the implementation of the Kistler Model wasn't that easy too. So i guess if u want to implement your own contact angle model, u should have pretty good experience with programming.. 
Dear callahance and boeleman,
First to clarify something:the dynamicalphacontactangle model in openfoam is NOT meant to model contact line pinning because, as the name already indicates, it is meant to model DYNAMIC contact angle behaviour so the dependence of the contact angle on the velocity of the contact line. The model in openfoam is rather limited for this, a better, well known model is the Cox voinov model, which is easy to implement. But again this is for dynamics so you don't want this. The thing that you two want is a model for contact angle hysteresis. This doesn't exist in Openfoam and is pretty difficult to implement because you need to derive the change in contact angle as a function of the change in alpha1 in a cell. I am currently working on an implementation of the method by Fang et al. (2008 in IJMF) Cheers, michiel 
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I also tried different implemented models such as Seebergh , Jiang, and others, but Kistler gave me the best results. Here is for example a result of the kistler model (contact angle vs. Capillary number). U can clearly see the hysteresis for Ca=0. 
Hi Callahance,
Could you explain to me why the Kistler model is supposed to give contact angle hysteresis?! If I look at the equation: Code:
thetaD=fHoff (Ca + 1/fHoff(thetaE)) 
I don't really know that "much" about the implementation of the Kistler model. But in the thread concerning this implementation (see link below), the hysteresis was briefly mentioned. You can take a look if you like.
http://www.cfdonline.com/Forums/ope...tactangle.html 
Ah ok, now I see what the thing is.
The Kistler model itself doesn't model hysteresis. It is just that adding the following lines will do that (see the post you mentioned for details): if uwall>0 theta0 = thetaR if uwall<0 theta0 = thetaA [Edit] I just tried what happens if I implement this condition in the CoxVoinov model implementation that I have and it behaves pretty badly. The contact angle jumps up and down between the advancing and receding angle due to small spurious currents in the boundary cells. 
Exactly! ... these currents cause a nonzero velocity in the cells which means that the droplets moves no matter what inclination angle the plane has. I tried to reduce these currents as much as possible but i think its impossible to make them disappear. Thats why its not trivial to simulate the critical inclination without doing any "trick" (i.e. adding a force or other kind of interaction between the droplet and the solid surface). Anyway if u find a solution for this problem i would be really interested..
I also guess that the solver interFoam is not built for such flows (milli and micro problems). 
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