This is a non-expert question on a (seemingly simple) text-book topic. The question is about "hydrostatic friction", defined as follows.
Consider a drop of water resting on a flat surface. If the surface is slightly inclined, then the drop will not run off but just stay in place.
Does this phenonemon have a simple description?
"Simple" as in "surface tension is simply described by a constant $\gamma$ which gives energy per unit area, $dE = \gamma \ dA$" or "Coulombic friction force is equal to normal reaction force times the coefficient of static friction $\mu_s$."
EDIT-1: First answer revived my hope for a simple gravity + surface-tension solution. If the glass plate were horizontal, the droplet "chooses" its energetically optimal contact area. Now the same with tilt (gravity):
- impose no-slip condition,
- minimize total energy with fixed contact area,
- compare two optimal shapes with slightly different contact areas.
I hope there will be a critical angle beyond which the gain of gravitational energy overcomes losses to surface tension. Need more effort to write down an solve the variational problem (in cylindrical geometry for simplicity).