The water drops on lotus leaf are spherical in shape. But when they join and make a big drop ,why it becomes flat?
Answers
Why does a drop of water form a spherical shape on a flat surface?
The drop of water wants to minimize its energy. The energy of the drop comes from two different places - surface tension and gravity. Surface tension wants to pull the drop into a ball while gravity wants to flatten it out. (There are always other sources of energy around, but these two are that govern the behavior here.) What happens to the drop depends on which type of energy is more important. That in turn depends on how big the drop is.
Take a sphere of radius r . Its surface energy is proportional to r2 , while its gravitational energy is proportional to r4 , so gravity becomes more and more important at larger r .
Specifically, for a surface tension σ , the surface energy of the sphere is σ4πr2 and the gravitational energy is gr(ρ43πr3) where ρ is the density of water and g is local gravitational acceleration. (We have assumed here a complete sphere. In reality, the drop must sit on something, so there will be different surface tensions for each material interface, etc. We'll look here at water sitting on a super-hydrophobic surface and keep in mind that the true shape depends a bit on the circumstances.)
The ratio of surface energy to gravitational energy is
3σρgr2
When this number is large, surface energy is bigger and we expect a nearly-spherical shape. As the number decreases with increasing r , we expect the sphere to flatten out. Setting the number to one and solving for r , using σ=72dyne/cm , we get
r≈0.5cm
Drops much smaller than half a centimeter are dominated by surface tension and will be roughly spherical, while drops much larger than half a centimeter are dominated by gravity and will flatten out.