The box is used as an emitter and for the Source's Outgoing Velocity there are two noise textures used as a mask to randomize the emission and create small and big droplets.
In the Dynamics rollout the Surface Tension to 1 so that the liquid can be accumulated in a bigger drops while travelling downwards and a Droplet breakup of 0.4 is set so that droplets can be formed. The Wetting is turned on and some Sticky liquid is added in order for the drops to stick to the surface.
As we want some drops to stay stationary and some to fall dawn there is a Phoenix Mapper node added which sets the Viscosity for the Grid to 0.2 using an Output map. As this works on the whole grid a noise texture is added as a mask so only some parts will be affected by the Mapper and the rest will not.
