Analiza kapljica vode: klasični i kvantni hidrodinamički okviri

The design of a sprinkler irrigation system is always associated with a full understanding of the kinematics of the droplets during their aerial path. Resolving this problem involves both theoretical and experimental considerations. Among the theoretical studies the classical mechanical approach, based on the Newton’s law, offers a useful tool to describe the trajectories of water droplets from the sprinkler nozzle to the ground. 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, it is also observed an inter-droplet reciprocal repulsion, mainly due to electrical interactions between the hydrogen and the oxygen atoms of the different water molecules. An alternative to traditional classical procedures, to analyse water droplet dynamics in sprinkler irrigation, has been recently proposed in the form of a quantum approach. In this context, the whole classic-quantum and single-droplet versus multi-droplet alternatives need to be discussed and pinpointed and these are 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 flow related phenomena. On the whole, the new approach leads to the concept of quantum trajectory in analogy to the well-established concept of classical trajectory and allows to recast the classical fluid dynamic equations into the so-called quantum equations.Konstrukcija sistema za navodnjavanje sa rasprskivačima uvek je praćena potpunim razumevanjem kinematike kretanja kapljica kroz vazduh. Rešavanje ovog problema uključuje, kako teorijska, tako i eksperimentalna razmatranja. Među teorijskim studijama, klasični mehanički pristup, zasnovan na Njutnovim zakonima, daje korisno sredstvo za opis putanja kretanja kapljica vode od rasprskivača do tla. Problem postaje još komplikovaniji kad se ne posmatra samo jedna sama kapljica, već system više kapljica. Pored inter-parametarskih zavisnosti, proučavano je i među-kapljično uzajamno odbijanje, najviše usled električnih interakcija između atoma vodonika i kiseonika iz različitih molekula vode. Alternativa tradicionalnim klasičnim postupcima za analizu dinamike vodenih kapljica pri rasprskavanju, nedavno je ponuđena u obliku kvantnog pristupa. U ovom kontekstu treba proučiti ceo sistem klasičnog i kvantnog pristupa kao i alternative jedno-kapljične i više-kapljične strukture, pa su ovo osnovni ciljevi predstavljenog rada, koji se fokusira na teorijski deo problema, čime naglašava nove perspektive i celovitije obuhvata fenomen toka rasprsnutog spreja. Uopšte, novi pristup vodi do koncepta kvantne putanje u analogiji sa dobro ustanovljenim konceptom klasične trajektorije i dozvoljava da se prerade klasične jednačine dinamike fluida u tzv. kvantne jednačine