Water droplets tend to have a spherical, round shape, explain ths fact in terms of the polar nature of water molecules

What does it happen in smallest scale? 
You have to look for "DUPRE' EQUATION" which treat about 
"TWO-PHASE INTERFACIAL FORCEs". 
At boundary surface between two aggregation phases, you may attribute upper energy level to molecules standing at the boundary zone. So, it has to define INTERFACIAL FORCEs WHICH ACT TO REMODEL SHAPE AND EXTENSION OF MEETING PHASEs. 
In your case, Water's Droplet is a liquid phase surrounded by Air (e.g. gas phase) and Interfacial Forces act to dominate Boundary-Surface. 
Mathematically, smallest possible Surface comes to SPHERICAL SHAPE. 

500bc indiais the answer.