contact angle between liquids
 

Hello,

I would like to know how the contact angle at the interface of two liquids (for ex : a water droplet on an oil surface) is determined. I tried a lot to find out any theories to give a quantitative model or formulae to find out the contact angle at the interface (as shown in fig. which I found in google, but couldn't find out the source of it !) but none was there. Can anybody pls explain or point out to me the way to obtain a contact angle for this problem ?

Moreover, when the oil droplet relatively moves over the water surface, do we still have the problem of moving contact lines as in the case of a droplet on a wall (with no slip) ? Is the shikhmurzaev model applicable to this case?

Regards,
Manxu.

Try this paper:

Chang-You Lin, Michael Widom, Robert F. Sekerka, "Mean-field Density Functional Theory of a Three-Phase Contact Line", Physical Review E, 85(1), 2012.

http://pre.aps.org/abstract/PRE/v85/i1/e011120

Thank you for your reply. :)

That was really worth a read.
Although implementing them might be difficult, by any chance, do you know if they are being taken care of in fluent or openFOAM's VOF or Euler-Lagrange model ?

Hmmmmm, the force balance is being satisfied in those solvers, so I'm guessing at least the equilibrium state equations should be satisfied (if they ask for all possible pair surface energy values). Not sure about the dynamic case though.

The Navier -Stokes equations are incompatible in a no-slip boundary condition and moving contact line (along the solid boundary).

So, as in my case, are the Navier Stokes equation compatible along the liquid-liquid-fluid (ie., oil-water-air) contact line ? If so, there shouldn't be a problem with the dynamic contact angle in my case if I run it in fluent or CFX right ?

It should be, but the thing that worries me is that the interfaces are not sharp. For a diffuse interface, such as the ones you get from VoF, there might be some issues.