What does the behaviour of water on the skin of an aircraft in flight tell us?
This effect is likely caused by something called the &quot;boundary layer,&quot; first defined by German engineer Ludwig Prandtl in a paper he presented in 1904 at the third International Congress of Mathematicians in Heidelberg, Germany. From Wikipedia:

The effect of the paper was so great that Prandtl became director of the Institute for Technical Physics at the University of Göttingen later in the year.
Over the next decades he developed it into a powerhouse of aerodynamics, leading the world until the end of World War II. In 1925 the university spun off his  research arm to create the Kaiser Wilhelm Institute for Flow Research (now the Max Planck Institute for Dynamics and Self-Organization).

The math in the paper is complicated and frankly well beyond my paygrade, but the way I understand it, what I think you are seeing is caused by a laminar boundary layer that forms very close to almost all surfaces of the aircraft. It is a layer of air with high viscosity, low turbulence, low speed relative to the air farther out from the surface, and causing an increase in drag. That's why the water doesn't blow away or evaporate.
The image below is one I found which does a good job of presenting the two types of boundary layer -- laminar and turbulent. Look at how smooth the laminar boundary layer looks compared to the turbulent boundary layer. This might help to understand the concept better.

The boundary layer is also something I experienced with an experimental aircraft I restored that had an opening on the top right of the fuselage to feed air into the fuel injection system intake. As it was, air would essentially stop flowing into the system when the aircraft accelerated, and the engine would stop. Not good. In order to stop that from happening, a raised scoop had to be installed that extended above the laminar boundary layer and into the turbulent boundary layer. That solved the problem.