Disclaimer: I work in applied math and have limited background in Physics. Need a bit of help here.
This droplet is also experiencing gravity, which points directly downwards.
Assuming the droplet has a mass of $m$, gravity constant $g$ and has some reasonable volume profile (shape) that you may specify (this is used to determine contact area and perhaps to get surface tension if need be).
What is the critical bifurcation volume of the droplet so it would stick to the surface?
Or an easier question maybe: what is the adhesive forces between the droplet and the surface?
Even easier question: what is the adhesive force, assuming the contact area is of size $A$?
I'm guessing some roughness constant might need to be specified. So just specify this constant if need be. Thanks in advance!