Abstract
One of the most challenging modelling problems in science is that of a particle crossing a gaseous mean. In sprinkler irrigation this applies to a water droplet travelling from the nozzle to the ground. The challenge mainly refers to the intense difficulty in writing and solving the system of governing equations for such complicate process, where many non-linearities occur when describing the relations and dependences among one influential parameter and another. The problem becomes even more complicate when not just a single droplet alone is assessed but a multi-droplet system is accounted for as, in addition to the inter-parameter dependencies, it is also observed an inter-droplet reciprocal affection, 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 have 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 and these 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 flow related phenomena.
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References
Molle B., Tomas S., Hendawi M., Granier J., Evaporation and wind drift losses during sprinkler irrigation influenced by droplet size distribution, Irr. and Drain., 2012, 61, 240–250
Edling R.J., Kinetic energy, evaporation and wind drift of droplets from low pressure irrigation nozzles, Trans. ASAE, 1985, 28, 1543–1550
Keller J., Bliesner R.D., Sprinkler and Trickle irrigation, Van Nostrand Reinhold, New York, 1990
Kincaid D.C., Longley T.S., A water droplet evaporation and temperature model, Trans. ASAE, 1989, 32, 457–463
Kinzer G.D., Gunn R., The evaporation, temperature and thermal relaxation-time of freely falling waterdrops, J. Meteor, 1951, 8, 71–83
Thompson A.L., Gilley J.R., Norman J.M., A sprinkler water droplet evaporation and plant canopy model: II. Model applications, 1993, Trans. ASAE, 36, 743–750
De Wrachien D., Lorenzini G., Modelling jet flow and losses in sprinkler irrigation: overview and perspective of a new approach. Biosystems Engineering, 2006, 94, 297–309
Lorenzini G., Simplified modelling of sprinkler droplet dynamics, Biosystems Engineering, 2004, 87, 1–11
Lorenzini G., Water droplet dynamics and evaporation in an irrigation spray, Trans. ASABE, 2006, 49, 545–549
Dirac P.A., Quantized singularities in the electromagnetic field, PRS, 1931, A133, 1–60
De Wrachien D., Lorenzini G., Mambretti S., Water droplet trajectories in an irrigation spray: the classic and Quantum Mechanical pictures. 40th International Symposium on Agricultural Engineering, (February 21–24, 2012 Opatija Croatia), 2012, 85–96
Nottale L., The theory of scale relativity, 1992, IJMP, 7, 4899–493
Goldstein S., Tumulka R., Zanghi N., Bohmian trajectories as the foundation of quantum mechanics, Quantum Trajectories, 2011, 1–15
Teske M.E., Hermansky C.G., Riley C.M., Evaporation rates of agricultural spray material at low relative wind speeds, Atomization and Spray, 1998, 8, 471–478
Teske M.E., Thistle H.W., Eav B., New ways to predict aerial spray deposition and drift, J. Forest., 1998, 96, 25–31
Teske M.E., Ice G.G., A one-dimensional model for aerial spray assessment in forest streams, J. Forest., 2002, 100, 40–45
Hewitt A.J., Johnson D.A., Fish J.D., Hermansky C.G., Valcore D.L., Development of spray drift task force database for aerial applications. Env. Tox. Chem., 2002, 21, 648–658
Bird S.L., Perry S.G., Ray S.L., Teske M.E., Evaluation of the AGDISP aerial spray algorithms in the AgDRIFT model, Env. Tox. Chem., 2002, 21, 672–681
Bird R.B., Steward W.E., Lighfoot E.N., Transport Phenomena, Wiley and Sons, New York, 1960
Lopreore C.L., Wyatt R.E., Quantum wave packet dynamics with trajectories, PRL, 1999, 82, 5190–5193
Wyatt R.E., Quantum Dynamics with Trajectories: Introduction to Quantum Dynamics, Springer, 2005, 1–405
Ghosh S.K., Quantum fluid dynamics within the framework of density functional theory, Quantum Trajectories, 2011, 183–195
Hermann R.P., Numerical simulation of a quantum particle in a box, J. Phys. A: Math. Gen., 1997, 30, 3967–3975
Al-Rashid S.N.T., Habeeb M.A., Amed K.A., Application of the scale relativity (ScR) theory to the problem of a particle in a finite one-dimensional square well (FODSW) potential, JQIS, 2011, 1, 7–17
Madelung E., Eine anschauliche Deutung der Gleichung von Schroedinger, Naturwissenschaften, 1926, 14, 1004–1004
Bohm D., A suggested interpretation of the quantum theory in terms of hidden variables — I, Phys. Rev., 1952, 85, 166–179
Bohm D., A suggested interpretation of the quantum theory in terms of hidden variables — II, Phys. Rev., 1952, 85, 180–193
Kendrick B.K., Direct numerical solution of the quantum hydrodynamic equation of motion, Quantum Trajectories, 2011, 325–344
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De Wrachien, D., Lorenzini, G. Water drops kinematic analysis: the classic-quantum and single-multiparticle viewpoints. cent.eur.j.eng 3, 121–125 (2013). https://doi.org/10.2478/s13531-012-0027-z
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DOI: https://doi.org/10.2478/s13531-012-0027-z