{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T20:05:43Z","timestamp":1762113943878,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T00:00:00Z","timestamp":1688428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The design of continuous thickeners and clarifiers is commonly based on the solid flux theory. Batch sedimentation experiments conducted with solid concentrations still provide useful information for their application. The construction of models for the velocity of settling allows the estimation of the flux of solids throughout time, which can, in turn, be used to find the area of the units required to achieve a given solid concentration in the clarified stream. This paper addresses the numerical treatment of data obtained from batch sedimentation experiments of calcium carbonate particles. We propose a systematic framework to fit a model that is capable of representing the process features that involve (i) the numerical differentiation of data to generate initial estimates for the instantaneous velocity of settling; (ii) the integration of a differential equation to fit the model for the velocity of settling; and (iii) the assessment of the quality of the fit using common statistical indicators. The model used for demonstration has a theoretical basis combined with an empirical component to account for the effect of the particle concentrations and their state of aggregation. The values of the numerical parameters obtained are related to the characteristic dimensions of the aggregates and their mass-length fractal dimensions.<\/jats:p>","DOI":"10.3390\/ma16134822","type":"journal-article","created":{"date-parts":[[2023,7,5]],"date-time":"2023-07-05T00:37:28Z","timestamp":1688517448000},"page":"4822","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Modeling the Batch Sedimentation of Calcium Carbonate Particles in Laboratory Experiments\u2014A Systematic Approach"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5883-5516","authenticated-orcid":false,"given":"Maria J.","family":"Moura","sequence":"first","affiliation":[{"name":"Instituto Polit\u00e9cnico de Coimbra, Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, Quinta da Nora, 3030-199 Coimbra, Portugal"},{"name":"Centro de Investiga\u00e7\u00e3o em Engenharia dos Processos Qu\u00edmicos e dos Produtos da Floresta, Universidade de Coimbra, Rua S\u00edlvio Lima, P\u00f3lo II, 3030-790 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4217-6349","authenticated-orcid":false,"given":"Carolina S.","family":"Vertis","sequence":"additional","affiliation":[{"name":"Centro de Investiga\u00e7\u00e3o em Engenharia dos Processos Qu\u00edmicos e dos Produtos da Floresta, Universidade de Coimbra, Rua S\u00edlvio Lima, P\u00f3lo II, 3030-790 Coimbra, Portugal"}]},{"given":"V\u00edtor","family":"Redondo","sequence":"additional","affiliation":[{"name":"LED&MAT, Instituto Pedro Nunes, Rua Pedro Nunes, Edif\u00edcio A, 3030-199 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7220-0584","authenticated-orcid":false,"given":"Nuno M. C.","family":"Oliveira","sequence":"additional","affiliation":[{"name":"Centro de Investiga\u00e7\u00e3o em Engenharia dos Processos Qu\u00edmicos e dos Produtos da Floresta, Universidade de Coimbra, Rua S\u00edlvio Lima, P\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":"Instituto Polit\u00e9cnico de Coimbra, Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, Quinta da Nora, 3030-199 Coimbra, Portugal"},{"name":"Centro de Investiga\u00e7\u00e3o em Engenharia dos Processos Qu\u00edmicos e dos Produtos da Floresta, Universidade de Coimbra, Rua S\u00edlvio Lima, P\u00f3lo II, 3030-790 Coimbra, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cheremisinoff, P.N. (2019). 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