What forces act on a droplets hanging from surfaces? What are the different forces acting on a hanging water droplet (tension of the droplet itself, surface adhesive forces, meniscus formation, etc)? What is the direction of each force, and how does each affect droplet stability?
Will these forces be affected if the surface is flat vs patterned with some tiny structures? (assuming the surface material is the same)

 A: *

*Adhesion, normal to the solid-liquid interface, found only very near
the solid-liquid interface, increasing with proximity to the
solid-liquid interface. Makes the droplet stick to the solid surface.

*Cohesion, radially inward and uniform
throughout - each little bit of water is pulling on all the adjacent little bits. Tends the droplet towards spherical/hemispherical shape.

*Surface tension, tangent to the surface in all
directions, found only at the liquid-gas
interface. Not really its own force, this is just a consequence of the bulk force imbalance between inside the droplet where the cohesion force is present and outside the droplet where there is no such force. Tends the surface towards spherical / hemispherical shape and opposes penetration of the surface.

*Gravity, downward, uniform throughout. Tends the droplet to an elongated shape for the configurations depicted.

If we slowly dialed up gravity, the one on the left would drip first, since the total adhesive force is smaller.
