{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T21:29:52Z","timestamp":1761427792111,"version":"build-2065373602"},"reference-count":42,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T00:00:00Z","timestamp":1749081600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005713","name":"Technische Universit\u00e4t M\u00fcnchen","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005713","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Chromatography A"],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1016\/j.chroma.2025.466099","type":"journal-article","created":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T21:44:29Z","timestamp":1749159869000},"page":"466099","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Nonlinear liquid-liquid chromatography: A comprehensive modeling approach"],"prefix":"10.1016","volume":"1757","author":[{"given":"Melanie","family":"Gerigk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daili","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-4192-5039","authenticated-orcid":false,"given":"Daniel","family":"Espinoza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3568-7706","authenticated-orcid":false,"given":"Bernt","family":"Nilsson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9820-7410","authenticated-orcid":false,"given":"Mirjana","family":"Minceva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"12","key":"10.1016\/j.chroma.2025.466099_bib0001","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.1042\/bj0351358","article-title":"A new form of chromatogram employing two liquid phases: a theory of chromatography. 2. application to the micro-determination of the higher monoamino-acids in proteins","volume":"35","author":"Martin","year":"1941","journal-title":"Biochem. J."},{"key":"10.1016\/j.chroma.2025.466099_bib0002","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/S0021-9258(18)51183-2","article-title":"Identification of small molecules of organic compounds by distribution studies","volume":"155","author":"Craig","year":"1944","journal-title":"J. Biol. Chem."},{"key":"10.1016\/j.chroma.2025.466099_bib0003","doi-asserted-by":"crossref","first-page":"4218","DOI":"10.1016\/j.chroma.2008.11.088","article-title":"Universal counter-current chromatography modelling based on counter-current distribution","volume":"1216","author":"de Folter","year":"2009","journal-title":"J. Chromatogr. A"},{"issue":"1\u20132","key":"10.1016\/j.chroma.2025.466099_bib0004","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.chroma.2007.03.061","article-title":"Modelling counter-current and dual counter-current chromatography using longitudinal mixing cell and eluting counter-current distribution models","volume":"1151","author":"Kostanyan","year":"2007","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0005","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1134\/S0040579523010098","article-title":"Mathematical modeling of processes of separation by liquid\u2013liquid chromatography methods","volume":"57","author":"Kostanyan","year":"2023","journal-title":"Theor. Found Chem. Eng."},{"key":"10.1016\/j.chroma.2025.466099_bib0006","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.chroma.2017.03.039","article-title":"Trapping multiple dual mode centrifugal partition chromatography for the separation of intermediately-eluting components: operating parameter selection","volume":"1496","author":"Goll","year":"2017","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0007","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.chroma.2013.06.023","article-title":"Intermittent counter-current extraction-Equilibrium cell model, scaling and an improved bobbin design","volume":"1303","author":"Hewitson","year":"2013","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0008","doi-asserted-by":"crossref","DOI":"10.1016\/j.seppur.2021.120330","article-title":"The cell utilized partitioning model as a predictive tool for optimizing counter-current chromatography processes","volume":"285","author":"Choi","year":"2022","journal-title":"Sep. Purif. Technol."},{"key":"10.1016\/j.chroma.2025.466099_bib0009","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.chroma.2004.03.055","article-title":"Countercurrent chromatographic separation: a hydrodynamic approach developed for extraction columns","volume":"1040","author":"Kostanian","year":"2004","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0010","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1002\/ceat.201100266","article-title":"Sequential centrifugal partition chromatography: a new continuous chromatographic technology","volume":"35","author":"Hopmann","year":"2012","journal-title":"Chem. Eng. Technol."},{"key":"10.1016\/j.chroma.2025.466099_bib0011","doi-asserted-by":"crossref","DOI":"10.1016\/j.chroma.2021.462608","article-title":"Separation of minor cannabinoids from hemp extract with trapping multiple dual mode liquid-liquid chromatography","author":"Luca","year":"2021","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0012","doi-asserted-by":"crossref","DOI":"10.1016\/j.chroma.2020.461272","article-title":"Trapping multiple dual mode liquid-liquid chromatography: preparative separation of nootkatone from a natural product extract","volume":"1625","author":"Morley","year":"2020","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0013","doi-asserted-by":"crossref","DOI":"10.1016\/j.chroma.2023.463824","article-title":"Nonlinear liquid-liquid chromatography: beyond a constant distribution coefficient","volume":"1691","author":"Gerigk","year":"2023","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0014","doi-asserted-by":"crossref","DOI":"10.1016\/j.chroma.2023.464361","article-title":"Nonlinear liquid-liquid chromatography: modeling a binary mixture separation","volume":"1708","author":"Gerigk","year":"2023","journal-title":"J. Chromatogr. A"},{"issue":"1","key":"10.1016\/j.chroma.2025.466099_bib0015","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10826079408013432","article-title":"Centrifugal partition chromatography: stability of various biphasic systems and pertinence of the \u201cstoke's model\u201d to describe the influence of the centrifugal field upon the efficiency","volume":"17","author":"Foucault","year":"1994","journal-title":"J. Liq. Chromatogr."},{"key":"10.1016\/j.chroma.2025.466099_bib0016","doi-asserted-by":"crossref","first-page":"6092","DOI":"10.1016\/j.chroma.2011.01.063","article-title":"Multiphase flow modeling in centrifugal partition chromatography","volume":"1218","author":"Adelmann","year":"2011","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0017","doi-asserted-by":"crossref","unstructured":"F. Buthmann, S. Volpert, J. Koop, G. Schembecker, Prediction of bleeding via simulation of hydrodynamics in centrifugal partition chromatography, Sep. 11 (2024) 16. https:\/\/doi.org\/10.3390\/separations11010016.","DOI":"10.3390\/separations11010016"},{"key":"10.1016\/j.chroma.2025.466099_bib0018","doi-asserted-by":"crossref","DOI":"10.1016\/j.chroma.2019.460742","article-title":"Correlating physical properties of aqueous-organic solvent systems and stationary phase retention in a centrifugal partition chromatograph in descending mode","volume":"1615","author":"Fromme","year":"2020","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0019","article-title":"Correlating the phase settling behavior of aqueous-organic solvent systems in a centrifugal partition chromatograph","volume":"1620","author":"Fromme","year":"2020","journal-title":"J. Chromatogr. A"},{"issue":"1\u20132","key":"10.1016\/j.chroma.2025.466099_bib0020","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/S0021-9673(03)00879-3","article-title":"Rational improvement of centrifugal partition chromatographic settings for the production of 5-n-alkylresorcinols from wheat bran lipid extract","volume":"1005","author":"Marchal","year":"2003","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0021","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.chroma.2013.08.053","article-title":"Purification of a modified cyclosporine A by co-current centrifugal partition chromatography: process development and intensification","volume":"1311","author":"Amarouche","year":"2013","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0022","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.chroma.2016.10.040","article-title":"Sample injection strategy to increase throughput in counter-current chromatography: case study of Honokiol purification","volume":"1476","author":"Peng","year":"2016","journal-title":"J. Chromatogr. A"},{"issue":"9","key":"10.1016\/j.chroma.2025.466099_bib0023","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1051\/analusis:1999140","article-title":"Polyphenols in countercurrent chromatography. An example of large scale separation","volume":"27","author":"Berthod","year":"1999","journal-title":"Analusis"},{"key":"10.1016\/j.chroma.2025.466099_bib0024","doi-asserted-by":"crossref","first-page":"3374","DOI":"10.1021\/acs.iecr.1c03312","article-title":"Model-based simultaneous solvent screening and column design based on a holistic consideration of extraction and solvent recovery","volume":"61","author":"Kampwerth","year":"2022","journal-title":"Ind. Eng. Chem. Res."},{"key":"10.1016\/j.chroma.2025.466099_bib0025","doi-asserted-by":"crossref","first-page":"490","DOI":"10.3390\/pr9030490","article-title":"Novel intensified alternatives for purification of levulinic acid recovered from lignocellulosic biomass","volume":"9","author":"Errico","year":"2021","journal-title":"Processes"},{"year":"1975","series-title":"The Theory of backmixing: The design of Continuous Flow Chemical Plant With Backmixing","author":"Mecklenburgh","key":"10.1016\/j.chroma.2025.466099_bib0026"},{"key":"10.1016\/j.chroma.2025.466099_bib0027","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1002\/aic.690270618","article-title":"Model-based analysis of data from countercurrent liquid-liquid extraction processes","volume":"27","author":"Spencer","year":"1981","journal-title":"AIChE J."},{"key":"10.1016\/j.chroma.2025.466099_bib0028","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1021\/je0255269","article-title":"Liquid\u2212liquid equilibria for methanol + water + hexane ternary mixtures","volume":"47","author":"Liu","year":"2002","journal-title":"J. Chem. Eng. Data"},{"key":"10.1016\/j.chroma.2025.466099_bib0029","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1002\/aic.690140124","article-title":"Local compositions in thermodynamic excess functions for liquid mixtures","volume":"14","author":"Renon","year":"1968","journal-title":"AIChE J."},{"year":"1999","series-title":"Molecular Thermodynamics of Fluid-Phase Equilibria","author":"Prausnitz","key":"10.1016\/j.chroma.2025.466099_bib0030"},{"key":"10.1016\/j.chroma.2025.466099_bib0031","doi-asserted-by":"crossref","first-page":"3573","DOI":"10.1021\/acs.jced.3c00532","article-title":"A geometric approach for the calculation of the nonrandomness factor using computational chemistry","volume":"69","author":"Velho","year":"2024","journal-title":"J. Chem. Eng. Data"},{"key":"10.1016\/j.chroma.2025.466099_bib0032","doi-asserted-by":"crossref","DOI":"10.1016\/j.chroma.2024.464888","article-title":"Model-based design of gradient elution in liquid-liquid chromatography: application to the separation of cannabinoids","volume":"1722","author":"Gerigk","year":"2024","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0033","doi-asserted-by":"crossref","first-page":"121","DOI":"10.4236\/wjnst.2017.72010","article-title":"Quality assessment statistic evaluation of X-Ray fluorescence via NIST and IAEA standard reference materials","volume":"07","author":"Ahmed","year":"2017","journal-title":"WJNST"},{"key":"10.1016\/j.chroma.2025.466099_bib0034","doi-asserted-by":"crossref","first-page":"882","DOI":"10.1016\/j.chroma.2009.03.078","article-title":"Estimating uncertainty in analytical procedures based on chromatographic techniques","volume":"1217","author":"Konieczka","year":"2010","journal-title":"J. Chromatogr. A"},{"key":"10.1016\/j.chroma.2025.466099_bib0035","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1021\/acs.jced.3c00673","article-title":"Liquid\u2013liquid equilibria of green and biobased solvents 2-methyltetrahydrofuran + (ethanol or 1-butanol) + water and cyclopentyl-methyl-ether + (ethanol or 1-butanol) + water at 298.15 K","volume":"69","author":"Buchweitz","year":"2024","journal-title":"J. Chem. Eng. Data"},{"key":"10.1016\/j.chroma.2025.466099_bib0036","doi-asserted-by":"crossref","first-page":"3548","DOI":"10.1021\/acs.jced.6b00472","article-title":"Liquid\u2013liquid equilibria of quaternary systems composed of 1,3-propanediol, short-chain alcohol, water, and salt","volume":"61","author":"Gerlach","year":"2016","journal-title":"J. Chem. Eng. Data"},{"key":"10.1016\/j.chroma.2025.466099_bib0037","doi-asserted-by":"crossref","DOI":"10.1002\/aic.17805","article-title":"What does the NRTL model look like? determination of boundaries for different fluid phase equilibrium regions","volume":"68","author":"Labarta","year":"2022","journal-title":"AIChE J."},{"key":"10.1016\/j.chroma.2025.466099_bib0038","doi-asserted-by":"crossref","first-page":"48","DOI":"10.2174\/1874396X01105010048","article-title":"GE models and algorithms for condensed phase equilibrium data regression in ternary systems: limitations and proposals","volume":"5","author":"Gomis","year":"2011","journal-title":"TOTHERJ"},{"key":"10.1016\/j.chroma.2025.466099_bib0039","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.fluid.2016.11.009","article-title":"Should we trust all the published LLE correlation parameters in phase equilibria? necessity of their assessment prior to publication","volume":"433","author":"Marcilla","year":"2016","journal-title":"Fluid Phase Equilib."},{"key":"10.1016\/j.chroma.2025.466099_bib0040","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1134\/S0040579506060054","article-title":"General regularities of liquid chromatography and countercurrent extraction","volume":"40","author":"Kostanyan","year":"2006","journal-title":"Theor. Found. Chem. Eng."},{"key":"10.1016\/j.chroma.2025.466099_bib0041","doi-asserted-by":"crossref","first-page":"6667","DOI":"10.1016\/S0009-2509(01)00342-6","article-title":"Application of gradients in the simulated moving bed process","volume":"56","author":"Antos","year":"2001","journal-title":"Chem. Eng. Sci."},{"key":"10.1016\/j.chroma.2025.466099_bib0042","doi-asserted-by":"crossref","first-page":"2647","DOI":"10.1021\/ac00174a022","article-title":"Shock effects in nonlinear chromatography","volume":"60","author":"Lin","year":"1988","journal-title":"Anal. Chem."}],"container-title":["Journal of Chromatography A"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021967325004455?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021967325004455?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T21:26:28Z","timestamp":1761427588000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0021967325004455"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8]]},"references-count":42,"alternative-id":["S0021967325004455"],"URL":"https:\/\/doi.org\/10.1016\/j.chroma.2025.466099","relation":{},"ISSN":["0021-9673"],"issn-type":[{"type":"print","value":"0021-9673"}],"subject":[],"published":{"date-parts":[[2025,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Nonlinear liquid-liquid chromatography: A comprehensive modeling approach","name":"articletitle","label":"Article Title"},{"value":"Journal of Chromatography A","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.chroma.2025.466099","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2025 The Authors. Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"466099"}}