contact angle

Dear all,
I'm trying to simulate the transient behavior of a fluid and I'm finding it very difficult to capture the wetting angle.
To begin with, I only considering the idealized case.

The common approach is to apply the pressure load
p = 2 H γ
where p is the pressure (normal traction) on the surface, H is the Gaussian curvature of the surface, and γ is the surface energy
This load will of course always yield the same equilibrium shape for a viscous fluid, regardless of the value of γ.

Now, comparing with Young's relation, where one obtains a balance containing surface energies for every interface.