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# Capturing wetting angles in transient simulations of fluids

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.

This equation is only valid for equilibrium, but even if I were to apply

p = 2 H γ

for each interface, the solid flat surface would still have zero curvature, H=0, thus resulting in zero pressure anyway, p=0.

I have seen some work, which more or less forces the wetting angle to a certain predetermined parameter (i.e. treating it as a material parameter), but then again, in that case only the equilibrium state would be correct.

This leads to my current predicament. What am i missing? Where should the surface energies for the other interfaces come into play?

I would love to hear someone else's input on this.

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