{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:34:20Z","timestamp":1760146460491,"version":"build-2065373602"},"reference-count":152,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T00:00:00Z","timestamp":1730937600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT","award":["PTDC\/EQU-EPR\/ 114990\/2009"],"award-info":[{"award-number":["PTDC\/EQU-EPR\/ 114990\/2009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Modelling"],"abstract":"<jats:p>This paper investigates the production of nanoparticles via detonation. To extract valuable knowledge regarding this route, a phenomenological model of the process is developed and simulated. This framework integrates the mathematical description of the detonation with a model representing the particulate phenomena. The detonation process is simulated using a combination of a thermochemical code to determine the Chapman\u2013Jouguet (C-J) conditions, coupled with an approximate spatially homogeneous model that describes the radial expansion of the detonation matrix. The conditions at the C-J point serve as initial conditions for the detonation dynamic model. The Mie\u2013Gr\u00fcneisen Equation of State (EoS) is used, with the \u201ccold curve\u201d represented by the Jones\u2013Wilkins\u2013Lee Equation of State. The particulate phenomena, representing the formation of metallic oxide nanoparticles from liquid droplets, are described by a Population Balance Equation (PBE) that accounts for the coalescence and coagulation mechanisms. The variables associated with detonation dynamics interact with the kernels of both phenomena. The numerical approach employed to handle the PBE relies on spatial discretization based on a fixed-pivot scheme. The dynamic solution of the models representing both processes is evolved with time using a Differential-Algebraic Equation (DAE) implicit solver. The strategy is applied to simulate the production of alumina nanoparticles from Ammonium Nitrate Fuel Oil aluminized emulsions. The results show good agreement with the literature and experience-based knowledge, demonstrating the tool\u2019s potential in advancing understanding of the detonation route.<\/jats:p>","DOI":"10.3390\/modelling5040086","type":"journal-article","created":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T07:47:16Z","timestamp":1730965636000},"page":"1642-1673","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling the Production of Nanoparticles via Detonation\u2014Application to Alumina Production from ANFO Aluminized Emulsions"],"prefix":"10.3390","volume":"5","author":[{"given":"Pedro M. S.","family":"Santos","sequence":"first","affiliation":[{"name":"Research Center for Chemical Engineering and Renewable Resources for Sustainability, Universidade de Coimbra, Rua S\u00edlvio Lima\u2014P\u00f3lo II, 3030-790 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2550-4320","authenticated-orcid":false,"given":"Belmiro P. M.","family":"Duarte","sequence":"additional","affiliation":[{"name":"Research Center for Chemical Engineering and Renewable Resources for Sustainability, Universidade de Coimbra, Rua S\u00edlvio Lima\u2014P\u00f3lo II, 3030-790 Coimbra, Portugal"},{"name":"Instituto Polit\u00e9cnico de Coimbra, Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, 3030-199 Coimbra, Portugal"},{"name":"INESC Coimbra\u2014Instituto de Engenharia de Sistemas e Computadores de Coimbra, Universidade de Coimbra, Rua S\u00edlvio Lima\u2014P\u00f3lo II, 3030-790 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7220-0584","authenticated-orcid":false,"given":"Nuno M. C.","family":"Oliveira","sequence":"additional","affiliation":[{"name":"Research Center for Chemical Engineering and Renewable Resources for Sustainability, Universidade de Coimbra, Rua S\u00edlvio Lima\u2014P\u00f3lo II, 3030-790 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3575-9733","authenticated-orcid":false,"given":"Ricardo A. L.","family":"Mendes","sequence":"additional","affiliation":[{"name":"ADAI-LAETA, Universidade de Coimbra, Rua Lu\u00eds Reis Santos, P\u00f3lo II, 3030-788 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6067-3069","authenticated-orcid":false,"given":"Jos\u00e9 L. S. A.","family":"Campos","sequence":"additional","affiliation":[{"name":"ADAI-LAETA, Universidade de Coimbra, Rua Lu\u00eds Reis Santos, P\u00f3lo II, 3030-788 Coimbra, Portugal"}]},{"given":"Jo\u00e3o M. C.","family":"Silva","sequence":"additional","affiliation":[{"name":"Innovnano, Parque Tecnol\u00f3gico de Coimbra, 3040-540 Coimbra, Portugal"},{"name":"Lifthium Energy, Rua do Silval 37, 12\u00b0 piso, 2780-373 Oeiras, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1016\/j.jaerosci.2007.05.008","article-title":"Development of a phenomenological scaling law for fractal aggregate sintering from molecular dynamics simulation","volume":"38","author":"Hawa","year":"2007","journal-title":"J. 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