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To find the contact angle made by a droplet on a flat surface at equilibrium, we take the sum of all surface tensions at the boundary of the droplet to be equal to zero (Wikipedia link). Projecting surface tensions in the horizontal direction gives Young's equation: $\gamma_{SG}=\gamma_{SL}+\gamma_{LG}\cos(\theta)$.

My problem is with the vertical component of these tensions: enter image description here Taking only surface tensions into account, clearly the vertical component is different from zero ($\gamma_{LG}$ is the only tension with a vertical component and there's nothing to counter it), so the boundary point cannot be at equilibrium. What is missing?

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Gravity and the normal contact force are the other two forces that balance the vertical component, such that it will be in equilibrium.

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  • $\begingroup$ And what if the droplet was sticking to the ceiling? $\endgroup$ – Tofi Sep 24 '18 at 10:54
  • $\begingroup$ @Tofi: There will be no normal contact force, and the gravity will balance the adhesive and cohesive forces. $\endgroup$ – user7777777 Sep 24 '18 at 11:29
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The vertical component induces a state of stress in the material (tensile at the boundary of the drop, potentially compressive or shearwise elsewhere). It's typically assumed that the solid wall is rigid or at least sufficiently stiff that the resulting wall deflection from this stress is negligible. See here for what happens if this assumption is not met. The emerging field addressing this scenario is called elastocapillarity.

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