Water droplet trajectories in a sprinkler spray flow: the classic versus quantum and single versus multi-droplet pictures

One of the most challenging modelling problems in modern engineering is that of a particle crossing a continuous phase (air). In sprinkler irrigation practice this may refer to a water droplet travelling in air from the nozzle to the ground. The challenge mainly refers to the diffi culty in designing and solving the system of governing equations for that very complicate process, where many non-linearities occur when describing the relations and dependences among the parameters that rule the phenomenon. The problem becomes even more complicated when not just a single droplet alone is assessed but a multi-droplet system is accounted for. In addition to the inter-parameter dependencies, an inter-droplet reciprocal connection is also observed, mainly due to electrical interactions between the hydrogen and the oxygen atoms of the different water molecules. An alternative to traditional classic approaches to analyse water droplet dynamics in sprinkler irrigation has been recently proposed in the form of a quantum approach, but the whole classic-quantum and single-droplet versus multi-droplet alternatives need to be discussed and pinpointed which are among the main aims of the present paper which focuses on the theoretical part of the issue, thus highlighting the new perspectives of a deeper comprehension in the spray fl ow related phenomena.