{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:42:47Z","timestamp":1760244167676,"version":"build-2065373602"},"reference-count":8,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2003,12,31]],"date-time":"2003-12-31T00:00:00Z","timestamp":1072828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The maximum entropy principle (MEP), which has been popular in the modeling of droplet size and velocity distribution in sprays, is, strictly speaking, only applicable for isolated systems in thermodynamic equilibrium; whereas the spray formation processes are irreversible and non-isolated with interaction between the atomizing liquid and its surrounding gas medium. In this study, a new model for the droplet size distribution has been developed based on the thermodynamically consistent concept - the maximization of entropy generation during the liquid atomization process. The model prediction compares favorably with the experimentally measured size distribution for droplets, near the liquid bulk breakup region, produced by an air-blast annular nozzle and a practical gas turbine nozzle. Therefore, the present model can be used to predict the initial droplet size distribution in sprays.<\/jats:p>","DOI":"10.3390\/e5050417","type":"journal-article","created":{"date-parts":[[2008,10,25]],"date-time":"2008-10-25T13:44:42Z","timestamp":1224942282000},"page":"417-431","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Droplet Size Distribution in Sprays Based on Maximization of Entropy Generation"],"prefix":"10.3390","volume":"5","author":[{"given":"Xianguo","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada"}]},{"given":"Meishen","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2003,12,31]]},"reference":[{"key":"ref_1","first-page":"195","article-title":"A Prediction of the Drop Size and Velocity Distribution in a Spray from First Principles","volume":"1","author":"Sellens","year":"1985","journal-title":"Atomization and Spray Technology"},{"key":"ref_2","first-page":"65","article-title":"Droplet Size Distribution: A Derivation of a Nukiyama-Tanasawa Type Distribution Function","volume":"55","author":"Li","year":"1988","journal-title":"Combustion Science and Technology"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1615\/AtomizSpr.v3.i3.30","article-title":"A Simplified Maximum-Entropy-Based Drop Size Distribution","volume":"3","author":"Ahmadi","year":"1993","journal-title":"Atomization and Sprays"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1615\/AtomizSpr.v6.i5.50","article-title":"Coupling of Classical Linear Theory and Maximum Entropy Formalism for Prediction of Drop Size Distribution in Sprays: Application to Pressure-Swirl Atomizers","volume":"6","author":"Cousin","year":"1996","journal-title":"Atomization and Sprays"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1615\/AtomizSpr.v9.i1.20","article-title":"A Predictive Model for Droplet Size Distribution in Sprays","volume":"9","author":"Mitra","year":"1999","journal-title":"Atomization and Sprays"},{"key":"ref_6","unstructured":"Li, X., Li, M., and Fu, H. Modeling the Initial Droplet Size Distribution in Sprays Based on the Maximization of Entropy Generation. Atomization and Sprays, submitted."},{"key":"ref_7","unstructured":"Fu, F. (2003). Experimental Characterization of Sprays from an Air-blast Annular Research Nozzle. [Master\u2019s thesis, University of Waterloo]."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1002\/ppsc.200390011","article-title":"A Predictive Model for the Initial Droplet Size and Velocity Distributions in Sprays and Comparison with Experiments","volume":"20","author":"Kim","year":"2003","journal-title":"Part. Part. Syst. Charact."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/5\/5\/417\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:26:43Z","timestamp":1760221603000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/5\/5\/417"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12,31]]},"references-count":8,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2003,12]]}},"alternative-id":["e5050417"],"URL":"https:\/\/doi.org\/10.3390\/e5050417","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2003,12,31]]}}}